DEVELOPMENT OF HAPTIC ELECTROTACTILE RENDERING DEVICE:
DESIGN IMPLEMENTATION AND TESTING
By
John W. Gregory

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Electrical Engineering
2011

ABSTRACT

DEVELOPMENT OF HAPTIC ELECTROTACTILE RENDERING DEVICE:
DESIGN IMPLEMENTATION AND TESTING
By
John William Gregory
The purpose of this research is to build and test a haptic rendering system using skin
surface electro-tactile stimulation for a fingertip interface. A new driver output stage for
delivering tactile signals is implemented to improve power inefficiency and reduce circuit
area relative to traditional open-loop constant current driver (CCD)-based haptic
renders. This will be realized in a constant voltage driver (CVD) method for haptic
rendering. The challenge will be to make the system aware of the skin impedance
loading conditions and to use this information to introduce a closed-loop solution that is
necessary due to implementing this type of driver.
The system will be made load-aware by identifying parameters of a proposed electronic
impedance model of skin that is done online and in real-time with customized software
and hardware. Output sensors will be used to measure the voltage and current at the
loaded output. An extended least squares algorithm will identify the parameters from the
measurements. The paper will introduce a model reference adaptive control law, using
the direct method, with nonlinear feedback to test a closed-loop CVD design. To aid in
determining normal operating conditions, and validating parameter estimation and
simulated closed-loop control, related experiments will be carried out. This work is
based on an older version electro-tactile haptic rendering system used in the laboratory.

ACKNOWLGEMENTS
A small feat dedicated to the giant character of my father, William L. Gregory, whose
death eventually motivated me to start building my own for the better, and continues
still, with the aid and comfort of my lovely wife, Tracy M. Gregory.
I would also like to thank Drs. Ning Xi and Yantao Shen in their support for this work, as
well as, for National Science Foundation and the Army Research Lab for their generous
funding of this project.

iii

TABLE OF CONTENS
LIST OF TABLES ........................................................................................................... VI
LIST OF FIGURES ........................................................................................................ VII
1. INTRODUCTION ......................................................................................................... 1
1.1 BACKGROUND AND MOTIVATION .............................................................. 1
1.2 RELVAVENT BIOLOGY OF RECEPTORS CONCERNING ELECTRONIC
STIMULATION OF THE FINGERTIP ................................................................... 2
1.3 TYPES OF DISPLAYS, SENSORY CONTENT, AND MECHANISMS ........... 4
1.4 ORGANIZATION OF THESIS ........................................................................ 7
2. LITERATURE REVIEW ............................................................................................... 8
2.1 ELECTRICAL IMPEDANCE PROPERTIES AND CHARACTERSTIC OF
SKIN ..................................................................................................................... 8
2.2 TACTILE INTENSITY AND PERCEPTION .................................................. 12
2.3 TYPES OF ELECTROTACTILE DRIVERS .................................................. 16
2.4 DESIGN CHALLENGES WITH EXISTING OUTPUT DRIVER METHODS .. 18
3. SYSTEM DESIGN ..................................................................................................... 23
4. HARDWARE, SOFTWARE, AND SYSTEM CALIBRATION ..................................... 25
4.1 HARDWARE DESIGN .................................................................................. 27
4.1.1 DIGITAL ACQUISITION (DAQ) BOARD ........................................................... 27
4.1.2 HIGH VOLTAGE DC-TO-DC CONVERTER POWER UNIT ............................. 27
4.1.3 CONSTANT VOLTAGE DRIVER (CVD) ........................................................... 31
4.1.4 CVD OUTPUT VOLTAGE SENSOR ................................................................. 33
4.1.5 CVD OUTPUT CURRENT SENSOR ................................................................ 35
4.1.6 ELECTRO-TACTILE DISPLAY HARDWARE DESIGN..................................... 43
4.2 SOFTWARE DESIGN .................................................................................. 46
4.2.1 GUI FRONT END AND RESULTS GRAPHICAL DISPLAY .............................. 47
4.2.2 SOFTWARE DESIGN AND PROGRAM FLOW ................................................ 51
4.2.3 SOFTWARE WAVEFORM GENERATOR AND TYPICAL WAVEFORM
PRIMITIVES............................................................................................................... 57
4.3 HARDWARE CALIBRATION ........................................................................ 59
5. MODELING AND ANALYSIS OF ADAPTATION LAW .............................................. 66
5.1 CONTINUOUS TIME BIO-IMPEDANCE (CTBI) MODELING ....................... 66
5.2 DISCRETE TIME CONDUCTANCE (DTC) MODELING .............................. 72
5.2.1 DTC MODEL PARAMETER ESTIMATION AND ADAPTATION ALGORITHM IN
Z-DOMAIN ................................................................................................................. 73
5.2.2 ITERATIVE EXTENDED LEAST SQUARES WITH FORGETTING FACTOR
ADJUSTMENT (ELSFF) MODEL ALGORITHM ........................................................ 75
iv

5.3 PARAMETER ESTIMATION FOR THE CONTINUOUS TIME LINEAR
PARAMETERS BIO-IMPEDANCE (CT-LPBI) MODEL ...................................... 82
6. EXPERIMENTAL SETUP AND TESTING................................................................. 86
6.1 HARDWARE AND ADAPTATION ALGORITHM TESTING.......................... 86
6.1.1 EXPERMINETAL SETUP ................................................................................. 86
6.1.2 EXPERMINETAL RESULTS AND ANALYSIS .................................................. 89
6.2 EXPERIMENTATION ................................................................................... 99
6.2.1 EXPERIMENTAL SETUP ............................................................................... 100
6.2.2 EXPERIMENTAL RESULTS USING STATISTICAL ANALYSIS .................... 105
6.2.3 ELECTRO-TACTILE DYNAMIC RANGE STUDY ........................................... 106
6.2.4 CVD POWER OUTPUT STUDY ..................................................................... 115
6.2.5 STATISTICAL STUDY BETWEEN ESTIMATION MODELS AND PLANT
OUTPUT ESTIMATION ERROR ............................................................................. 118
6.2.6 OBSERVATIONAL RESULTS FOR LARGE SIGNAL I-V CHARACTERISTIC
................................................................................................................................. 124
6.2.7 STATISTICAL RESULTS FOR LARGE SIGNAL I-V CHARACTERISTIC AND
LARGE SIGNAL MODELING................................................................................... 131
6.2.8 OUTPUT ESTIMATION UNDER TIME VARIATION STUDY .......................... 139
6.2.9 ESTIMATION MODEL OUTPUT AS A FUNCTION OF CVD WAVEFORM TYPE
STUDY ..................................................................................................................... 145
7. ADAPTIVE CONTROL MODELING, SIMULATION AND ANALYSIS ..................... 160
7.1 MODEL ....................................................................................................... 160
7.2 STOCHASTIC PARAMETER IDENTIFICATION FROM POPULATION DATA
......................................................................................................................... 162
7.3 PROPOSED BIO-IMPEDANCE DYNAMICS MODEL ................................ 164
7.4 DERIVATION OF ADAPTIVE CONTROL LAW .......................................... 165
7.5 SIMULATION OF THE BIO-IMPEDANCE MODEL (OPEN-LOOP) ............ 167
7.6. SIMULATION ON CLOSED LOOP STIMULATION CURRENT CONTROL
......................................................................................................................... 173
8. CONCLUSIONS AND FUTURE WORK .................................................................. 178
9. REFERENCES ........................................................................................................ 181

v

LIST OF TABLES

Table 1. Bio-impedance parameters for 10 individuals using offline identification [34]:
dry and damp Index fingertip case. ............................................................................... 88

Table 2. Known RC circuit elements of impedance networks built on breadboard with
known analog pole and zero frequency locations used in online identification testing:
built using table 1 parameter sets. ................................................................................ 89

Table 3. Resulting online estimation of circuit element parameters and analog pole and
zero frequency locations for the corresponding known parameters of the plants in table
2. ................................................................................................................................... 90

Table 4. Absolute error and standard deviation between plant and estimated
parameters: first column shows which variable held constant for calculating the
associated row statistics. ............................................................................................... 91

Table 5. Pain threshold sensation description reported from subjects and frequency of
occurrence for the three CVD waveform types. ........................................................... 115

Table 6. Two sample KS test for similarity between ECDFs of apparent power
distributions for CVD waveform type (5% Significance): samples of apparent power for
each waveform type are calculated at sensation and pain threshold for each subject
(N=21). ........................................................................................................................ 118

Table 7. Experimentally estimated bio-impedance parameters for subject #2 with square
wave voltage pulse amplitude conditions shown ......................................................... 168

vi

LIST OF FIGURES
Figure 1. Illustration of fingertip electro-tactile stimulation via an electrode array. ......... 1

Figure 2. Improved Howland current pump with master-slave configuration adapted from
[3]. Rs = 1 kΩ, R1 = R3 = 5 kΩ, R2 = 10 kΩ, R4 = 9 kΩ, and ZL is load impedance. .... 20

Figure 3. System level diagram of implemented project. ............................................... 26

Figure 4. High voltage DC-to-DC converter circuit. ....................................................... 30

Figure 5. Constant voltage driver (CVD) circuit. ............................................................ 33

Figure 6. CVD voltage output sensor circuit. ................................................................. 35

Figure 7.CVD current output sensor circuit. .................................................................. 37

Figure 8. Tactile display: dimensions are 10.16x7.62x2.54 centimeters with an active
area of 2.74x2.31 centimeters. ...................................................................................... 45

Figure 9. Ground-isolated return electrode.................................................................... 46

Figure 10. GUI front end................................................................................................ 48

Figure 11. Identification results dialogue. ...................................................................... 50

Figure 12. Program flow control: top level. .................................................................... 52

Figure 13. Flow control for D/A output thread and DAQ shared memory write. ............. 53

Figure 14. Flow control for D/A output thread and DAQ shared memory read. ............. 54

vii

Figure 15. Flow control for initiating or stopping A/D and identification threads along with
identification shared Memory read from results display thread. .................................... 55

Figure 16. Flow control, shared memory access and data accessing for online
identification thread. ...................................................................................................... 56

Figure 17. CVD output pulses generated from software waveform primitives utilized in
testing tactile display. .................................................................................................... 58

Figure 18. Calibration of the CVD input-output voltage amplitudes. .............................. 61

Figure 19. Calibration of the load voltage sensor. ......................................................... 63

Figure 20. Calibration of load current sensing circuit. ................................................... 65

Figure 21. Continuous time bio-impedance (CTBI) model of the fingertip under electrotactile stimulation. .......................................................................................................... 68

Figure 22. Overview of parameter identification. ........................................................... 74

Figure 23. Top level block diagram of parameter estimation using iterative ELS
algorithm in Z-Domain. .................................................................................................. 77

Figure 24. Measured and decomposition of estimated output current from terms in
(5.4a) plotted by driving load #5-Damp in table 2: output for one triangle wave CVD
pulse shown at 60 Hz, 11% duty cycle at Vpp = 140 volts, λ = 1. ................................. 94

Figure 25. 10 second estimation of measured state current at pulse midpoints using
model (5.4a). Results produced from square wave pulses driven under load #1-Dry in
table 2. The mth step is the mth duty cycle pulse midpoint: output is at 60 Hz, 11
percent duty cycle at Vpp = 100 volts, λ = 1. ................................................................. 96

viii

Figure 26. Typical output estimation error convergence characteristic versus time
calculated from (5.21) when driving LTI loads in table 2: assessed for #5-Damp
impedance load. ............................................................................................................ 98

Figure 27. View of user forearm resting comfortably on gel pad while index fingertip is
placed firmly on tactile display for stimulation and measurement. ............................... 102

Figure 28. View of anodic return electrode proper placement secured with a Velcro strap
on thenar eminence..................................................................................................... 103

Figure 29. Mean dynamic range ratio for RMS stimulation current for each type of CVD
output waveform pulse (N=21). The 95% confidence interval is included. The sample
mean and standard deviation for the square saw tooth, and triangle wave are: M = 4.78,
SD = 1.86; M = 7.21, SD = 2.69; M = 7.29, SD = 2.74, respectively. .......................... 107

Figure 30. Average sensation and pain thresholds for stimulation currents versus wave
form (N=21). The 95% confidence interval is shown for the mean. ............................. 109

Figure 31. Five statistic box and whiskers plot for mean dynamic range ratios for RMS
stimulation current versus waveform shape (N = 21). ................................................. 111

Figure 32. Five statistic box and whiskers plot for mean sensation and pain thresholds
concerning RMS stimulation current versus waveform shape (N = 21). ...................... 112

Figure 33. Mean CVD Voltage Amplitudes for corresponding RMS current thresholds
versus CVD pulse type (N = 21). ................................................................................. 113

Figure 34. Apparent power bar chart shown at mean sensation and pain stimulation
current thresholds for each individual (N = 21) and each CVD waveform type: standard
error bars are shown. .................................................................................................. 117

Figure 35. Modeling error given by power inefficiency. Percentages of average power
consumed in the CED filter normalized to average power estimated in the DTC model
for all waveform types calculated at reported threshold levels: results graphed at the
sensation and pain thresholds of subjects (N=21)....................................................... 122
ix

Figure 36. Mean power efficiency of DTC model estimation output normalized to
measured power delivered to skin-tactor load for each waveform type: results calculated
at the reported sensation and pain thresholds of subjects (N = 21). ........................... 123

Figure 37. Mean power efficiency of physical impedance (CT-LPBI) model estimation
output normalized to measured power delivered to skin-tactor load for each waveform
type: results calculated at the reported sensation and pain thresholds of subjects (N =
21). .............................................................................................................................. 124

Figure 38. Identification of Rp and Rs as a function of stimulation current and subject
(N=21): results are from square wave CVD pulses starting at Vpp = 30V and
incremented to pain threshold for each subject. .......................................................... 126

Figure 39. Measured and DTC estimation model (from 5.4a) I-V characteristic curves
for each subject as a function of square wave CVD pulse amplitude and subject (N=21).
.................................................................................................................................... 128

Figure 40. Identification of Cp as a function of stimulation current and subject (N=21):
results are from square wave CVD pulses starting at Vpp = 30V and incremented to
pain threshold for each subject. .................................................................................. 130

Figure 41. Five statistic box and whiskers plot produced from each average Rs value
per individual from 30 volts to maximum pain threshold voltage (N = 21). .................. 132

Figure 42. Scatter plot of all identified Rs values versus stimulation current independent
of subject (N=278): results generated from applied square wave pulses from 30 volts to
maximum pain threshold voltage per individual. .......................................................... 133

Figure 43. Scatter plot of identified Rp values for sample population (N = 278) as a
function of stimulation current with power-fitted regression curve using square wave
CVD pulse: lower 5th and upper 95th percentile confidence intervals are shown for
identified Rp calculated using the mean of the Rp power-fitted regression curves for
each individual (shown as the dashed line). ................................................................ 135

x

Figure 44. Histogram of percent error between the identified Rp and Interpolated Rp
values using square wave CVD pulse (N = 278). ........................................................ 136

Figure 45. Scatter plot of measured CVD Vpp for sample population (N = 278) as a
function of stimulation current with log-fitted regression curve using square wave CVD
pulse: lower 5th and upper 95th percentile confidence intervals are shown for measured
CVD Vpp calculated using the mean of the Vpp log-fitted regression curves for each
individual (shown as the dashed line).......................................................................... 138

Figure 46. Histogram of percent error between the measured CVD and interpolated
CVD amplitude values using square wave CVD pulse (n = 278)................................. 139

Figure 47. Output estimation of measured stimulation current for human subject using
DTC model in (5.4a): square wave CVD pulses with λ = 1.0, time = 10 sec, and Vpp =
90V. ............................................................................................................................. 142

Figure 48. Output estimation of measured stimulation current for human subject using
DTC model in (5.4a): square wave CVD pulses with λ = 0.9975, recording time = 10
sec, and Vpp = 90V. .................................................................................................... 144

Figure 49. One of 60 square wave pulse of measured and estimated model output
current, using models in (5.3) and (5.4a), for CVD square wave pulse train administered
at reported pain threshold for subject #4: Vpp = 125V, λ = 0.99975 and recording time =
1 sec............................................................................................................................ 148

Figure 50. Estimated Rp, Rs, and Cp as a function of time and square wave CVD
pulses for subject #4: Vpp = 125 volts, λ = 0.99975 and recording time = 1 sec. ........ 150

Figure 51. One of 60 saw tooth wave pulse of measured and estimated model output
current, using models in (5.3) and (5.4a), for CVD saw tooth wave pulse train
administered at reported pain threshold for subject #2: Vpp = 135V, λ = 0.99975 and
recording time = 1 sec. ................................................................................................ 152

Figure 52. Estimated Rp, Rs, and Cp as a function of time and saw tooth wave CVD
pulses for subject #2: Vpp = 135 volts, λ = 0.99975 and recording time = 1 sec. ........ 154
xi

Figure 53. One of 60 triangle wave pulses of measured and estimated model output
current, using models in (5.3) and (5.4a), for CVD triangle wave pulse train administered
at reported pain threshold for subject #20: Vpp = 142V, λ = 0.99975 and recording time
= 1 sec. ....................................................................................................................... 156

Figure 54. Estimated Rp, Rs, and Cp as a function of time and triangle wave CVD
pulses for subject #20: Vpp = 142 volts, λ = 0.99975 and recording time = 1 sec. ...... 158

Figure 55. Illustration of bio-impedance model of skin and frequency model for constant
voltage pulse driver (CVD) .......................................................................................... 161

Figure 56. Large-signal stochastic representation of Rp and A and B power law
coefficients for sample population (N = 21) versus RMS stimulation current for 60 Hz,
5% duty cycle square wave pulses.............................................................................. 163

Figure 57. The mean of the average values of Rs for each member of the population 164

Figure 58. Measured and estimated output current pulse shape to subject #2 at 150 volt
square wave pulse; measured and estimated Istim at steady state equals 0.63 mA .. 169

Figure 59. Simulated current pulse from square wave voltage pulses inputted into
equations 7.2a- 7.2b using experimental data in Table 7 for one subject; Istim steady
state equals 0.5 mA..................................................................................................... 171

Figure 60. Simulated value of Rp stratum corneum resistance (Ohms) using equation
7.2b during the current pulse time in Figure 59; the minimum of Rp equals 231 kΩ ... 172

Figure 61: Reference Current ...................................................................................... 174

Figure 62. Simulation results: Tracked stimulation current. ......................................... 175

Figure 63. Simulation results: behavior of Rp. ............................................................. 176

Figure 64. Simulation Results: Voltage output of closed loop CVD. ............................ 177
xii

1. INTRODUCTION

1.1 BACKGROUND AND MOTIVATION
Electrodes designed to substitute touch sensation have been performed on various
locations on the body. For example, the tongue [16] [17], forearm [20], abdomen [12]
[15], and fingertip [9]-[14] [24] are areas most studied to assess the ability of human
subjects to detect and identify patterns using these devices. Research in this area has
shown that electrical stimuli can effectively deliver a significant amount of information
about patterns and physical properties of stimuli such as texture, geometry, contour,
movement, pressure, elasticity, etc; thus, ample research supports the notion that
electrical stimuli are a viable means for delivering sensory information [4]. Our research
interest pertains to investigation of the ability to induce touch sensations on the fingertip
skin using an electrical array. This mechanism, also called electro-tactile or electrocutaneous stimulation is illustrated in Figure 1.

Figure 1. Illustration of fingertip electro-tactile stimulation via an electrode array.
1

1.2 RELVAVENT BIOLOGY OF RECEPTORS CONCERNING ELECTRONIC
STIMULATION OF THE FINGERTIP
The fingertip skin consists of several horizontal layers of skin each consisting of
receptors: four classes of mechanoreceptors, two classes of thermo-receptors, four
classes of nociceptors, and three classes of proprioceptors. All are found within these
layers of the skin. The four classes of mechanoreceptors are located in the first three
layers under the stratum corneum, which are the epidermis, dermal and subcutis
(connective) tissue layers [22]. To an extent, all provide the perceived tactile sensations
during mechanical or electrical stimulation [3] [4] [14] [21] [22] [24].

Different receptors sense different tactile modalities such as pressure, vibration,
temperature or pain to name a few. Especially, when considering the different classes of
mechanoreceptors, the most commonly investigated tactile receptors include: Merkel
cells that encode pressure sensation and edge detection over a small distance;
Meissner corpuscle that encode low frequency vibration, touch, changes in pressure
and motion over small regions on the skin; and Pacinian corpuscle that register high
frequency vibration and changes in shear stretching on the skin over large distances. A
fourth type not often discussed as the previous are the Ruffini endings that encode
static shear stretching on the skin over large distances [4] [14] [22].

The mechanoreceptor afferents can be categorized by their orientation, depth,
innervation densities, adaptation, receptive field and frequency response. In terms of
innervation density and receptive field, Merkel and Meisner Corpuscles have a higher

2

density and smaller receptive field in the hand and fingers than compared to both
Pacinian Corpuscles and Ruffini endings [22]. This suggests that the first two types of
receptors are responsive to finer details in stimuli, in contrast to Pacinian and Ruffini
afferents which are fewer and have a much larger, less well-defined boundary for their
detection region.

As well, the action potential firing characteristic from an applied mechanical deformation
to the skin, such as a ramped square wave, differ for the classes of receptors [7]. The
Merkel and Ruffini receptors are referred to as slow adapting one and two (SA-I and
SA-II), respectively, since their action potentials fire continually while the deformation is
present. Alternatively, the Meisner and Pacinian receptors, classified as fast adapting
one and two (FA-I and FA-II), respectively, fire only during the application and removal
from the mechanical indentation. These adaptation schemes along with the different
receptive fields to an extent define the mechanoreceptors‟ roles in encoding the tactile
dynamics on the skin that are sent to and interpreted by somatosensory areas in the
brain to elicit perception. It is noteworthy that the classes of mechanoreceptors are not
mutually exclusive to their primary function since the mechanical detection thresholds of
each versus their frequency response overlap [24]. Hence, temporal integration of the
induced action potentials by mechanical stimuli, for instance by scanning the fingertip
over a fine texture, probably lends to a richer encoding scheme, such as frequency
encoding, for higher-level functions in the brain to process.

3

Several

research

findings

in

the

areas

of

psychophysics,

neurocytology,

electrochemistry, and cognitive science have shown that mechanical or electrical
stimulations to these mechanoreceptors produce or mimic tactile feelings in humans [7]
[13] [18] [19] [25] [26]. Following these explorations, extensive research in rehabilitation
engineering has been performed to elucidate the properties, characteristics, and
mechanisms underlying the sensation of touch delivered through electrode arrays on
the fingertip skin [10]-[14] [24]. As a result, electro-tactile research and development
have been driving the potential to advance assistive, diagnostic, and rehabilitative
devices such as Braille readers, sensory substitution systems, teleoperation and
telepresence, and computer games [1] [2] [5] [6] [9] [10] [20] [23] [24].

1.3 TYPES OF DISPLAYS, SENSORY CONTENT, AND MECHANISMS
Broadly, a haptic renderer senses tactile information originating from a real or virtualmodeled source and encodes it to be delivered to the touch sense via the user
interfacing with a peripheral device called a tactile display. One class of haptic
renderers are used to display tactile information encoded from a virtual world, such as in
computer gaming or texture patterns, or as a tactile feedback display in teleoperation
and telepresence applications [23] [20]. These devices are meant to allow the user to be
knowledgeable about or allow for better interaction with the physical or media construct
in question using relatively high resolution tactile displays. Another classification of
sensory substitution haptic displays have a long tradition and include applications for
visual or auditory substitution, such as Braille readers, acoustic encoders in the
frequency domain [12], or tactile vision substitution systems (TVSS) [16] [17]. Here,

4

sensory information that is intended for a particular sense is measured and inputted in
to the haptic renderer for re-encoding as output to the tactile display for recognition by
the sense of touch. The principle relies on neuroplasticity of the brain which, in this
case, is the ability of the somatosensory cortical area to interface with and transmit the
relevant information to the cortical area(s) responsible for processing the sensory
information that is now substituted for, as studied by Bach-y-Rita in the 1960‟s. A third
class of applications for haptic renders involves information delivery systems which
allow the user to process media-rich content through the sense of touch. One such
system discussed in [6] is a donned vest with arrays of vibrating tactors used as a
navigation-assistance system that delivered tactically-encoded orientation and speed
content for the user in his surrounding environment. The last classification for haptic
rendering applications, in the area rehabilitative engineering, concerns sensory
feedback integration in and neuromuscular activation of prostheses [12] [29]. Whereas
the origins of content or media amenable for haptic encoding are nearly endless to
exploit, the traditional means of delivery to the tactile sense are specific.

The means for traditional tactile interfaces are accomplished using either servo driven
pins, called vibrotactile displays, or electrode stimulators, called electrotactile displays
that are applied to various surface regions of the skin [4]. Each type has its advantages
and disadvantages. For instance, the vibrotactile displays can control pressure and
vibration sensation intensity and gradients delivered to the cutaneous area directly by
current spatial configuration and frequency modulation of its pins. However, tactile
information conveyed electronically seems more complex since the perceived intensities

5

of rudimentary sensations, such as pressure and vibration must be coded indirectly to
elicit a desired mechanical sensation; thus, attempting to replicate these physical
sensation and intensities is done using amplitude, pulse width or frequency modulation
of the electronic signals [12]. They are also more difficult to provide a stable sensation
level due to coupling effects between the electro-chemistry of the skin locus under
stimulation and amplitude and modulation properties of the signals [29] [32]; whereas
mechanical stimulation does not change drastically the inherit mechanical properties of
the cutaneous region interfaced. However, electrotactile terminals are amenable to
compact construction, improved compliance to the skin, finer tactor pitch, and are more
energy efficiently versus mechanical displays due to their lack of moving parts.

A recent and emerging class of haptic rendering devices uses smart materials as
actuators to build the tactile display tactor elements. For instance, research into high
density tactile displays utilizing dielectric electro-active polymers (D-EAPs) are
discussed in [8]. These devices have the potential for being compact in size and
possess a dense active area of stimulators, with substrates that are mechanically
compliant to the skin. They can also be made energy efficient, while delivering
mechanical stimulation to the skin surface. In the case of D-EAPs, miniature
diaphragms are used as actuators against the skin. Unfortunately, acrylics or silicone
polymers used for this purpose requires voltages in excess of 1 kV to actuate, with low
current levels compared to the mechanical pin actuators.

6

1.4 ORGANIZATION OF THESIS
In section two, the electronic impedance properties of dermal skin, and tactile
perceptive parameters and sensation control of the tactile sense are overviewed. A brief
survey of previous haptic designs employed by others using electrotactile haptic
systems is presented along with some of the design challenges and possible solutions;
the overview for a new electrotactile driver design is given in Section 3. As well, this
laboratory‟s specific applications for the original, fully-implemented haptic display
system are presented; section 4 details the hardware and software implementation, and
output signals used for experimentation by haptic rendering system. Additionally, the
last subsection in section 4 goes over the method for calibrating the driver output and
measurement circuitry; in section 5, biologically-inspired formulation of electronic
impedance models for skin surfaces under electronic stimulation is introduced and
analyzed. The last part of the section is devoted for elaborating the real-time, online
adaptation law used to identify the parameters for the models; section 6 is the start of
the experimental section to test the hardware and software, validate the proposed
models and test the adaptation law. The first major subsection explains the
experimental setup to test the haptic system and validate the load identification
algorithm which is then carried out; in the second major part of this section, the setup
and motivations for human experimentation are explained and the types of experiments
carried out presented. The experimental results and analysis are given in this section,
as well; in Section 7, the adaptive control rule for controlling driver output to an
electrode-skin interface is derived based on experimental and theoretical findings.
Simulations of the indirect MRAC law are provided for demonstration of the control;

7

concluding remarks about the results and future work are given in Section 8; finally, all
references used in this work are given in Section 9.

2. LITERATURE REVIEW

2.1 ELECTRICAL IMPEDANCE PROPERTIES AND CHARACTERSTIC OF SKIN
The dead, multi-layered protective barrier of skin that is exposed to the environment is
known as the stratum corneum (SC). The SC cells are densely packed lattice of layered
corneocytes composed of relatively high resistivity keratin (pk = 105 Ωm at DC)
compared to other tissues in the body, such as muscle, bone and underlying dermal
tissue which averages pc = 255 Ωm [39]; therefore, it is considered the main insulative
barrier to transcutaneous current flow. Cellular membranes that enveloped corneocytes
are electrically insulative and composed of dielectric lipid bilayers. The intercellular
spacing is heterogeneous consisting of in-series and stacked (approx. 100) dielectric
laminar lipid bilayers, perforated with pores and sweat gland pathways in an ionic
aqueous fluid [32]. Hence, there are at least two distinct types of electrical conductance
through the skin in reference to the SC model presented in [27]: 1) the intercellular
route, which is mainly due to ionic conduction in aqueous electrolyte whose flow is
dependent on applied voltages magnitudes [32]; 2) the transcellular pathway formed
between SC mater, dielectric lipid bilayers, and extracellular ionic fluid which can be
modeled to form a capacitive element for displacement current [32]. The complex
electro-physiologic makeup mean that electronic bulk impedance of SC skin exhibits
nonlinearities dependent on waveform stimulation dynamics and time history, frequency

8

dependency, spatial and time variation. For square wave electronic pulses, empirical
evidence indicates that the electronic resistivity of the SC layer decreases almost
inversely with increasing current amplitude [3] [4] [12] [29]. SC thickness and moisture
content also tend to increase and decrease skin bulk resistance, respectively [34] [39];
the electrical resistance and capacitance of the skin are extrinsic properties; hence, skin
impedance is dependent on effective electrode area against the stimulated skin surface
which in turn depends on applied force between skin-electrode interfacing. In contrast,
the resistivity and non-linear dynamics of subdermal skin tissue and other soft tissues is
shown to be mostly invariant of frequency and amplitude (i.e. it exhibits an ohmic
relationship) and is much lower and constant spatially in value compared to the SC [29]
[30] [39] [43]. For related statistical comparison studies of resistivities and moisture
content of various organs and tissues, including skin, as a function of frequency, see
[43]. An observed effect in SC electrical impedance under square wave stimulation for
current amplitudes greater than 2 mA is a recovery in skin resistance over time during
the pulse. This second order phenomenon becomes more dramatic as current
amplitudes are increased. The illustrations of the effect are shown in [3] and [29].

The researchers in [3] demonstrated that by applying square wave current pulses of
increasing magnitude to the skin surfaces of participants, specific resistance of the
epidermis decreased as a power function of current density with an exponent of 0.80.
Extrapolating the authors‟ relationship by normalizing their results to a 1 mm 2 electrode
area, resistance is predicted to be 5 MΩ at 50 µA down to about 100 kΩ at 1mA.
Investigators in [39] determined an exponential law inversely relating DC skin resistivity

9

to skin depth by experimentally determining the resistivity distribution by successively
stripping away SC layers. As well, skin impedance measured at high frequency
stimulation of unmodified SC asymptotically approached low frequency impedance of
completely stripped SC. The authors of [32] state that effective shunting of each stacked
lipid layer in the SC totaling about 100 occurs from electrical field induced formation of
aqueous pores leading to increased ionic conduction in each layer; the number of
effectively shorted SC layers was indicated as a linear function of voltage amplitude.
The studies in [32] and [39] could indicate the physiological reason for the inverse
functional relationship between SC bulk impedance and pulsed current amplitude

The investigators of [30] studied the resistance of un-cleansed, dry, and un-abraded
epidermal skin using a 0.550 cm2 electrode stimulator as function of sinusoidal
frequency from 1 Hz to 1 MHz and held independent of current amplitude by applying
current in the microamperes; multiple subjects and body locations were used for testing.
If the electrode geometry used in the study is normalized to a 1 mm2 area in this review,
then impedances ranged from a mean of 10 MΩ at 1 Hz down to 12 kΩ at 1 MHz for
various subjects and body locations. Interestingly, findings showed a decrease in the
variance of impedance versus subject and body location as frequency increased that
was attributed to increased capacitive conduction at higher AC frequencies; hence, the
variation of real impedance due to differing SC skin thicknesses are not as apparent at
higher frequencies as should be expected. The residual measurable resistance at high
frequency is likely from deep tissue which is modeled in series with the SC resistive and
capacitive modeled impedance in parallel.

10

A physiologically-inspired model used to predict time hysteresis in SC skin impedance
from intra-modulated square wave current pulses is investigated in [29]; however, the
electrode areas, stimulation current amplitudes, and pulse widths used in this work were
larger than ones used for typical tactile information delivery. The psyological or electrochemical changes to the SC structure over time that can occur from electronic pulsing
include: the electrolytic effect, ion migration, and spontaneous (with or without recovery)
generation of pores [32]. The later is called electroporation by the same authors. These
effects cause the skin bulk impedance to exhibit time variation, usually having the effect
of lowering impedance magnitudes over time; in general higher magnitudes of
stimulation usually result in more drastic time variation and longer lasting effects.
Investigators in [32] observed a marked reduction in barrier resistance with high voltage
pulses applied to the SC with the recovery time after stimulation (if any) dependent on
amplitude and pulse history. Hence, the skin impedance exhibits remarkable hysteretic
dependency on pulsing history.

Since electrotactile displays are usually a matrix of spaced electrodes, spatial variation
in impedance is a function of localized epidermal morphology, such as thickness,
porous regions, and hydration levels. As such, the rate of time variation changes
according to electrode stimulation position. Localized hydration concentration of the
epidermal layer may change over time due to biofeedback or sweat buildup due to
electroporation and ion migration at the stimulation interface. The thickness of the SC
shows slight variation in individuals and, more significantly, relative to specific body

11

locations as observed from population studies from [40] and [41]. Susceptibility to
changes in hydration-to-mass percentage of SC was investigated with Raman
spectroscopy in [41]. The lower granular layer directly underneath the SC, in contrast, is
hydrated homogeneously and with a high ratio showing little variation between
individual and body location [41] (indicated by Raman spectroscopy results) and has
low electrical resistance [39]. For skin bulk resistance and capacitance measurements
as a function of dampness from applying electronic pulsing using skin surface
electrodes, see the results in [34]. Finally, the distribution of natural pores over the skin
does not seem to be uniform as is indicated by studies [31]. Pores in general, lead to
marked reduction in impedance when stimulated and can act as positive feedback for
current density leading to stinging sensations.

2.2 TACTILE INTENSITY AND PERCEPTION
Coding for tactile sensation is based on measured or created reference stimuli and is
done by tailoring the spatial configuration and temporal properties of the stimulating
waveforms. In turn, the delivered waveform content to the tactile display should emulate
the

reference

when

interfaced.

For

stimulators

using

electronic

actuation,

transcutaneous current is thought to directly stimulate the afferent nerve fibers in the
dermis. In relation to time, one of the most relevant parameters for predicting perceived
intensity of stimulation is found by the time integral of delivered charge which is
discussed and illustrated in [4].

The amount of delivered charge versus intensity

perception relationship is non-linear and increases monotonically. Because of this wellestablished phenomenon, square-wave pulses are traditionally a popular method for

12

encoding tactile sensation. In terms of perceived intensity from encoded stimuli, the
square wave signal can be coded by modulating the electronic pulse amplitude, width,
or burst rate per cycle, as is explained in [12]. An experiment relating the sensation of
intensity of physical roughness to electronic current pulse width and amplitude
modulation is carried out in [20]. The quantification of just noticeable detection levels
(JNDs) that relates gradations in perceived intensity to that of the intensity range of the
reference stimuli has also been studied using mechanical and electronic stimulators for
the sense of touch. Similar to visual and auditory senses, the JND for skin under tactile
stimulation seems to follow either a Weber‟s or Steven‟s power law in terms of
amplitude or pulse width modulation [22]. The JND levels can be controlled to an extent
by manipulating the same waveform parameters as discussed above. Further the
number of differentiated JND levels increases with the fundamental frequency of the
stimulating waveform.

The tactile sense has both time and spatial resolution. It has limited resolution for both
when consideration of minimum pulse dead-time and spatial separation for two-point
discrimination for the CNS to discern new tactile content. JND resolution is based on the
fundamental frequency with which square wave electronic pulses are delivered to a
single contact point on the skin. The optimal JND frequency resolution is said to fall
between 1 and 100 Hz. At 100 Hz, the number of identifiable JND levels will not follow
the increasing trend versus frequency found for frequencies below 100 HZ [12].
Additionally, waveform parameters can be set to target mechanoreceptors to evoke
specific sensations to the user such as pressure, vibration, or softness by combined

13

coding of spatial, temporal and fundamental frequency of square wave signals, as was
theorized and demonstrated in [24]. An example of spatial coding using two spaced
electrodes involves their respective current magnitudes that average together to form an
intermediate location for a new phantom point where the stimulation is perceived and is
discussed in [12]. Papers elucidating typical experiments in pattern recognition,
directionality, and tactile resolution of skin using electronic or mechanical stimulation
can be found in [17], [20], [42] and [7].

Dynamic range of sensation for tactile perception is defined as the ratio of pain
threshold over the initial registration as stimulation intensity is increased using some
consistent coding scheme. The metric is a psychophysically assessed measurement for
an individual. The ratio is shown to increase as the user habituates to the applied
waveform pulses over time or with the amount of experience the user has on the
stimulator device [4]. The voltage dynamic range of the driver to achieve a given
maximum current magnitude scales inversely with the effective electrode-skin contact
area [3] and hydration level [34] of the epidermis since skin resistance likewise under
these conditions. However, there is a tradeoff between a desire to decrease the
electrode area and increase the pain sensation threshold, and dynamic range of
sensation in general, since current densities will also increase with smaller electrodes.
According to [4], pain sensation threshold lowers with increasing current density;
however, electrodes larger than a given area can also cause unwanted concentration of
current density. Larger areas can increases the probability that low resistance pores or

14

areas around hair follicles, which are relatively highly conducive, could shunt current
and cause a runaway condition at a point [12].

Electronic stimulators can be configured to generate either biphasic or monophasic
square wave pulses where the phase is the polarity of the voltage signal referenced to
the return electrode. The associated current signal outputs can have a DC component
or be configured as pure AC in either case. If monophasic pulses configured as pure AC
signals are used, then a small DC voltage offset of opposite polarity in the inactive pulse
region would be required. A biphasic voltage pulse is mainly used to avoid electrobiological alterations to stimulated skin areas that would occur from net DC currents.
Current Pulses applied that are pure AC and for charge transfers much less than 4
µC/mm2 do not produce convective migration of ions, electrolysis of water in the tissue,
or non-native injection of ions in to cutaneous tissue [4] [12] [32]. Interestingly,
monophasic pulses exhibit longer adaptation times versus biphasic pulses [12].
Biphasic electronic pulses usually include a transition time duration in-between the
change in polarity on the order of microseconds. The short duration is needed to allow
time for charge accumulation to initiate action potential firings by depolarizing the
targeted nerve endings before changing polarity [12]. This helps to set the intended
sensation intensity. Studies have shown that electrode pulse polarity and also the
spatial superposition of nearby electrode polarities can influence the comfort and coded
perception by targeting and isolating specific classes of mechanoreceptors [24],
dynamic range threshold of sensation [4], and lasting alterations in skin biology from the
stimulation pulses.

15

2.3 TYPES OF ELECTROTACTILE DRIVERS
The stimulator topologies used for electrotactile haptic rendering are prevalently openloop constant current driver (CCDs) as seen in literature reviews. CCDs deliver and
maintain constant current square wave pulses to an unknown and potentially changing
bio-impedance load and are modeled as current sources. The CCD circuitry design and
output stimulation signals are dictated by how where on the human body the tactile
display is interfaced. For instance, electrodes for the display can be implanted
subcutaneously or placed on untreated skin surfaces meaning that voltage compliance
and current magnitude would differ greatly between these cases. When interfaced as a
skin surface display, the CCD must be able to drive potentially high and changing bioimpedance during application. The voltage compliance of the driver must be high under
these conditions, usually in the hundreds of volts to produce the required current in the
milliamp regime. However, CCD drivers interfaced to dermal surfaces with much lower
impedance with comparably less variable loading, such as on the tongue in [17] or with
abraded or hydrated SC do not require high voltage drivers. Resulting Output voltage
during active current pulsing can be under 10 volts on the tongue and under 100 volts
for stripped SC. Other systems can completely bypass impedance barriers of the skin to
stimulate nerve fibers directly via electrode implantation. CCD drivers in this case
require very low voltage compliance that results in stimulation currents in the
microamperes. For a system that uses subcutaneous microelectrode implantations as a
tactile display interface which targets SAI afferent nerve fibers directly and uses low
amplitude stimulation currents in the microamperes, see [10].

16

For surface interfaces that are designed for non-moistened and unaltered skin loci,
many high voltage systems have been proposed. The traditional electronic driver is
composed of a choice of OpAmp at the input stage with ether passive or active voltage
to current conversion (VIC) circuitry at its output stage. CCDs biased using passive
networks use a high voltage amplifier with feedback resistors for VIC. For one such
design that uses a Howland current pump configuration, see [3]. Alternatively, active
VIC networks use a low voltage operational amplifier with a high voltage transistorbased output biasing stage. Such classes of drivers are popular since they control
current with accuracy and precision over passive types since they can be designed for
extremely high output impedance. For detailed designs of such systems used in
application settings, see [20], [24] or [28]. The authors in [28] developed CCDs with a
16-channel scanning to a display matrix of terminal electrodes. The output of the VIC
topology could deliver high current square wave pulses using 8 customizable waveform
parameters for each channel that also aided in reducing skin irritation by having a zero
net DC current.

Conversely, an alternative to CCD-based systems would be open-loop voltage source
square wave pulsed drivers. Such drivers can be referred to as open-loop constant
voltage drivers (CVDs). Here, output voltage signals are independent of the variable
bio-impedance loading conditions. However, as skin surface stimulators, CVDs are not
conducive to a non-moistened and unaltered SC resistive barrier. Intact and dry stratum
corneum barriers would cause positive feedback in CVD current output because the

17

barrier resistance falls near-inversely to current amplitude in this state. When the
electrode is interfaced directly to the nerve fiber subcutaneously, or if the stratum
corneum of the skin is dampened or removed through abrasion, open-loop CVDs could
be considered. Skin impedance is either no longer a factor in the former case, and the
current output no longer influences appreciably the impedance of the skin in the latter,
which shows a near ohmic relationship under such conditions [29]. Also, by hydration of
skin, time variation of skin resistance is reduced and quality of sensation increased [12]
[15]. In reality, open-loop CVD drivers are not seen in application settings, since
ultimately a strong need to control precise current gradations and accurate ranges are
needed for most tactile information coding schemes and proper regulation of
pain/sensation (P/S) thresholds. Furthermore, the current signal that is directly
responsible for delivering the tactile information by some form of encoding would be
largely unknown without knowledge of the impedance state of the skin.

2.4 DESIGN CHALLENGES WITH EXISTING OUTPUT DRIVER METHODS
Open-loop CCD stimulators must be calibrated to a user‟s pain/sensation dynamic
range which differs between individuals, over time and with electrode contact location
as was previously discussed. To resolve this issue, researchers in [20] allowed users to
individually set current magnitude ranges for each electrode using dials for
potentiometers, thus allowing the individuals to customize their P/S dynamic range per
electrode on the display. The amount of pressure that the user applies to the electrotactile display can influence the effective electrode contact areas and thus concentrate
or diffuse localized current density accordingly. With CCDs, sudden stinging, burning or

18

uncomfortable sensations could occur from insufficiently applied pressure since P/S
dynamic range ratio is inversely related to contact-area; such a feedback condition
would not occur with open-loop CVD-based displays since dermis bulk impedance
increases with decreased contact effective area for an electrode. Complicating factors
of this approach are the number of set-points, and possible readjustments if the locus
under stimulation shifts relative to the electrodes, to name a few. To compensate for
P/S dynamic range ratio thresholds versus applied pressure, the researchers in [24]
incorporated load cells for pressing force feedback to dynamically adjust current
amplitude levels based on overall pressing force; however, this approach was not
electrode-specific but controlled P/S dynamic range display-wide likely because of
prohibitive size and cost of load cells. A passive stage VIC for CCD design is in shown
in Figure 2, and adapted from [3]. The human-equivalent DC resistance will typically be
much higher in magnitude than the feedback resistor magnitudes shown. Power loss
from biasing increases through this path as the equivalent load magnitude decreases,
as will typically happen when the load current is increased. However, using higher
resistance resistors in the feedback path reduces bandwidth, introduces Johnson noise
and increases voltage offset. Other design complications include precise resistor
matching in the feedback path, and choosing an appropriate Rs, which, depending on
the value, can reduce load current SNR if set too low or reduce load voltage compliance
of the HV OpAmp if set too high in value.

19

Figure 2. Improved Howland current pump with master-slave configuration adapted from
[3]. Rs = 1 kΩ, R1 = R3 = 5 kΩ, R2 = 10 kΩ, R4 = 9 kΩ, and ZL is load impedance.

For active VIC circuitry, the output stage usually consists of a current mirror. The mirror
serves two purposes: 1) converts a low voltage, low reference current amplitude
waveform to a high voltage, low current output; 2) sets the output impedance of the
driver to a high value. The advantage of using this approach is the availability of low
voltage OpAmps and high voltage transistors to design for frequency response, output
impedance, and power efficiency of the output stage when compared to a passive VIC
solution. However, significant power can go in to transistor biasing, and losses from
transistor switching, reference current generation due occur. Specifically, if the SC
electrical impedance approaches that of the current mirror output impedance, power
efficiency of the circuit decreases, and transistor saturation may occur. One final
consideration for open-loop CVD and CCD designs is the layout size. The current mirror
components for CCD add to the overall layout size. However, open-loop CVDs require
no additional real-estate other than that of a few resistors in their feedback path if HV
OpAmps are available.

20

Open-loop CVD designs are not generally used as surface displays because of
previously stated reasons. Since both current and bio-impedance are coupled and
inversely related unknown variables in a CVD topology, an open-loop method is
unstable and an offline calibration approach to P/S dynamic range ratio unrealistic.
However, the design advantages for CVDs warrant investigation. CVDs are more
energy efficient, simpler to design, and take up smaller layout real-estate versus CCDs
as discussed. As the number CCDs in a system increases, these tradeoffs become
considerable enough to explore the CVD method.

Designing for CVD stimulation implies some prior knowledge skin bio-impedance where
interfaced and necessitates a closed-loop solution. Real-time identification of bioimpedance parameters according to a reasonable load impedance model, along with
closed-loop design methodologies, means that current output tracking can be
accomplished under load-varying conditions. Moreover if a relationship between P/S
dynamic range and the known bio-impedance can be found, current signals delivered to
each electrode can be adjusted dynamically. Such a possibility means: 1) offline
calibration is minimal or no-longer required; and 2) that the user could spatially scan the
display and that the respective magnitudes of current signals would be adjusted to the
changing bio-impedance conditions during the process. Power efficiency is increased
over CCDs because the output impedance of the driver is low and not dependent on
load magnitude. The design of the driver in theory is simple since high-voltage OpAmps
with adequate slew-rates for square wave generation exist; further, the power needed
for driving unmodified and dry SC skin are possible with OpAmps on the market due to

21

the relatively small current requirements. A line of OpAmps for such a purpose are
available by Cirrus Logic [37].

Since electrically stimulated intact-SC tissue is a complex system, one possibility for the
use of CVDs as surface stimulators would require monitoring of I-V outputs combined
with a real-time adaptive control solution. The tradeoff for the desirable power efficiency
and minimal layout area with CVD drivers would be the additional circuitry for monitoring
outputs, the control scheme for regulating output current, and the real-time software and
systems overhead to integrate these aspects. With a load-aware system, the
parameters of the skin impedance models for each electrode-skin contact point could be
known at all times; hence, further power reduction and cost saving could be achieved by
turning off driver power to un-interfaced electrodes, as sensed by the high impedance.

Though the process is natural for a closed-loop CVD system, as of the writing of this
paper, the author could find no papers for review for such an approach. The synthesis
relies on using CVD drivers that are simple to design, manage, and, are above all,
compact, and consume less power than the CCD topologies. Therefore, with closedloop design, the CVD can be accomplished with minimal driver overhead if output
measurement circuitry is introduced.

22

3. SYSTEM DESIGN

The haptic renderer was designed for surface electrotactile stimulation of the index
fingertip using a matrix of electrodes for untreated and dry SC skin boundaries. This
work is a redesign of an earlier developed electrotactile renderer whose design is
detailed in [1]. The previous version has successfully functioned as the haptics display
in a telediagnostic and telepresence system for researching breast tumor pathology
diagnosis (see [1] for a description of the overall system). In [2], it is presented as a tool
for haptics investigation in to perception of car seat leather qualities coded for using
electro-tactile stimuli. The physical properties of the leather were measured using a
high-resolution optical sensor that included roughness, geometry, and contour
information for haptic encoding and rendering. The application was for quality control
purposes regarding car seat inspection in the automobile industry as a telepresence
application.

The newly developed haptic system in this paper features a CVD OpAmp stimulator as
proof-of concept for a new type of stimulator topology. It adds intelligence to the system
by making it a real-time, load-aware module for bio-impedance by incorporating customdesigned I-V sensors necessary for online system identification of the given impedance
model. Pertaining to the output, voltage waveform output parameters that can be
adjusted in software include: voltage amplitude, duty cycle, fundamental frequency, and
three types of waveform pulse shape geometries; the last setting is research-specific
that pertains to psychodynamic and output power experiments that were carried out.

23

This is in contrast to the older system which does not have software settings for output
amplitude; the possible pulse states to any given electrode are either on or off. The
motivation for the new haptic system is to maximize power efficiency in the output driver
that accompanies CCD design and study bio-impedance identification and its
implications. Power analysis of the driver will be presented under real loading
conditions. As a first step, system identification of bio-impedance loading models using
the CVD hardware was accomplished through custom software, online and in real-time,
which will be demonstrated. As well, a model reference adaptive control (MRAC) law
will be introduced as a means to overcome the challenge of tracking the output current
under changing load conditions. Simulations of the control law will be shown as a first
step to prove efficacy.

In summary, the first version of the haptic renderer is constructed with hardware
including: CVD stimulator, output sensors, high voltage power supply, and a revamped
electro-tactile display terminal. It also includes a high speed DAQ card for sampling data
from the I-V sensors and output signal rendering. As well, the initial system software
and GUI was designed in Windows to carry out preliminary tests of the hardware and
load identification algorithm. Simulations and preliminary analysis of the closed-loop
algorithm will be presented based on realistic scenarios from bio-impedance
identification experiments and results.

24

4. HARDWARE, SOFTWARE, AND SYSTEM CALIBRATION

Figure 3 shows the system-level diagram of the implemented haptic renderer. The main
hardware modules can be grouped as follows: PC and high speed digital acquisition
board (DAQ), CVD stimulator, load measurement circuitry (current and voltage), high
voltage bi-polar power supply, and designed electro-tactile display unit. The CVD
amplifies the voltage waveforms to appropriate stimulation levels with a set gain. The
CVD interfaces to one electrode on the electrotactile display at its output. The
multiplexing circuitry for time-division scanning the output to the electrotactile array was
not developed at this time. The two functions of the measurement circuitry are signalconditioning and scaling down load signals for sampling by the DAQ.

The software is custom designed. It serves as the software-controlled waveform
function generator and controls the sampling and processing of load measurement
circuitry for the DAQ. Other main functionalities of the software include real-time load
impedance identification, a GUI front-end used for setting I/O and waveform generator
parameters and displaying identification results. The design details on, and
interrelationships between each block diagram are summarized in Figure 3 and will be
expanded upon in sections to follow. As well, the details of calibrating the measurement
sensors and the CVD amplifier will be explained.

25

Figure 3. System level diagram of implemented project.
26

4.1 HARDWARE DESIGN

The following subsections discuss the haptics hardware design criteria, such as for the
selection of DAQ, OpAmps for output sensors and CVD stimulator, and also elaborate
on the custom hardware built, for this project. As well, the specifications and
construction for the revised tactile display are presented.

4.1.1 DIGITAL ACQUISITION (DAQ) BOARD
The DAS 6025 DAQ from Measurement Computing was selected for I/O interfacing
between haptic renderer hardware and software. The DAQ board features 12-bit
resolution, 10,000 samples/sec D/A output channels, and 12-bit resolution, A/D input
channels with conversion rate of 200,000 channel-samples/sec. A high speed A/D
sampling rate is necessary to capture the output current transient response delivered to
the skin-electrode interface. Based on known output dynamics under usual human
loading conditions, a DAQ board with twice the sampling rate was desired; however,
budget limitations constrained the choice. The project required one analog out channel
for inputting analog data to the CVD input and two A/D conversion channels (100,000
samples/sec) for sampling the load current and voltage measurement circuitry outputs,
respectively. As well, bipolar voltages can be outputted and sampled by the DAQ
allowing for biphasic pulsing to the skin and measurement.

4.1.2 HIGH VOLTAGE DC-TO-DC CONVERTER POWER UNIT
The haptic renderer requires a high voltage, bipolar power source for powering the high
voltage CVD stimulator OpAmp which can be powered at ±450 volts. For this, a custom
27

bipolar, high voltage converter configuration was designed; the schematic is shown in
Figure 4. The core components are duel unregulated 300 volt EMCO DC-DC converters
supplying 10 watts output at full scale (U3 and U4 in the schematic) [36]; the output
voltage is proportional to the input voltage, and the isolated output of the converter
allows for polarity selection. Thus, one converter functions as the high voltage positivereferenced power supply, while the other functions as the symmetric negativereferenced counterpart. The duel reference sources are added for the option of
producing biphasic pulses on the CVD stimulator output if desired. The positive and
negative output voltage levels are adjusted symmetrically at the input by tuning a set
point Vset with output dynamic range from ±50V to ±300V.

Since the output is

unregulated, each converter was designed with negative feedback regulation circuitry
as to reduce the dependency of current draw on the output voltage. The negative
feedback from the outputs of U3 and U4 to the corresponding inverting terminal of U1
and U2 are used to bias the Darlington BJT transistors configurations, Q1, Q2 or Q3, Q4,
for regulation of input power to the converters based on the high-side power draws,
respectively. The effect is to keep the high-side output voltages invariant of output
current draws. The feedback capacitors, C2 and C12, are used as low pass filters to
reject high frequency influence on the regulation. Q2 and Q4 are transistors with high
collector current ratings in case it is necessary to source input current to the converters
operating at full power rating.

High voltage tank capacitors, C1 and C4, with large capacitances at the converter output
side are included to filter out high frequency switching noise attributed to DC-DC boost
28

conversion and to isolate the regulated voltages from transients that can occur from
high current draws. These capacitors assist the regulation circuitry, which is only able to
respond to low frequency changes in current draw.

An important safety concern is the isolation of the DC-DC converters from ground as to
avoid possible electrical shock to the user. The electro-tactile display and, hence, the
user is referenced to COM2 of this module and must be isolated from ground well. The
isolation of the converters was tested empirically and provided at least 5 MΩ of ground
isolation during operation and human use.

29

Figure 4. High voltage DC-to-DC converter circuit.

30

4.1.3 CONSTANT VOLTAGE DRIVER (CVD)
The CVD component of the haptic renderer delivers high voltage pulsatile signals to the
electro-tactile display. The schematic for the CVD circuit is shown in Figure 5. The
OpAmp component U1 is high voltage, which is configured as a non-inverting amplifier.
The output is given by:

VDAQ_OUT is the software-generated waveform from the DAQ D/A output channel to the
CVD input terminal; VCVD is the output voltage signal available for application to a
user‟s fingertip as referenced to COM2. The PA97 OpAmp manufactured by Cirrus
Logic was selected for its maximum ±450V voltage output swing, high 8Volts/µs slew
rate, and capability to source or sink 10 mA of DC current [37]. The current and voltage
output ratings far exceed the normal electro-tactile stimulation ranges based on prior
work that identified haptic design parameters now pertinent to this work (see [34]) as
well as values discussed in the literature review section. From the slew rate
specification, the minimum rise time of the OpAmp output at full-scale is 37.5 µs. The
rise time is insignificant since the voltage pulse durations in this application ranges from
0.5 to 2.2 ms. The OpAmp closed-loop gain is set at approximately 50 and can deliver
bipolar waveform pulses of approximately 300 volts in amplitude; the bipolar voltage
sources powering these OpAmps, discussed in the previous subsection, sets this upper
magnitude limitation. Vbias is a low voltage source that can be adjusted to cancel DC
offset at the CVD output. A large 4.7 MΩ feedback resistor (R3) minimizes power loss in

31

the feedback path since it will be shown to be much greater than the typical DCequivalent impedance of human skin for this application.

It is important that the large value of R3 will not inject instability in to the circuit.
According to [37] the conservative gain-bandwidth product is:

where Av is the designed closed-loop gain of the circuit and fGB is the maximum largesignal bandwidth frequency for a certain Av (in this case about 50). The open-loop unity
gain bandwidth for the PA97 from (4.2) is 1 MHz. Per the specification sheet [37], the
internal input capacitance Cin is equal to 4 pF. With the value of the resistor used for R1
set at 10 kΩ, the added pole to the active network is related by:

The values introduce a closed-loop pole at 4 MHz. Consequently, the additional pole far
exceeds the bandwidth of the OpAmp and is not a concern for closed-loop instability.

32

Figure 5. Constant voltage driver (CVD) circuit.

4.1.4 CVD OUTPUT VOLTAGE SENSOR
Figure 6 shows the schematic for the developed CVD voltage sensor configured as a
voltage follower with a voltage divider stage for scaling the high input voltage. The
purpose of this circuit is to proportionally scale down the CVD voltage output pulses for
compliance and buffer the signal to one of the A/D channels of the DAQ for
measurement. The circuit can measure voltages of both polarities, as well. COM1 is the
input node and is referenced to the voltage delivered to the tactor under measurement.
The voltage divider network has a resistor R1 of high value to minimize loading and
effectively keep electrical isolation between COM1 and COM2.

Since the OpAmp has input capacitance, low-pass filtering of CVD pulses under
measurement from the large resistor values shown could occur. The analysis will follow.

33

The equivalent common mode input capacitance for U OpAmp is a CIN of 2.5 pF. The
CVD output voltage seen at the non-inverting input of U in Figure 6 is the output of the
filter given by:

where Vcom1 (COM1 in the figure) is the voltage measured at a given tactor on the
electro-tactile display. The relationship in (4.4) should approximate a flat band pass filter
over the dominant frequencies in the CVD output pulse waveform. The 3 dB down
impedance pole of (4.4) is located at:

Using (4.2) and the value of Av equaling 50, the large signal frequency cutoff of the CVD
OpAmp is roughly 20 kHz so that voltage divider scaling will not depend on frequency in
this case. At the output side of the OPA37, the slew rate is 11.9 V/μs which is greater
than that of the PA97 CVD OpAmp. In summary, the voltage sensing circuit will not act
as a low pass filter because of the location of the pole given by (4.5) and higher slew
rate versus that of the CVD OpAmp.

34

Figure 6. CVD voltage output sensor circuit.

4.1.5 CVD OUTPUT CURRENT SENSOR
Figure 7 shows the schematic of the designed high-side current sense amplifier circuit
used for measuring human load AC currents from applied CVD voltage pulses. Rsense is
a high-precision resistor of 1.000 kΩ in series with the fingertip load. Load current
measurements occur across the Rsense resistor by transduction to low differential
voltages since RMS load currents sourced to the display are typically in the low to sub
milliamp range. OpAmp U4 buffers the differential voltage across Rsense. The voltage at
the sensor output U5 is linearly related to an acceptable degree to the stimulation load
current. U1, which is a standard voltage DC-to-DC converter, powers the currentsensing circuitry and has galvanic isolation between its primary and secondary sides.
The ground reference COM1 for the converter on the secondary side is galvanically
isolated from COM2 and is the reference potential for the current sense resistor and
circuitry powered by it. When viewed from COM2, high common mode voltages due to
CVD high voltage pulses referenced to COM2 are canceled on the input to U4 and
35

circuit elements powered by U1 since these elements will float on the pulsed voltages.
However, U1 possesses some inter-winding capacitance which means noticeable
capacitive current will flow between secondary and primary windings if the CVD voltage
pulses changes quickly and with great magnitude in a short duration of time, as is the
case with square wave voltage signals. This could result in transient high voltage spikes
across circuit element nodes referenced to COM1. The selection of U1 was based on
choosing one with small interwinding capacitance as to reduce the effects of capacitivecoupled currents on the isolation and measurement process. The analysis of the current
sense circuit and why it is necessary will now follow.

36

Figure 7.CVD current output sensor circuit.

37

The high common mode (CM) input voltage for this application would be problematic for
conventional high side current sense amplifiers. Most affordable OpAmps do not have
inputs that are rated for high common mode voltages in the 100s of volts. The common
mode introduced from the CVD pulses is usually well above the 100 volt level and can
be as high as 250 volts. There were two observed ways to contend with this issue: 1)
use a current sense difference amplifier that scales the high common mode to a
compliant range; 2) construct a floating voltage reference for the current sense circuit
using the CVD pulse as the voltage reference. Solution one is idea in theory, due to the
minimal number of components needed, but is difficult to implement in practice for this
application. There are many differential OpAmps on the market that achieve the desired
CM attenuation using laser-trimmed resistors for good matching leading to accurate
current measurement. However, differential amplifiers not only scale down the common
mode voltage, they also scale down the differential mode input across R sense. Since the
typical stimulation currents are in the milliamp range, Rsense would have to be increased
in value proportional to the CM magnitude attenuation scaling so not to decrease SNR.
However, doing so would add unintended loading to the CVD stimulator voltage which
would negate one of the intended purposes of its use. Therefore, approach two is
promising because it does not rely on scaling down voltages across Rsense and also
cancels the common mode seen by the input of U4 in Figure 7. The tradeoff is an
increased complexity in the accompanying circuit design.

Choosing a DC-to-DC converter to provide the necessary reference isolation is the main
design challenge for the second approach. The component U1 met such a requirement,
38

which also has a three-tap secondary winding to provide a positive and negative power
supply to the OpAmps incorporated for measuring bipolar current across Rsense. The
secondary side of U1 provides +12 and -12 volt duel power with a center-tapped
common reference terminal and 2.5 pF inter-winding capacitance, while also providing
galvanic isolation. The effect is twofold: 1) the high voltage common mode is canceled
when powering the current sense circuitry by using U1; 2) the current sense amplifier,
U4 only sees the differential voltage across Rsense. Therefore, small voltage OpAmps
can now be employed to measure current while keeping Rsense small in value as well.

The barrier capacitance of the converter is 2.5 pF. With the maximum slew rate of 8V/μs
for the HV CVD OpAmp [37], an expected leakage current from the transient response
would be 2 μA. This is negligible leakage for the application. However R1 being high
forms a low pass filter with this barrier capacitance and should be kept as small as
possible as not introduce a significant time constant in the measurement circuitry; the
effect would result in transient high voltages on the circuit from the CVD pulses which
could damage the measurement circuitry. Selection of R1 has another constraint that
will be discussed later.

The last consideration is reducing switching noise on the secondary side of U1. For this,
a CLC filter (π-filter) was employed for both the positive and negative voltage
references on the secondary side. The inductor was chosen to have low winding
resistance to minimize power dissipation, and the decoupling capacitors are low ESR
tantalum types to minimize high frequency impedance. The capacitors on the other side
39

of the inductor choke are low-valued ceramic capacitors with very low ESR to filter out
the highest frequency noise.

The current measurement voltage signal outputted on U6 must be re-referenced to
COM2 for DAQ sampling. The isolation linear optocoupler U7 serves this purpose. The
optocoupler has an LED emitter with a feedback photodiode referenced to COM1 and
another photodiode on the opposite barrier referenced to COM2. The servo diode is
used as a negative feedback to amplifier U6 to regulate the LED emitter‟s forward
current IF and to make this current highly linear since it is directly related to the current
through R1. The photodiode current referenced to COM2 is also proportional to IF since
it is directly related to the current through feedback resistor R2. U5 is the
transconductance linear amplifier on the output side of U7 and buffers this signal to the
input of the analog DAQ channel.

The isolation amplifier is configured in the

photovoltaic state. This state was selected to give the best linearity, and lowest noise
characteristic. Having a high SNR for 12 bit resolution and good linearity is paramount
for accuracy in the identification algorithm when compared to the photoconductive state.
The bandwidth of the optocoupler in photovoltaic operation is about 50 kHz [38]. This
exceeds the bandwidth requirement for measuring load current since it is greater than
the bandwidth of the CVD stimulator of 20 KHz given by (4.2) with Av equaling 50.

The circuit topologies of U2 and U3 provide precision current sources whose output is
given by:

40

where the voltage reference in the equation is produced by D1 and D2 with good
precision. The purpose of the current sources allow for bipolar current measurement.
They can also cancel unwanted DC offset voltage at the output of U5 via adjustment of
each ones biasing resistor (Rbias). For the load identification algorithm to be valid, it is
important to measure any potential current undershoot even if bipolar voltage pulses are
not used.

Referring again to Figure 7, the relationships for the isolation amplifier circuitry are:

The diode forward current IF is responsible for the non-linear, time and temperature
dependencies using optocouplers without servo-current feedback. However, with
feedback, (4.13) shows that IF is factored out. The ratio of R2 and R1 is kept close to

41

unity as well for measurement purposes. Now, the output at U5 is only dependent on
resistor values and the transfer gain K3, which itself is a ratio of the output transfer gain
K1 and the transfer gain K2. The transfer gain K3 is close to unity and drifts very slightly
with respect to forward current magnitude and ambient temperature but otherwise
remains constant.

The resistor values, Rsense, and R1, must be selected in consideration of the
optocoupler‟s maximum IF current rating for best linearity, knowledge of the maximum
load current levels to be measured so not to damage the IC, and the SNR of the input
signal. The latter of which is based on the magnitude of Rsense. In addition, the voltage
magnitude going to the A/D channel of the DAQ cannot exceed 10 volts. From previous
studies in [34], the absolute maximum current amplitude of 5 mA will be taken as the
upper limit. In actuality, the typical current amplitude to a human load is about 1 to 4 mA
with dry skin. For this reason, the sense resistor was selected at 1.000 kΩ, which will
give a good SNR while also minimizing loading influence on the CVD stimulator. Taking
5 volts to be the maximum voltage across R1 and K1 in (4.9) with a nominal value equal
to 0.007, R1 was selected to be 20 kΩ to give a maximum IF of 36 mA by using to (4.8)
and (4.9). According to [38], the linearity of the optocoupler is not compromised with this
maximum value of IF. R2 was then selected to give unity gain. However, the biasing
current for bipolar current measurement can effectively reduce the maximum current
rating (60 mA) and upper bound in forward photodiode current IF for optimal linearity (30
mA) of the optocoupler. The current biasing of U2 took in to consideration that negative

42

current pulses are much lower in magnitude than the positive pulses to the anode
electrode for the intended uses of the system; hence, the biasing is optimized for
positive non-symmetric bipolar or positive monophasic voltage pulses. In summary, the
isolation amplifier should provide a highly linear relationship between the measured
stimulation current across Rsense, and the output of U5 in the face of high common
mode voltage stimulation pulses delivered to the electro-tactile display.

4.1.6 ELECTRO-TACTILE DISPLAY HARDWARE DESIGN
The electro-tactile display is the interface for the fingertip surface to elicit various
sensations to the somatosense by electronic stimulation. The tactile display shown in
Figure 8 was developed to make improvements to the previous one presented in [1].
The enhancements include doubling the electrode density, more intuitive fingertip
placement, ergonomic design, such as fingertip and arm rest padding, and making the
unit more compact. The dimensions of the encasement of the display are
10.16x7.62x2.54 centimeters. Soft rubber padding resides at the base of the display to
serve as a stable resting position for the index finger. The electrode active area, where
stimulation occurs on the fingertip, is 2.74x2.31 centimeters. The active area is made
intentionally larger than the average area of actual index fingertip regions for ability to
temporally scan the matrix. Scanning the electrodes with the fingertip has been shown
to improve richness of perceptive experience in some cases [7] [42]. To determine the
lower bound of the active area corresponding to the index fingertip, subjects were asked
to make fingerprints with this region on paper so that the resulting ink perimeter that
occurred from pressing against a hard surface could be measured and averaged. The

43

pressing force was kept between 4 to 8 ounces to make the prints, which were typical
preferred forces by users as determined beforehand.

The display features 192 copper electrodes with tin plating. Tin platting is necessary so
that the electrodes will not oxidize, which would increase interface resistances and,
hence, voltage amplitudes for the same current stimulation levels. The electrodes are
0.762 mm in diameter with 1 mm pitch. The pitch of the electrodes is less than reported
distances of two point discrimination tests (DPDT) with static-placed fingertip, which
according to [4] ranges from 2 to 7mm, and can be greater for temporal scanning. From
[22], the innervation density of the densest receptors, the FA1s, is on average 1.4 units
per square millimeter, which is on the order of the tactor density of the active area of
this display.

Choosing the electrode diameter was done to maximize the electrode density without
compromising physical or quality of sensation. The electrode diameter determination
took in to consideration dielectric breakdown of air, and the effects of electrode
geometry on sensation intensities. In general, the breakdown voltage of air is 3000
volts/mm with rounded electrodes if voltage potential is static but will decrease as a
function of increasing change in voltage or air humidity. Increasing the electrode area
increases the pain-to-sensation (P/S) dynamic ratio because the current density over
the skin-electrode contact area decreases on average [4]. Keeping the electrode
diameter small minimizes the chance of dielectric breakdown between electrodes by
keeping electrode pitch large at the cost of reduced P/S threshold ratio. However, the

44

electrode diameter used in the former tactile display of comparable dimension gave
good quality of sensation over a wide range of current amplitude and pulse width.
Quality of sensation in this case was a blunt vibration sensation experienced by the
individual without notable stinging or sharpness present.

Figure 8. Tactile display: dimensions are 10.16x7.62x2.54 centimeters with an active
area of 2.74x2.31 centimeters.

The electro-tactile display is isolated from ground for the safety of the user. Having high
impedance isolation assures that no current flows through the cardiac tissue. In the
unlikely possibility that the system forms a path to ground through the human user, the
45

maximum current that can be delivered from the CVD is 10 mA. Figure 9 shows the
developed return electrode for the isolated system. It features a large copper cathode
return with Velcro strap so that the user can easily attach it to the thenar eminence
region of the palm for minimal interference. The lack of hair follicles in this area helps
with making low impedance contact to the return. Without a connection to the isolated
return, no stimulation can be felt which supports the conclusion that most of the
stimulation current flows between the index fingertip and the electrode return path.

Figure 9. Ground-isolated return electrode.

4.2 SOFTWARE DESIGN
The software for this project was custom designed and programmed in the Windows
environment. The three main features of the software are: 1) a GUI front-end for
configuring voltage pulse output parameters, I/O sampling rates, load identification
algorithm and to display the real-time results dialog; 2) control of system-level
components such as DAQ functions, and algorithm for real-time identification of human
46

impedance models; 3) and software-based waveform generator for pulsed stimulation.
Each of these features and functions in relation to software design will be discussed in
the subsections to follow.

4.2.1 GUI FRONT END AND RESULTS GRAPHICAL DISPLAY
The GUI front end, shown in Figure 10, allows the user to configure settings for the
waveform generator and identification algorithm. Referring to the “Initial Driver Output
Parameters”, the output waveform settings include: pulse shape, CVD pulse amplitude
at output, fundamental frequency of the waveform, and duty cycle. One additional
setting is the number of equally-spaced, intra-duty cycle modulations in an active duty
cycle pulse. As well, the calibration coefficients necessary for scaling the input from the
DAQ output to achieve desired CVD amplitude at its output are entered here. The other
settings, including waveform pulse shape, are provided for the researcher to study
configurations that impact psychophysical perception of the media being displayed,
such as pressure, edge, tickle, vibration, or motion to name a few. Also, the researcher
can experiment with the parameter space to determine their influence on perception.

Referring to the “Identification Algorithm Settings”, the responsiveness of the
identification algorithm to time variation in the plant is done by setting the sample
memory N. As seen under the heading, “Record ELS Results in Seconds”, the program
can be used to record results and relevant data as a function of time for offline analysis.
As well, gain measurement calibration coefficients can be entered which are necessary
to proportionally rescale the current and voltage output sampled data to actual values.

47

Figure 10. GUI front end.

48

Figure 11 shows the dialogue of the GUI that displays the real-time metrics of the
identification algorithm. The results dialogue provides visual feedback for output error
convergence, most recent set of identified parameters in the S and Z domain, and other
states for the identification algorithm in real-time and as a function of relative time. The
metrics can be stored when the operator uses the software record feature.

49

Figure 11. Identification results dialogue.
50

4.2.2 SOFTWARE DESIGN AND PROGRAM FLOW
Figure 12 illustrates the top-level hierarchical structure and interactions between the
GUI, underlying process, and child threads. The software processes GUI front-end
requests, controls I/O and access to DAQ shared memory, selects (de)activation of the
load identification algorithm based on GUI request, and generates digital waveform
primitives from desired GUI inputted parameters. Digital waveform primitives are
defined as DAQ analog output waveforms inputted to the CVD stimulator. Waveform
D/A conversion and output are handled by the “DAQ D/A Out” thread. Programming for
the DAQ was done using the C routines of the Universal Library API by Measurement
Computing. GUI requests may be disregarded based on in-program software interlocks
if they would lead to unsafe operating conditions for the user. The “DAQ A/D In” thread
intermediates the run/stop state of the “Online Identification” thread based on GUI
request. The load identification thread is programmed for speed and priority level since
it must process the load model in real-time. As well, the load identification thread grants
access to inter-thread read requests by the “Results Display” dialogue thread for
displaying the most current load identification results. Figure 13, Figure 14, Figure 15
and Figure 16 expand graphically the program logic and shared memory read/write
schemes inside the block diagrams of each child thread and their interrelation to one
another.

51

Figure 12. Program flow control: top level.

52

Figure 13. Flow control for D/A output thread and DAQ shared memory write.

53

Figure 14. Flow control for D/A output thread and DAQ shared memory read.

54

Figure 15. Flow control for initiating or stopping A/D and identification threads along with
identification shared Memory read from results display thread.

55

Figure 16. Flow control, shared memory access and data accessing for online identification thread.

56

4.2.3 SOFTWARE WAVEFORM GENERATOR AND TYPICAL WAVEFORM
PRIMITIVES
Waveform primitives are generated from GUI-inputted parameters and stored in PC
memory as a digital period template of one period. The digital waveform generation
corresponds to desired CVD output pulse characteristics entered in the GUI such as
shape, amplitude, frequency and pulse duration (duty cycle). Digital waveforms must be
generated for D/A converted input to the CVD stimulator; hence, the relationship via
calibration from CVD stimulator output settings to corresponding analog input must be
known. This is discussed in the next sub-section.

Figure 17 illustrates the different waveform primitive types as seen at the CVD output
that the can be generated in software; they are square, saw tooth, and triangle wave
pulses. The graphs were generated by sampling and magnitude rescaling the voltage
output and saving the measurements with the software save feature; only one pulse for
each waveform primitive type is shown out of the multiple pulses that occurred in the
sampling duration The CVD output parameters settings were 60 Hz, 11 percent duty
cycle and between 140 to 170 volts in amplitude. Each displayed measurement was
sampled using a load impedance of 50 kΩ at output. As seen, the voltage pulses had
low noise, and well defined geometry at high voltage. The quantization levels from D/A
conversion are apparent in the waveform, especially with the non-square wave shaped
geometries; however, when applied as stimulation to the skin, the quantization levels
were not experienced tactilely likely do to smoothing from both action potential response
time and JND level gradation. The shown waveform primitive shapes were selected

57

primarily for testing hardware dynamics capability, load parameter identification results
as a function of waveform shape, sensation threshold levels and psychophysical
responses from stimulation to be presented in later sections. They do not necessarily
reflect the optimal choice of waveforms for delivery of tactile content in application
settings. The hardware is fully capable of generating biphasic or monophasic voltage
pulses which have no net average DC current when in application settings. Researchers
have shown that these later waveform classes are less electro-chemically reactive to
the skin which lessens creation of sweat pores (electroporation), irritation of the skin,
injection of non-native ions, and net ionic flow inside the dermal tissue over extended
time of operation [12] [28] [32].

Figure 17. CVD output pulses generated from software waveform primitives utilized in
testing tactile display.
58

4.3 HARDWARE CALIBRATION
This section explains calibration of the CVD output voltage and measurement circuitry.
The identified relationships are programmed in to the software with respective
calibration coefficients that can be set before or at run-time. The result is that the CVD
output voltage amplitude can now be reliably set programmatically by the GUI interface
and that output measurements sampled by the DAQ can be scaled back to original
magnitudes for load identification purposes.

The calibration process utilized a 50 MHz analog oscilloscope and two voltage probes
which allowed for simultaneous measurements of I/O voltages at either the CVD or one
of sensor networks, respectively. Best-fit regression analysis between the input and
output of a given network was then done using obtained multiple sampled voltage pairs
to characterize the network accurately. A known high precision load resistance of RL =
50 kΩ was used for calibration in all cases, which was chosen since it is the minimum
allowable impedance the haptic renderer can reliably drive. The types of pulses used for
calibration were square wave voltage pulses at 60 Hz with an 11 percent duty cycle.

The CVD voltage output amplitude versus voltage amplitude seen at the DAQ analog
output channel is illustrated in Figure 18 for multiple measured pairs. The fitted
regression line and equation of the measurements points is given. CVD output voltage
measurements were taken before the current sensor and directly at CVD output so that
the relationship was independent of loading conditions. The CVD output voltage

59

amplitude spanned from 50 to about 180 volts with good full-scale linearity. A power
fitting curve gave the best regression model (R2 = 0.996).

60

Figure 18. Calibration of the CVD input-output voltage amplitudes.
61

Figure 19 shows the plot relating voltage amplitude seen at the voltage sensor output
versus that at the load standard. The regression line and corresponding equation are
shown. The relationship is used in program to rescale the DAQ sampled CVD
measurement voltages to load values. Measurements of the CVD output voltages were
taken after voltage dropped across the current sense resistor since the interest is in the
voltage relationship due to loading of the CVD, as is the case under actual fingertip
impedance loading conditions. For calibration purposes, the standard resistor
aforementioned is used. Regression analysis was performed and the result shows the
lower bound of linearity. Pairs of voltage samples were collected under CVD output that
ranged from 50 to 180 volts. An affine linear model gave the best coefficient of
determination (R2 = 0.997). The constant DC term is a negligible percentage of the
scaling term which is likely due to either probe measurement or OpAmp offset voltage
error from the measurement circuitry.

62

Figure 19. Calibration of the load voltage sensor.
63

The results for the calibration of the current sensing circuit voltage output amplitude to
that of the load current are given in Figure 20. The horizontal axis ordinals are the
steady-state load currents obtained by dividing the measured voltages at the load with
the known 50 kΩ impedance standard. The vertical axis corresponding ordinals are
voltage points from measurements at the current sensor output. The CVD output
voltages were chosen to emulate typical current magnitudes flowing through human
skin at the region of application.

An affine linear regression model gave the best goodness-of-fit for the plotted data
points (R2 = 0.9996). The DC offset voltage for the load current-measuring circuitry is
only 0.0206 volts. The low DC offset is due to offset canceling circuitry as discussed in
section 4.1.5. The transconductance gain coefficient in the linear regression is 1051 kΩ
and close in value to the precision sense resistor of 1000 kΩ. Ideally, the measurement
gain should equal the value of the current sense resistor; however, the offset depends
on the isolation amplifier used in the current sensing circuit having a gain of exactly
unity. Finer precision instruments for voltage calibration could be used to correct this
disparity.

64

Figure 20. Calibration of load current sensing circuit.
65

5. MODELING AND ANALYSIS OF ADAPTATION LAW

The subsections to follow will introduce and analyze two electronic conductance models
of the skin when current is applied. Both models have the CVD voltage pulse as input
and the estimated current response to the skin as output. The first model to be
discussed is parameterized as a transfer function in the S-domain and is called the
continuous time bio-impedance (CTBI) model, where the “bio” prefix emphasizes that it
represents some of the skin‟s bulk electronic properties. The parameters for this model
correspond to passive electronic circuit elements that have been shown to reproduce
the dynamics of the response of skin to electronic stimulation.

The other model is parameterized as a conductance transfer function in the Z-domain
whose parameters are estimated online in the discrete time domain. The parameter
estimates corresponding to the CTBI model are then derived from a function of the
identified Z-domain model parameters. The Z-domain model will be referred to as the
discrete time conductance (DTC) model; its parameters do not have any direct physical
correspondence to the underlying plant. However, the model order and number of
unknown parameters are based on the CTBI model structure. Subsequently, the
adaptation law for online parameter estimation that occurs in the Z-domain will be
introduced and analyzed.

5.1 CONTINUOUS TIME BIO-IMPEDANCE (CTBI) MODELING
The CTBI model is shown in Figure 21 as a first order impedance network with time and
spatial varying properties. The elements are functions of measured stimulation current
66

Istim, skin location of electrode contact δloc, effective skin-electrode contact area Aeff,
and the fingertip pressing force on the electrode Fapp. As seen, Rp and Cp are coupled
to the stimulation current Istim. The network comprises a resistor Rp in parallel with a
capacitor Cp in series with another resistor Rs. The electrical impedance model
reproduces the shape of the output current from high-voltage monophasic square wave
voltage pulses to the skin. The much larger return electrode is attached to thenar area
on the palm to complete the circuit. Istim will be taken as the measurable output to the
interface with VLoad as the measurable input to the system for simplicity. Referring to
(4.1) and (4.7), VLoad is related to the CVD haptic renderer output VCVD as:

67

Figure 21. Continuous time bio-impedance (CTBI) model of the fingertip under electrotactile stimulation.

68

Rp models electrical resistance of the natural protective barrier of the skin, called the
stratum corneum (SC). Large signal analysis done on Rp indicates that it is an
approximate power function of the RMS value of Istim, which will be called ISTIM_RMS.
The characteristic is:
,

for A and B to be identified, which are themselves assumed to be a functions of time,
space, electrode area and pressing force. Therefore, Rp is inversely related to the
stimulation current amplitude. The physical interpretation of the dependency can be
viewed as increased ion flow in to the pores of the stratum corneum due to the higher
voltage potential, which increases conductivity in the SC [29]. Rp has been shown to be
related to the effective skin contact area at an electrode [3]; that is, with all other
variables held fixed:

where rp is the specific resistance of the SC; hence, the fingertip pressing force Fapp
against the electrode can influence the value of Rp since it may alter Aeff. Last, time and
spatial variation δloc of Rp arises from changes in electro-chemistry of the stratum
corneum from the applied signal over time, and the structure and moisture content of
SC tissue at different regions on the skin, respectively.

Cp models the bulk capacitance that is a result of the skin cell membrane structure in
relation with water and ion content in the extra- and intra-cellular regions of the skin.
69

The cellular membranes are built from lipid-bilayers, which are two lipid layers that each
has outward-facing hydrophilic boundaries and mutually inward-facing hydrophobic
molecules when viewed in cross-section. Likely, the cellular membrane causes
polarization of molecules from an applied electric field, since the membrane boundary
will attempt to oppose the flow of ionized material through or into the cellular membrane.
The cellular capacitance is assumed to be a function of the same parameters as Rp. A
relationship between Cp and stimulation current is not as clear when compared to that
of Rp. However, the variation in order of magnitude versus current is about two to six,
maximum, where as for Rp it can be from 10 to 100 orders of magnitude. Based on
experiment, Cp is assumed to have a slower time variation, and be well within a tight
lower and upper bound, depending on skin location, user, and stimulation current
magnitude, as compared to that of Rp.

Rs model the deep tissue resistance in the skin. Rs is usually measured 10 to 100
orders less in magnitude compared to Rp at quasi-static DC frequencies; this is likely a
result from better conduction in this tissue because of the higher water and ion content
compared to the stratum corneum. In contrast to Rp and Cp, Rs is relatively constant
versus skin location, user, and current stimulation amplitude because of increased
isotropy of the environment compared to the stratum corneum. As well, ion conduction
is not influenced by the stimulation levels in this tissue because of the relative
homogeneity [29] [32]. It will be assumed that Rs is dependent on the pressing force
Fapp and electrode skin contact area Aeff.

70

The coupling between Rp and the stimulation current level, as given in (5.1), will
influence the accuracy in output estimation if the relationship is not included in the
modeling and adaptation law. This is especially true for current output generated with
long rise and fall times where the effect will be noticeable. In general, if this second
order effect is neglected in the identification process, then the CTBI model cannot be
used as a model estimator for output current since the estimation error will not even
converge. However, it can be shown through experiment and analysis that sufficient
conditions exist for when the effects due to (5.1) can be lumped in to time variation of
the model so that the output estimation error will still converge. The set of assumptions
that make the model linear in the parameters are (5.1.1):
1) The input signal voltages are square monophasic pulses less than 5
milliseconds in duration.
2) The stratum corneum of the index fingertip to be stimulated is intact without
damage and not overly damp.
3) The current amplitude is in an experimentally determined range, usually from
0.5 mA to 5 mA.
Assuming (5.1.1) is true, the CTBI model now consists of three linear parameters to be
estimated online as a function of time and space, Rp(t, δloc), Cp(t, δloc), and Rs(t, δloc),
that have been shown to reproduce the measured transient and steady state current
response to a high degree. Here, the pressing force Fapp and effective electrode skin
contact area Aeff are lumped in to time variation of the model.

71

In lieu of (5.1.1), the continuous time linear parameters bio-impedance (CT-LPBI) model
in transfer function form is given by:

δ

where

is the model output when the parameters are known.

5.2 DISCRETE TIME CONDUCTANCE (DTC) MODELING
Parameter estimation occurs in the Z-domain for the DTC model. The parameterization
and form of the DTC model is specified for: 1) using this model to calculate the
parameter estimates for the CT-LPBI model (5.3) at each time k; 2) introducing a term
that will give improved minimization of output estimation error for classes of input or
output not specified in (5.1.1). It will be argued that when conditions in (5.1.1) are met,
along with conditions on the sampling rate Ts of the DAQ, the CT-LPBI and DTC models
are equivalent.

The DTC model is given by:
δ

72

where Y(Z, k, δloc) will be referred to as the discrete time small signal conductance (DTSSC) model, and Ψ(Z, k, δloc) the correlated error dynamics (CED) filter; e(k δloc) is the
output error at time k caused by all un-modeled dynamics by the DT-SSC model; the
filtered error term improves output estimation error convergence for when large signalnonlinearity is present due to violation of (5.1.1).

is the model stimulation

current output when the parameters are known; and VLoad(k) is the measured tactor
voltage. The coefficients α1(k, δloc), β2,(k, δloc) β1(k, δloc), c1(k, δloc) are the Z-domain
parameters to be estimated at time k. As in (5.3), the model parameters vary with time
and space δloc, where the variation of the parameters due to pressing force Fapp and
effective skin-electrode contact area Aeff have been lumped into the time variation of the
parameters.

5.2.1 DTC MODEL PARAMETER ESTIMATION AND ADAPTATION ALGORITHM IN
Z-DOMAIN
Figure 22 shows the system-level scheme for real-time parameter identification. The
goal is to use an adaptation law derived from a Lyapunov function V(t, θ) that gives the

ˆ
set of estimated parameter θ for (5.4a) that minimizes the difference between
measured and estimated output, termed the residuals ε, versus time. As illustrated, a
function is used to map the Z-domain estimated parameters to the S-domain estimated
model parameters of (5.3).

73

Figure 22. Overview of parameter identification.

74

5.2.2 ITERATIVE EXTENDED LEAST SQUARES WITH FORGETTING FACTOR
ADJUSTMENT (ELSFF) MODEL ALGORITHM
Let:

which is the set of parameter estimates for (5.4a) at a fixed tactor-skin location C1 at
time k; and let:

be the regressor vector with entries that hold the time-delayed estimated current output,
delayed and most recent measured voltage input, and the error input term from (5.4a) at
time k. The error input, which is not measurable, can be approximated by the a
posteriori residual εp(t), which is the measurable most up-to-date output error
estimation:

where Istim(k) is the measured stimulation current output at time k. Then, the finalized
regressor vector becomes:

The estimation model for (5.4a) to follow is in the form of a difference equation so that
the adjustment model for it can be implemented online. Utilizing (5.5) and (5.8), the
estimation linear parametric model (LPM) estimation is:

75

The iterative ELSFF adjustment model to update the parameters online in (5.5), under
the constraint that the output estimation error should converge over time, is derived by
minimizing the function:

where N is the final time and the output estimation error at the kth step is given by the a
priori residual:

Here, λ is the forgetting factor that weights the recent residuals exponentially more
significantly than older ones. Including the forgetting factor is necessary in the
adaptation law because of the assumed time variation of the model parameters in
(5.4a), which will help make the parameter estimates more responsive to reflect the
electro-biological changes in the skin. The minimization problem is to drive the a priori
residual εa(k) to zero over time. In this respect, the model output Îstim should approach
physical plant output Istim. The ELSFF adaptive law was chosen because its good ability
to filter measurement noise injected from the sensors since it accounts for previous
sampled data as well as current.

Figure 23 illustrates the inputs to the adjustment model to estimate the parameters for
(5.9). Software gains K1 and K2 rescale the measured and sampled voltage and current
from the skin-electrode tactor back to their original magnitudes once acquired and
stored by the DAQ. The bio-impedance parameters estimates corresponding to (5.3)

76

are extracted per iteration by a one-to-one and onto function in the frequency domain
that will be disused in the next section.

Figure 23. Top level block diagram of parameter estimation using iterative ELS
algorithm in Z-Domain.

The iterative ELSFF algorithm has the following initial conditions:

The P covariance matrix of the iterative ELSFF algorithm is selected to be a large
magnitude, positive definite matrix as required. The adjustment model to identify the
parameters every iterative cycle is calculated by the following algorithm:
For k = 1,…,n,
where n is an index for an even subset of the circular input buffer queue of length
M for storing samples of VCVD_IN(VLoad(k)) and VCVD_IN(Istim(k)),
77

1.

magnitude rescale the measured and sampled load current and voltage to

the nearest quantization level:

2.
λ

3.

4.

υ

5.
6.
7.
8.

Extract bio-impedance parameters from Z-model parameters.

The algorithm is repeated by indexing the start of the next data subset in the
circular input buffer queue, and so on, until the identification is stopped at time N.
Normally, P(k) would have to be reset to P(1) in (5.12) if the minimum eigenvalue of
P(k) becomes too small which implies adaptation slows by observing step 5. However,
to save computation time, and the fact that almost always the forgetting factor is set to

78

be less than one, this can be neglected. Clearly, with λ < 1, the P(k) in step 3 grows
exponentially fast when the CVD does not produce a pulse. This in effect allows P(k) to
be reset autonomously. Also, since ϕ is always persistently exciting and bounded, P(k)
will not become unbounded.

K(k) in (5.17) is the adaptive gain matrix weight on the a priori error output estimation in
(5.18). Ideally, the adaptive gain matrix should tend to zero as the error output
estimation converges so that parameter estimates remain set. However, when ϕ is
“turned off”, P(k) grows exponentially so that K(k) will be nonzero when ϕ “turns on”
again, which injects noise in to the output and parameter estimation process. The
tradeoff is that the smaller the forgetting factor value used, the more time responsive the
ELSFF algorithm is to correcting for estimation error due to time varying plant. In
contrast, if the forgetting factor is too small, the parameter estimation signal will be noisy
due to gain sensitivity on the estimates. It is up to the operator to decide on an optimal λ
for the application.

The resetting moving mean square error derived from (5.10) is used as the goodnessof-fit criterion on the output estimation error over some time period given by:

which resets for every time interval of length L. This gives the average power in the
error output estimation over during the interval.

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Assume the parameters and error input in 5.4b are known and C1 is a fixed skin-tactor
interface location, the change in the estimated output current to that of the parameters
or input as a function of time is related by:

Assume that initially that the model (5.4a) estimates the measured current exactly and
that the input is fixed. Suppose the plant becomes time varying; the first and second
term, illustrate that the magnitudes of the resulting output estimation error around time k
will depend on how quickly the adaptation law updates the respective model parameters
to account for the plant time variation. As well, the last term output and its influence on
the estimation error will be coupled to the time variation. Assume again that for the last
two terms there is perfect output estimation and that now the plant is not time varying,
then the third term relates the change in the output estimate to a change in the voltage
input. In the absence of all other influences such as modeling error and noise, the
change in output estimation from this model equals the change in measured current.
The last term and its input account for the change in output estimation from the change
in estimated output related to all model uncertainty. It acts as a correcting factor when
the model fails to account for plant dynamics. In general, the magnitude of this term
becomes large if (5.1.1) is not guaranteed or for sudden and unexpected time variation
of the plant.

As is implied by the assumption in (5.1.1), the nonlinear properties of the unknown
physical plant become increasingly apparent as the stimulation current amplitude or

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transition times of the CVD pulse increases. This later condition makes apparent the
non-Ohmic DC resistance dependency on output current given (5.2) during the
transitions of the pulse. The most important factor is that the pulse transition times are
fast and that the stimulation current pulse amplitudes change slowly from pulse-topulse, then the adaptation law can construct an estimation model that gives good output
estimation without the need of the last term in (5.4b); appropriately set forgetting factor
aids in the responsiveness to steady state changes in the pulse. The empirical results of
these phenomena will be shown in the experimental section 6 of this paper.

The forgetting factor can be related to a designing time constant that helps with
selecting the forgetting factor for the adjustment model to keep parameter estimation
responsive to a time varying plant, assuming that the time constant for plant time
variation is known. Let N represent the approximate current and past discrete time
memory that are significantly weighted by the ELSFF in the adaptation law.

The

relationship to the forgetting factor is [33]:

If N is neither too large nor small, then a time constant in the continuous time domain
can be defined, which is used for approximating the lag time in the adaptation law it
takes to respond to a continual time variation of the plant. The time constant is:

Ts is the A/D sampling rate. N is the value from (5.23) selected by the operator based
on experiment that is a tradeoff between tracking sensitivity and stability in the output
and parameter estimation. If by assumption, the electro-biological plant of the skin has a
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minimum time variation constant of τθ, then the time constant in (5.24) should be
designed so that:

That is the time lag in the adjustment model should be less than that of the significant
variation in time of the plant so that the output estimation can track the actual output.
Experimentally determining this condition helps with optimally tuning the adaptation law.
Experiments that determined the acceptable choices of λ from N to obtain the lower
bound for τθ in (5.25) were carried out in the experimental section 6 of this paper.

5.3 PARAMETER ESTIMATION FOR THE CONTINUOUS TIME LINEAR
PARAMETERS BIO-IMPEDANCE (CT-LPBI) MODEL
To iteratively estimate the bio-impedance parameters associated with the CT-LPBI
model in (5.3) from the Z-domain model (5.4a), assume that the inequality from (5.25)
holds, and that:

which means that ELSFF algorithm should have a much greater updating time constant
than the DAQ sampling rate time so that the adaptation law estimation is not prone to
noise.

The estimated bio-impedance parameters should model the underlying dynamics, which
under ideal circumstances implies:

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for all k in (5.22), where K1 is arbitrary time when the estimated parameters converge to
the true parameters in (5.3) and (5.4a), respectively. As well, when (5.25-5.27) hold, the
following terms in (5.22) become negligible with influencing output estimation:

Based on experiment, (5.27) it is not guaranteed at high stimulation current levels from
CVD pulses with slow rise and fall time transition. This is because the current signal
must transition through its non-ohmic I-V characteristic, as seen by the relationship
(5.2), which becomes more apparent as amplitude increases. The CVD square wave
pulse on the other hand has fast rise and fall time compared to its steady state time
duration versus the transition times of the other types of pulses explored, such as
triangle- and saw tooth-shaped.; hence, (5.27) is almost always valid when estimating
the CVD square wave load current when using the CT-LPBI model, which validates the
set of assumptions presented in (5.1.1). However the stringency of the conditions for
(5.1.1) can be relaxed depending on the specific application.

Given that (5.25-5.27) hold over some time interval including time k, (5.22) reduces to
the small-signal model term:

The bio-impedance parameters can be found from the estimated parameters of (5.29) to
get the physical impedance model:

so that the following filters are equivalent:
83

To produce the filter equivalence, the Tustin transform is used on the current estimate
of the model in (5.4a):

By assuring that the DAQ A/D sampling rate Ts of the system is:

model uncertainty that would occur from frequency aliasing due to under-sampling the
output is eliminated since the pole location of the CT-LPBI model is always closer to the
imaginary axis. Here,

and the „starred‟ parameters is the „true‟ zero location and

parameter set in (5.30a), and ωA and ωD are the radian analog and digital frequencies
corresponding to the filters in (5.31b), respectively. Further, since the mapping (5.32) is
one-to-one and onto, the frequency response is the same in both domains. The
mapping functions from Z-domain parameter estimates to the S-domain are:

So that the pole and zero locations of (5.30a) are, respectively:

84

where for all estimates:

85

6. EXPERIMENTAL SETUP AND TESTING

There were two main classes of experiments that were undertaken with the haptic
renderer and real-time identification of load parameters: proof-of-concept and human
experimentation. Proof-of-concept experiments will be presented first to obtain a
benchmark for the modeling, adaptation law and haptic rendering system when using
known LTI circuit models attached to the output. In subsequent sections, the
experimental setup, undertaking, and analysis involving human testing with the haptic
rendering system, in regard to bio-impedance identification, plant modeling and
psychophysical experiments, will be presented

6.1 HARDWARE AND ADAPTATION ALGORITHM TESTING
What follows are proof-of-concept experiments to establish the workings of the
hardware and identification algorithm to identify load impedances connected to the
haptic driver with a model structure corresponding to (5.3). The method is to identify
known parameters in RC networks and compare empirically these sets of values and
model output estimations to the actual values and measured current responses,
respectively. The purpose is to obtain evidence for convergence of parameter
identification and output estimation under known loads assuming the ideal human bioimpedance model in (5.3).

6.1.1 EXPERMINETAL SETUP

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Table 1 shows impedance parameter estimation sets from 10 subjects versus index
fingertip condition that were fitted to the CT-LPBI model given in (5.3). The impedance
values were obtained by using the offline bio-impedance identification setup and
method, which is described in previous work of [34]. RC impedance networks with
circuit component values used from Table 1 were built on a breadboard and re-identified
using the online method described in section 5.2.1; the built loads to be driven by the
haptic renderer are shown in Table 2. The element values for each network were
measured with an LCR meter to assure accuracy of the standards. The set of values
seen in Table 2 were chosen because they represent a range of typical human loading
conditions that the revised haptic renderer should encounter. In Table 1, the index
fingertips of the subjects were dry or moistened with tap water to simulate sweat. The
parameter sets in Table 1 selected to build the RC networks were: #5 Damp, #7 Damp,
#1 Dry, and #9 Dry. The two damp fingertip circuit models were chosen because the
corresponding circuit impedances will load the haptic driver and measurement circuitry
the greatest. Any Rp values in Table 1 that are below 100 KΩ were not used for testing
due to safeguarding the hardware at this time. The measured impedance sets in Table
2 differ slightly from the corresponding values in Table 1 due to resistor or capacitor
tolerances. All online identification experiments consisted of applying voltage pulses to
the loads at a fundamental frequency of 60 Hz and 11 percent duty cycle. Online
identification experiments were carried out with using the pulse types shown in Figure
17, the square, triangle and saw tooth waveform shapes, and also varying the CVD
voltage amplitude pulse for each load under investigation.

87

Table 1. Bio-impedance parameters for 10 individuals using offline identification [34]:
dry and damp Index fingertip case.

88

Table 2. Known RC circuit elements of impedance networks built on breadboard with
known analog pole and zero frequency locations used in online identification testing:
built using table 1 parameter sets.
subject number Finger Model

Rp (Ω)

Cp (F)

Rs (Ω)

Fp (kHz) Fz (kHz)

#5

Damp

1.25E+05 2.16E-10 1.59E+04

5.895

52.23

#7

Damp

1.65E+05 1.60E-10 1.98E+04

6.028

56.27

#1

Dry

1.94E+05 1.70E-10 1.90E+04

4.825

54.10

#9

Dry

2.72E+05 1.40E-10 2.22E+04

4.179

54.79

6.1.2 EXPERMINETAL RESULTS AND ANALYSIS
The following experimental results were calculated from N=60 trials of one second
recordings of load impedance identification, which were the four loads, each driven
under the three CVD waveform pulses, with voltage amplitude that ranged from 100 to
140 volts using 10 volt increments. The rows of Table 3 show the average of an
identified parameter in an impedance network for each known corresponding entry in
Table 2, independent of amplitude and waveform type.

89

Table 3. Resulting online estimation of circuit element parameters and analog pole and
zero frequency locations for the corresponding known parameters of the plants in table
2.
Mean Parameter Values
Sample
Rp (kΩ) Cp (pF) Rs (kΩ) Fp (kHz) Fz (kHz)
#5-DAMP 124.47 245.45

16.85

5.21

44.55

#7-DAMP 163.15 192.98

20.52

5.06

45.73

#1-DRY

192.21 195.97

18.80

4.23

47.98

#9-DRY

264.95 169.28

22.27

3.55

46.26

Table 4 summarizes the average absolute errors between the plant parameters and
their corresponding estimated values for fixed haptic driver condition or driven
impedance load. The entry in first column of the table indicates the condition that was
held constant to calculate the corresponding row statistics. Error was not seen to be a
function of pulse amplitude levels due to the high SNR and not held constant for this
reason when calculating the descriptive statistics. There were no significant differences
found in the mean absolute error statistics by looking down each of the columns in
Table 4; thus for typical loading conditions on the haptic renderer, parameter
identification accuracy is not influenced by amplitude, waveform pulse shape, or
impedance load. As well the repeatability is sufficiently bounded when viewing the
columns on reported standard deviation in identification for each parameter and
condition.

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Table 4. Absolute error and standard deviation between plant and estimated
parameters: first column shows which variable held constant for calculating the
associated row statistics.
Variable Held
Constant

Mean Absolute % Error
Rp

Cp

Rs

Fp

Absolute % Error S.D.
Fz

Rp

Cp

Rs

Fp

Fz

None

1.62% 13.08% 9.89% 12.65% 13.05% 1.04% 7.47% 7.13% 2.76% 9.16%

#5-DAMP

1.59% 13.64% 12.22% 11.54% 15.71% 0.96% 4.00% 9.00% 1.83% 11.04%

#7-DAMP

1.35% 2.48% 9.23% 11.67% 8.66% 0.99% 1.75% 6.68% 2.32% 5.89%

#1-DRY

0.96% 15.27% 9.66% 12.31% 11.33% 0.65% 4.46% 6.28% 3.55% 8.74%

#9-DRY

2.59% 20.91% 8.46% 15.07% 16.49% 0.84% 2.11% 6.38% 1.45% 8.76%

square

1.88% 12.21% 10.17% 11.55% 16.08% 0.97% 7.36% 7.89% 2.73% 9.46%

saw

1.45% 15.65% 9.35% 13.81% 12.47% 1.06% 7.87% 8.01% 3.14% 9.48%

triangle

1.55% 11.36% 10.15% 12.59% 10.59% 1.10% 6.79% 5.57% 1.94% 8.05%

The absolute errors tended to be small for the identified Rp and larger for Cp and Rs.
The actual Cp and Rs on the breadboard largely determine the high frequency zero
location in the S domain, since Rp >> Rs in reference to (5.30a). Consequently, the
Nyquist sampling rate of the DAQ (50 KHz) is close to the zero frequencies in Table 2.
The increased absolute errors in the identification of Cp and Rs are likely associated
with frequency aliasing due to under-sampling the load current and voltage
measurements and not bandwidth limitations of the measurement circuitry itself; the
measurement circuitry was designed to exceed the bandwidth of the CVD driver.
Conversely, the estimated Rp has relatively small absolute error because its value is
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mostly determined at DC frequency, dominates the much lower frequency pole location,
and is not strongly coupled to the zero frequency location. The equations used to
calculate the estimated parameters are given in (5.34a – 5.34c). Overall, the methods
presented in chapter 5 for parameter identification for the CT-LPBI model given in (5.3)
give good estimation of plant parameters when the plant is a known LTI impedance
load. Parameter convergence for Cp and Rs could be improved by using DAQ cards
with higher sampling rates.

The ability of any one of the models presented in section 5 to estimate the output load
current is another important assessment of the online ELS-FF adaptive law and
modeling used for output estimation. In general, each model will give different accuracy
of output estimation depending on the extent for which nonlinearity present in the
human skin is excited under load. In the case of LTI plants used here for testing, that
have CT-LPBI model structure, (5.3) should give equivalent estimates to that of the full
DTC model structure in (5.4a). Hence, the impedance loads in Table 2 were driven by
the haptic renderer to assess the output estimation accuracies for the measured outputs
from each known impedance plant.

Figure 24 shows the plot of the estimated output current produced from the DTC model
in (5.4a) along with measured plant current versus time for one triangle wave pulse. The
model output has been decomposed in to the outputs from the DT-SSC and CED filter
components, as explained in section 5.2, to show that, with a known LTI plant, the DTSSC model is a highly accurate estimator. Here, the output from the CED filter is

92

negligible. The decomposed model outputs in the graph are called Imodel and IunModeled,
respectively, and the measured current is called Imeas. The attached load was #5-Damp
with 140 volt CVD amplitude pulses applied. The figure also gives the RMS values of
measured current and output estimation current from the DT-SSC model that was
averaged over the entire one second of recorded data. Their values are:
ImeasRMS = 0.18991 mA and ImodelRMS = 0.18978 mA, respectively.

(6.1)

Also seen, the RMS value of the CED filter output, whose output corrects for unmodeled dynamics, is negligible in the micro-amperes since the load is highly linear:
IunModeledRMS = 2.37 μA.

(6.2)

Figure 24 also demonstrated that the DT-SSC model accounts for the transient
response of the measured current pulse to a good degree. These results were typical
for all LTI loads in Table 2, relevant haptic renderer settings and waveform pulse types.

93

Figure 24. Measured and decomposition of estimated output current from terms in (5.4a) plotted by driving load #5-Damp
in table 2: output for one triangle wave CVD pulse shown at 60 Hz, 11% duty cycle at Vpp = 140 volts, λ = 1.
94

Figure 25 was created by using recorded data from 600, 100 volt square wave pulses
acquired in 10 seconds by driving the #1-Dry load impedance plant in Table 2. The
graph shows the estimated and measured steady state current taken at each current
pulse midpoint, which represents 600 trials of steady state output estimation. The
known process parameters are clearly time invariant as is evidenced by the nonfluctuating measured output current. Also shown, are the expected values of the
measured and estimated current using model (5.4a) averaged over the 10 second
recording. The values are almost identical at:
E(ImeasSS) = 0.47638 mA, and E(IcalcSS) = 0.47657 mA, respectively.

(6.3)

This result provides evidence that the estimations from (5.4a) are unbiased in the mean
if the load is linear. Figure 25 also illustrates that the typical repeatability in the DTC
adaptive model for estimating the 600 measured current pulses at steady state over
time is high, since the standard deviation is in line with that of the measured steady
state value:
sn(ImeasSS) = 2.2988 μA, and sn(IcalcSS) = 2.0386 μA.

(6.4)

Thus, Figure 24 and Figure 25 taken together provide evidence that the models used for
estimating the measured current are consistent in the mean when LTI loads are used.
Experiments using the other test impedance loads in Table 2 gave similar results.
Hence, the ELS-FF real-time adaptation law applied to the model structures in section 5
with associated driven LTI plants gives good output estimation of the measured current.

95

Figure 25. 10 second estimation of measured state current at pulse midpoints using model (5.4a). Results produced from
square wave pulses driven under load #1-Dry in table 2. The mth step is the mth duty cycle pulse midpoint: output is at 60
Hz, 11 percent duty cycle at Vpp = 100 volts, λ = 1.

96

Another desirable quality of the adaptive algorithm is to update the model in a way that
produces exponential convergence in output estimation. The output estimation error
convergence time was assessed using (5.21) for the driven LTI plants in Table 2 for one
recording of data. Figure 26 shows the results obtained for #5-Damp impedance load.
The algorithm converges in about 100 milliseconds and shows exponential
convergence. This is the nominal convergence time for the other impedance loads in
Table 2.

97

Figure 26. Typical output estimation error convergence characteristic versus time calculated from (5.21) when driving LTI
loads in table 2: assessed for #5-Damp impedance load.
98

6.2 EXPERIMENTATION
Tactile stimulation was administered to human subjects to test the capabilities and
quantify the power output of the haptic renderer, as well as to test the identification
algorithm using a sample population. By using a sample population, the haptic renderer
was subjected to robust loading conditions because of the wide differences in electronic
skin impedance between subjects. This was one of the motivating factors behind human
testing.

Another reason for using a sample of humans for testing was so to gain initial insight on
and study the comfortable stimulation ranges with the haptic renderer versus waveform
pulse type and stimulation level, which can differ between electronic tactile display
devices. Doing such an experiment can help aid in future calibration of the device by
knowing the statistical bounds in stimulation ranges. The comfortable range is defined
as the sensation and pain threshold and is a subjective measurement based on the
user‟s verbal response to a known stimulation level. In terms of incrementing the
voltage pulse amplitude for a fixed waveform pulse shape, the sensation threshold is
defined as when a user first notices a stimulus at an amplitude level and the pain
threshold is when the user feels that the sensation at the current level is just barely
tolerable. Besides the thresholds varying between individuals, it changes based on how
well the user is trained on the device so that the user should have some initial training
before these bounds are recorded.

99

The study can also be used to gain insight in to the ways of reducing power
consumption of the haptic driver by statistically analyzing how driver power output is
related to the average population dynamic range or threshold limits versus waveform
pulse shape. Dynamic range is the defined as the ratio of the pain over the sensation
threshold. Due to time constraints, psychophysical assessment could not be carried out
for just noncable detection and pulse width duration, which would also be important for
calibration. Thus, human experimentation can be subcategorized as either collection of
objective measurements or psychophysical assessment. Both of these experiments
were carried out concurrently for every participant to compose possible statistical
relationships. As well, the results of real-time identification on the models introduced in
section 5 are explored both statistically and in the time domain when applied to the
human population under study.

6.2.1 EXPERIMENTAL SETUP
In the following sections, it is assumed that the skin region to be stimulated with the
tactile display is on the surface of the index fingertip. The sample size for human
experimentation is N = 21. The sample group consisted of individuals 19 to 33 years of
age with approximately two-thirds of participants male. The finger condition was kept
free of sweat or moisture and otherwise not altered any other way for the entire
experiment. The required voltages to stimulate the underlying tactile receptor axons for
these conditions, and with the given electrode diameter of roughly one millimeter, are
typically between 100 to 300 volts [3] [4]. A visual inspection of the fingertip also took
place to assure no abrasions, scratches or open wounds; these defects may cause

100

painful stimulation to occur at low voltages due to compromised stratum corneum. A
damaged stratum Corneum can decrease resistance an order of magnitude.

The user was first trained how to use the tactile display including: showing the subject
how to properly place the index fingertip on the electro-tactile display, hooking up the
return electrode, and letting the user experience the tactile sensation beforehand.
Figure 27 shows the typical arm, hand, and index fingertip placement for the display.
Figure 28 shows the area on the palm to affix the return electrode for best skin contact
and minimal skin resistance due to the large planar area and lack of hair follicles. The
tactile display is designed so that the index finger can rest comfortably in the same
position over multiple trials of an experiment.

101

Figure 27. View of user forearm resting comfortably on gel pad while index fingertip is
placed firmly on tactile display for stimulation and measurement.

102

Figure 28. View of anodic return electrode proper placement secured with a Velcro strap
on thenar eminence.
Before testing commenced, each individual was given the experience of electronic
stimulation on the device for a short period by using the three voltage pulse shapes
(square, saw and triangle waveforms). The voltage amplitude was varied for each
waveform pulse type so that the user could become accustomed to the sensation. This
served two purposes: 1) it helped to determine if the subject‟s fingertip would
spontaneously sweat after application of high voltage; 2) it gave the user a priori
knowledge about the range of sensations that would be experienced from electronic
tactile stimulation. In the first case, the user was rejected as a participant. The training
helped to reduce the novelty of sensations and psychological apprehension to high
voltages brought about by electronic stimulation. This gave each person a similar point
of reference for the questions that were asked for the psychophysical portion of the
103

actual experiment. It also helped reduce the chance of the subject becoming startled,
which would undoubtedly influence the results due to variation of pressure on the skinelectrode interface. This was sometime noticed in earlier offline experiments.

A weight scale was placed underneath the tactile display to indicate the amount of
pressing force applied from the user‟s fingertip to the tactile display. A participant was
asked to keep the pressure between 8 and 16 oz for consistency between
measurements and the sample population as a whole. The subject was also asked to
keep the fingertip still during all trials in an experiment as bio-impedance can change
over potentially small distances on the skin.

Over time, cellular residue deposits on the electrodes were observed that influenced the
measurements by increasing the effective resistance between the fingertip and
electrode interface. Therefore, the electrodes were cleaned with isopropyl between
each experiment (three experiments per individual). As well, since the return electrode
is made of copper, it was cleaned after a session with a subject was completed using
vinegar to remove oxidation.

An experiment consisted of applying one of three CVD voltage waveform pulses in the
following order: saw tooth, triangle, and square wave, for a total of three experiments.
Each experiment consisted of multiple trials. A trial involved administering the voltage
pulses at given amplitude, recording the results, and noting the feeling reported by the
user. Voltage pulses started at 30 volts. The bio-impedance parameters and waveforms

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were recorded for one second once steady state was reached before the next voltage
increment. In this case, steady state meant that the observed identified impedance
parameters did not change significantly. A small recording time was used to decouple
possible influence of time variation at the active skin-tactor interface in the recordings.
The amplitude was then incremented or the experiment concluded based on whether
the pain threshold of sensation for the user was reached. The recorded parameters
include continuous and discrete time, Z- and S-domain estimated model parameters for
the models in (5.3) and (5.4a), and the current and voltage measurement samples
versus time.

For a trial, when the user first noticed a sensation, this value was noted as the
sensation threshold. When the trial reached the subjective pain threshold experiment
was stopped and level noted. The user was then asked to report what made the
stimulation level uncomfortable for him or her for later analysis. After an experiment was
completed, the subject was given a few minutes of rest period. This helped to reset any
short-term conditioning from sensory adaptation that might bias the results. After this
rest period, the next waveform in the set was applied and the process repeated; it was
not necessary that the fingertip be in the exact location between experiments as this
would be difficult to accomplish. Each experiment had the duty cycle set at 11 percent
with fundamental frequency of 60 Hz, regardless of waveform type. Only changes in
amplitude or selection of waveform pulse shape were studied.

6.2.2 EXPERIMENTAL RESULTS USING STATISTICAL ANALYSIS

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The first study involved determining how the three different waveform shapes influenced
the dynamic range for the sample population statistically. The stimulation dynamic
range is of interest and is a function of the RMS stimulation current. The second study
exams the predicted power based on the estimation models presented in section 5 that
is delivered from driver to the interfaced tactor versus waveform pulse shape. The
actual power transferred to the fingertip load predicted by a particular estimation model
will be assessed based on the waveform pulse shape and threshold levels. Finally, the
third experiment evaluates how the small signal bio-impedance model parameters vary
as a function of the output current. This should help aid in developing the model used in
the design of and adaptive control system for the implemented CVD method.

6.2.3 ELECTRO-TACTILE DYNAMIC RANGE STUDY
Figure 29 shows the mean stimulation dynamic range ratio in decibels for the sample
population as a function of waveform type. The graph is a result of subjective reporting
by the subject of his or her sensation thresholds relative to the physical measurement of
current stimulation amplitude and waveform type at time of recording; though the
reporting is subjective, the sensations experienced at pain threshold among subjects
share some commonality, as will be discussed. The samples of dynamic range ratios for
the population from each waveform type appeared normally distributed when analyzed,
which is supported by Q-Q plot analysis (R2 > 0.90 lowest) and rejection of significant
skewness and kurtosis at the 5% significance level for data collected for each waveform
type. The mean of the dynamic range ratio in stimulation current for applied square
wave pulses is significantly lower than the mean of the saw tooth (t(20) = 3.46, p < 0.05

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two-tailed) and triangle wave (t(20) = 3.49, p < 0.05 two-tailed) dynamic range ratios for
the population.

Figure 29. Mean dynamic range ratio for RMS stimulation current for each type of CVD
output waveform pulse (N=21). The 95% confidence interval is included. The sample
mean and standard deviation for the square saw tooth, and triangle wave are: M = 4.78,
SD = 1.86; M = 7.21, SD = 2.69; M = 7.29, SD = 2.74, respectively.

Figure 30 shows the average of the RMS currents measured at the reported sensation
and pain thresholds levels resulting from the applied pulse type to the sample
population. The measured current levels of the thresholds all appeared normally
distributed supported by Q-Q plot analysis (R2 > 0.93 lowest) and rejection of significant
skewness and kurtosis at the 5% significance level for each empirical distribution. The

107

mean of the measured currents at sensation thresholds for the square wave is level
shifted significantly higher compared to the respective means of the saw tooth (t(20) =
6.10, p < 0.05 two-tailed) and triangle wave (t(20) = 6.79, p < 0.05 two-tailed)
counterparts. This is also the case for the applied square wave pulses when compared
to the means of the RMS current levels at pain threshold for applied saw tooth (t(20) =
3.40, p < 0.05 two-tailed) and triangle wave pulses(t(20) = 2.82, p < 0.05 two-tailed).
The means of the current stimulation levels from applied saw tooth and triangle pulses
to individuals showed no difference at the 5% significance level for the respective
threshold level reports by the individuals.

Figure 30 indicates that subjects are more sensitive to stimulation currents that are
produced from saw tooth and triangle wave CVD pulses versus the square wave; this is
indicated by observing the shifting in the levels of both the threshold means when
comparing each applied waveform pulse type. However, the subjects appeared more
sensitive to the gradations in the stimulation current levels for produced by applying
square wave pulses, which is supported by the calculated dynamic range ratios for each
waveform type in Figure 29.

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Figure 30. Average sensation and pain thresholds for stimulation currents versus wave
form (N=21). The 95% confidence interval is shown for the mean.

Figure 31 and Figure 32 display the variance in the data for the tabulated results
corresponding to the means displayed in Figure 29 and Figure 30, respectively, in the
form of box and whiskers plots. Figure 31 shows the box and whiskers plot for the
variation in calculated dynamic range ratios corresponding to the means in Figure 29.
When the minima and maxima data under saw tooth and triangle waveforms pulses are
considered outliers, the percentiles in the box and whiskers indicate approximately
equal variance in the dynamic range ratio in all three waveform types under study for
the population. Figure 32 shows the box and whiskers plot for the variation in measured
stimulation current threshold levels in the sample population corresponding to the
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means in Figure 30. As can be seen, the sensation and pain thresholds for the same
waveform type show no overlap at their upper and lower quartile boundaries,
respectively, which indicates that there is a statistical commonality in reporting these
levels for a given applied waveform pulse type for the population as a whole. When the
graph is viewed across applied waveform pulse type, there is negligible to no overlap in
terms of the variances in the measured sensation and pain thresholds, which now
represents a commonality in reporting of these sensations for all applied waveform
types. The pain threshold for the applied square wave has significantly greater variance
compared to all other sensation and pain thresholds whose respective percentile
variances are about the same. This may be related to subjects being more sensitive the
change in stimulation current levels for the square wave pulse type leading to greater
variation in reporting, as was discussed in relation to Figure 29.

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Figure 31. Five statistic box and whiskers plot for mean dynamic range ratios for RMS
stimulation current versus waveform shape (N = 21).

111

Figure 32. Five statistic box and whiskers plot for mean sensation and pain thresholds
concerning RMS stimulation current versus waveform shape (N = 21).
Figure 33 displays the means of the applied lower and upper CVD voltage pulse
amplitudes to the subjects corresponding to the measured lower and upper stimulation
current thresholds, respectively, for each waveform type. These results did not fit well
with a normal distribution. However, from the graphs it can be inferred that lower and
upper CVD voltage pulse amplitudes for saw tooth and triangle wave pulses must be
higher to achieve the respective stimulation thresholds than the square wave CVD
pulses on average. Also, the square wave voltage pulse amplitude dynamic range is
seen to be much narrower than that of the other waveforms.

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Figure 33. Mean CVD Voltage Amplitudes for corresponding RMS current thresholds
versus CVD pulse type (N = 21).
Once the pain threshold for the individual was reached, the experiment was stopped.
The subject was then asked to describe what made the experienced stimulation current
level uncomfortable for the given waveform pulse type applied in his or her own words;
no pre-defined set of keywords were provided. The summary of the keywords are
shown in Table 5 along with the reported keyword frequency. The groupings were
created by the researcher based on commonalities. By far, the most reported
unpleasant sensation was needle poking, followed by intense vibration and stinging. In
many instances, these tactile experiences transitioned or occurred concurrently. For
instance, for some, a pleasant vibration transitioned to an intense vibration with a
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concentrated needle poking sensation that became noticeable as stimulation levels
increased. For this reason, the groupings are not mutually exclusive.

The importance of Table 6 will be to help determine if the experiences of maximum
tolerable sensation have a common theme for future analysis even though the
descriptions are subjective. In this respect, a list of precise keywords can be formed. A
list of the well-defined sensation keywords can be shown to the user once his or her
upper threshold sensation level is reached. In this respect, an individual who trained in
calibration of the haptic renderer can help the user determine his or her maximum
tolerable sensation levels based on objective keywords. As well, it gives the user an
initial appraisal of what to expect at the typical level of upper sensation threshold.

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Table 5. Pain threshold sensation description reported from subjects and frequency of
occurrence for the three CVD waveform types.

Sensation
needle poking

intense vibration

stinging

numbness
buzzing
muscle tension or
twitching or
shaking
burning
pinching
unpleasant slight
electrical shock
itching
cut in flesh
Friction

Description Keywords for Pain Threshold
Saw Tooth Wave
Triangle Wave
Square Wave
#1(M), #2(F),
#3(M), #4(F),
#5(M), #9(M),
#11(M), #18(M),
#21(F)
#1(M), #5(M),
#7(M), #10(M),
#14(M)
#6(M), #12(M),
#1(M)

tot
al
#1(M), #4(F), #5(M), #1(M), #4(F), #5(M), 23
#6(M),#9(M), #11(M) #6(M), #8(M), #9(M),
#11(M), #18(M)

#1(M), #3(M), #5(M),
#7(M), #14(M),
#16(M)
#12(M), #15(M)

#1(M), #11(M),
#14(M), #16(M)

15

#12(M), #20(F)

7

N/A
#13(F), #19 (M)
#11(M), #18(M)

#2(F), #13(F), #14(M)
N/A
#19(M)

#2(F), #14(M)
#13(F), #19(M)
#15(M)

5
4
4

#8(M)
#20 (F)
#17(M)

#8(M)
#21(F)
#17(M)

#8(M)
#21(F)
#17(M)

3
3
3

N/A
N/A
N/A

N/A
#18(M)
#20(F)

#3(M)
N/A
N/A

1
1
1

6.2.4 CVD POWER OUTPUT STUDY
Figure 34 gives a bar chart of the mean and standard error in apparent power delivered
from the driver, which is shown tabulated at reported sensation and pain thresholds, as
a function CVD waveform pulse type. For each applied waveform pulse type, the
apparent power data was calculated using the measured values at the reported
sensation and pain thresholds for the individual (N = 21) under study, respectively, and
averaged accordingly. The apparent power is the product of the RMS recorded current
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and voltage for a delivered waveform pulse type. The amount of power delivered from
the CVD is comparable to the power outputted by a typical red LED laser pointer. It is
easily seen, that no matter which waveform pulse type is delivered to the fingertipelectrode interface, the means in apparent power are about equal when calculated at
the respective subjectively-reported threshold level for the population. A two sample KS
test was done to statistically test the hypothesis that the apparent powers calculated at
a particular threshold came from the same empirical CDF to justify the above
observation. In neither case, could the hypotheses be rejected at the 5 % significance
level; see Table 6 for the test results. This is in contrast to the statistical results of
physical measurements (such as current and voltage magnitude) at subjectivelyreported threshold levels in previous sections, which were a function of delivered
waveform pulse type for the sample population. However, the mean apparent power at
the sensation and pain threshold levels remains constant in the mean irrespective of
wave form pulse shape. This suggests that the power delivered to the fingertip is more
of a reliable predictor of the reported threshold levels than stimulation current levels no
matter the shape of the delivered waveform pulse type for the ones used in this study.

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Figure 34. Apparent power bar chart shown at mean sensation and pain stimulation
current thresholds for each individual (N = 21) and each CVD waveform type: standard
error bars are shown.

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Table 6. Two sample KS test for similarity between ECDFs of apparent power
distributions for CVD waveform type (5% Significance): samples of apparent power for
each waveform type are calculated at sensation and pain threshold for each subject
(N=21).

df

sample comparison

SW. vs. STW S. Threshold Apparent
Power
SW. vs. TW S. Threshold Apparent Power
STW. vs. TW S. Threshold Apparent Power
SW. vs. STW P. Threshold Apparent
Power
SW. vs. TW P. Threshold Apparent Power
STW. vs. TW P. Threshold Apparent Power

p

KS

H0: The two
independent
samples come
from same
ECDFs

20

0.1545

0.333

not rejected

20
20

0.1545
0.9728

0.333
0.143

not rejected
not rejected

20

0.9728

0.143

not rejected

20
20

0.9728
0.9728

0.143
0.143

not rejected
not rejected

6.2.5 STATISTICAL STUDY BETWEEN ESTIMATION MODELS AND PLANT OUTPUT
ESTIMATION ERROR
This section concerns presenting statistical results for how well the estimations models
presented in section 5 estimates the measurable dynamics of the underlying human
electrical bio-impedance plant. The discrete time conductance (DTC) estimation model
in (5.4a) is an additive combination of the discrete time small signal conductance (DTSSC) model and correlated error dynamics (CED) filter introduced in section 5.2, where
the CED filter and its modeling error input correct for un-modeled dynamics, which are
heavily influenced by the CVD voltage pulse shape delivered to the skin-electrode
interface. The DT-SSC estimation model is parameterized and structured in such a way
that its estimation parameters map to the continuous time linear parameters bioimpedance (CT-LPBI) model presented in section 5.1 and given in (5.3); further, when
the assumptions of (5.1.1) are met, these estimation models will be equivalent since
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the CED filter should be negligible. It is desired that the CT-LPBI model and its
parameters reflect the measurable dynamics of the plant when in varies in time and thus
should estimate the output accurately, independent of the shape of the voltage pulses to
an extent.

The statistical approach used in this subsection to study efficacy of the estimation
models, based on the stated conditions, involved analyzing the power inefficiency or
efficiency derived from the estimation outputs from either the DTC or CT-LPBI model, or
measured load current. What will be used is statistical mean square analysis for quality
of fit between the selected model compared to human plant estimated or measurable
stimulation currents, respectively, for the individuals under study (N= 21). In this respect
the modeling error power is equivalent to the CED filter output.

Time domain results and analysis for estimating measured bio-impedance load current
in terms of the efficacy of which estimation model is used versus the types and
magnitude of input waveform applied to the skin are presented in sections 6.2.9 and
6.2.10 of this paper.

The CED filter output power, and the DTC model and CT-LPBI model output power in
the graphs that follow are normalized to a one Ohm test load so that the power
calculations are the square of the estimated current outputs for each model type. Since
the method deals with power inefficiencies or efficiencies, the results were normalized

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to either DTC model estimated or measured power consumption depending on the
context to from the ratios.

The average of the power inefficiencies was calculated from the CED filter power output
in modeling error normalized to the corresponding modeling power output calculated
from the DTC model. The power output calculations from each of the model
components was done using the output estimation in stimulation currents given by the
respective model component estimated for every subject at a specific reported threshold
level; then the averages in the modeling error represented by power inefficiency per
delivered waveform pulse type at a reported threshold level by the subjects could be
calculated. The calculations were done at the sensation and pain thresholds for each
member of the sample population and for each waveform type. The results of the power
inefficiency in modeling are shown in Figure 35. The smaller the power inefficiency for a
given applied voltage waveform to the fingertip, the more accurately the output
estimation from the CT-LPBI impedance model accounts for the measured load current
dynamics in the mean square sense (assuming that the CT-LPBI model reflects the
dynamics of the plant). This is because the CED filter function has as its input the
difference between measured and a posteriori estimation current, as is seen in (5.7). As
the L2 norm of this estimated error input decreases, then so too does modeling output
estimation error. The illustrations in Figure 35 give evidence that the physical
impedance, as represented by the CT-LPBI model, best represent the dynamics of the
measured output current for square wave CVD pulses. Referring to the same figure, the
mean square power inefficiency for either applied saw tooth saw tooth or triangle

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waveform pulses are relatively worse. The error of the physical impedance modeling
rises with voltage amplitude except for square wave input when normalized to the
estimated power from the DTC model.

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Figure 35. Modeling error given by power inefficiency. Percentages of average power
consumed in the CED filter normalized to average power estimated in the DTC model
for all waveform types calculated at reported threshold levels: results graphed at the
sensation and pain thresholds of subjects (N=21).
Figure 36 is included to show that the DTC model output is statistically predictive in the
mean square to the measured stimulation current output. This is indicated by the high
power efficiency between the estimated and actual power delivered to the fingertiptactor interface by the CVD for each voltage waveform pulse type and current amplitude
level. However, the square wave input gives the best overall power efficiency for the
DTC model. The efficiencies were calculated at each subject‟s sensation and pain
threshold levels. Thus, the DTC model is valid for the human loaded tactor in the mean
square. A desirable indicator is that the DTC model power efficiency improves with
increased voltage amplitude for all three waveform types, which is shown to occur.
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Figure 36. Mean power efficiency of DTC model estimation output normalized to
measured power delivered to skin-tactor load for each waveform type: results calculated
at the reported sensation and pain thresholds of subjects (N = 21).

Figure 37 is similar to Figure 36. Instead, it displays the mean power efficiency using
the physical impedance (CT-LPBI) model output estimations normalized to the
corresponding measured powers delivered to the human-loaded tactor under study. As
with the previous figures, the efficiencies are derived as a function of applied CVD
waveform pulse type and reported threshold levels in the sample population. Comparing
Figure 37 to Figure 36, the efficiencies are slightly less for each waveform as expected
and the variance shown by the standard error intervals larger. The reason being is that
the CED filter component is no longer included in the estimated power output as was
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the case in the previous results. The effects on efficiency by dropping the un-modeled
dynamics term is least pronounced for the square wave input, as expected. However,
the physical impedance models are still a good predictor for the actual plant impedance
in the mean square and on the average for all waveform types and current stimulation
levels, as is represented by the calculation at reported threshold levels.

Figure 37. Mean power efficiency of physical impedance (CT-LPBI) model estimation
output normalized to measured power delivered to skin-tactor load for each waveform
type: results calculated at the reported sensation and pain thresholds of subjects (N =
21).

6.2.6 OBSERVATIONAL RESULTS FOR LARGE SIGNAL I-V CHARACTERISTIC
It is desirable to quantify and model the large signal behavior for: 1) how the bioimpedance parameters change with stimulation current level; 2) and how the trends in
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current versus voltage characteristic curves behave. Though the bio-impedance model
is updated online, and has RC circuit elements associated with the electricalbiochemistry of the skin, it is not robust. It cannot account for the physics that cause
variation of its parameters, in general, unless the conditions in 5.1.1 are met. Statistical
approaches to be presented in the next subsection were used to study the large-signal
behavior in the measured output based on the collected data of the sample population
to study future improvements that may be made to modeling the dynamics. In this
section, the observations in large signal I-V characteristics are presented.

Figure 38 plots the identification of the Stratum Corneum-modeled electrical resistance
Rp and the deep dermal tissue modeled electrical resistance Rs for each subject as a
function of RMS stimulation current. The CVD input was square wave for one second
identification and recording time, as previously stated. No participant experienced a
sensation below a 60 Volt pulse. The voltage pulses began at 30 volts for all subjects
and ended at the increment when the subjective pain threshold for the subject was
reached. Rp decreases at least an order of magnitude over the entire stimulation region
for almost all individuals. Another observation is that the variability in Rp for low
stimulation currents is initially large but seems to take on similar minimal magnitudes as
stimulation current increased to each subject‟s maximum threshold. The Rp minima
magnitude seems asymptotic to about 100 kΩ at the maximum pain stimulation
threshold possible for any member of sample population. The shapes of the Rp
characteristic curves are in agreement with others who have studied the electrical
impedance models for tactile displays.
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It was also observed from Figure 38 that Rs is always smaller in magnitude than Rp
over the entire stimulation current domain. As well it shows hardly any variation in
magnitude as a function of stimulation current or subject. This is also in agreement with
others who have studied similar models.

Figure 38. Identification of Rp and Rs as a function of stimulation current and subject
(N=21): results are from square wave CVD pulses starting at Vpp = 30V and
incremented to pain threshold for each subject.

Figure 39 displays the I-V characteristic curves associates with each subject as a
function of the CVD square wave input voltage amplitude. The values plotted are for
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measured and process model predicted load current. This shows that the predictor can
track RMS current over a large variation in load current. The current is observed to rise
rapidly in most cases as the voltage pulse amplitude increases past a certain threshold
depend on the subject. From this, we can observe that even small changes in input
voltage can lead to large changes in stimulation current. For small voltages near 30
volts, the RMS current tends to be similar in value for all individuals. The nonlinear
increase in current is a result of positive feedback from Rp as it is an inverse function of
the stimulation current.

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Figure 39. Measured and DTC estimation model (from 5.4a) I-V characteristic curves for each subject as a function of
square wave CVD pulse amplitude and subject (N=21).

128

Figure 40 plots each identified and recorded intracellular capacitance Cp value for the
physical impedance model spanning the voltage amplitude increments for each subject.
This graph is shown for square wave input and plotted against the measured stimulation
currents. The trend shows an increase in capacitance as stimulation current increases
that occurred for almost every individual. Prima facie, the increase appears affine linear
for most individuals as a function of current. The rate of increase is less than that of Rp
over the region of interest; Except for two outliers, the change in value of Cp was at
most a factor of 3 for any individual, whereas Rp can vary greater than a factor of 10 for
the same stimulation current domain. As well, the capacitance values are grouped
closer together over the current stimulation domain versus Rp. The outliers are likely a
result of increased ionic moisture content at the point of stimulation that facilitates
dielectric polarization.

129

Figure 40. Identification of Cp as a function of stimulation current and subject (N=21):
results are from square wave CVD pulses starting at Vpp = 30V and incremented to
pain threshold for each subject.

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6.2.7 STATISTICAL RESULTS FOR LARGE SIGNAL I-V CHARACTERISTIC AND
LARGE SIGNAL MODELING
For the following results assume that all CVD outputs were generated from square wave
pulses starting at 30 volts and incremented to the point of pain threshold for a specific
subject. As well, it must be assumed that the results are valid only if the fingertip is
mostly dry and not altered or abraded and that dimensions of the tactors (stimulating
electrodes) on the PCB are of the dimensions discussed in the hardware design section
of this paper.

Figure 41 shows the box and whiskers plot for the average of all identified R s values per
individual (N=21). As seen, the median average Rs value is 62 kΩ for the sample
population. For this tactile display most of the averages of the Rs values fall between 45
and 70 kΩ.

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Figure 41. Five statistic box and whiskers plot produced from each average Rs value
per individual from 30 volts to maximum pain threshold voltage (N = 21).

Figure 42 is the bivariate plot of all identified Rs values (N = 278) versus stimulation
current, independent of subject. This scatter plot clearly indicates that there is no
correlation between Rs and stimulation current. A Spearman Rank correlation test
showed that there is only a small correlation (rs(276) = 0.1877, p < 0.05 two-tailed).

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Figure 42. Scatter plot of all identified Rs values versus stimulation current independent
of subject (N=278): results generated from applied square wave pulses from 30 volts to
maximum pain threshold voltage per individual.

Figure 43 displays the scatter plot of all identified Rp values versus stimulation current
irrespective of subject (N=278). The stimulation current is a function of the voltage
amplitude. This graph displays two related regression curves for the data for the
following two cases: 1) the power-fitted regression curve calculated from the Rp scatter
plot that gave the best goodness-of-fit (R2 = 0.874); 2) the mean of the fitted power
function regression curves to each subject‟s data, which itself is a vector of entries
produced from a power function (R2 = 1). The motivation for case 2 was to build the
lower 5 percent and upper 95 percent confidence intervals for any identified Rp value as
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a function of stimulation current. As seen, this regression curve is qualitatively similar to
the scatter-plot regression curve.

The goodness-of-fit for case 2 ranged from R2 = 0.9587 to R2 = 0.9981 with a mean of
R2 = 0.9730 and standard deviation of 0.02991 for the sample population (N =21).
Testing the values of these curves at a particular stimulation current for normality was
done at 4 different current magnitudes using Lilliefors (0.080 ≤ K(20) ≤ 0.139, 0.332 ≤
pCalc ≤ 0.979, p < 0.05), Q-Q plot analysis (R2 >0.9509),kurtosis (-0.104 ≤ γ2(20) ≤
1.70, p < 0.05), and skewness ((-0.0256 ≤ γ1(20) ≤ 0.496, p < 0.05). Testing indicated
that the interpolated Rp values for the population could not be rejected for normally;
hence, the conclusion is that the confidence intervals represent the lower 5th and upper
95th percentile for the identified Rp values referenced to the power-fitted curve of the
second case. As well, the mean sensation and pain stimulation thresholds at 0.0998
and 0.176 mA corresponded to 273±103 kΩ and 186±67.9 kΩ stratum corneum skin
resistances, respectively, with tolerances at the 5 percent significance level.

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Figure 43. Scatter plot of identified Rp values for sample population (N = 278) as a function of stimulation current with
power-fitted regression curve using square wave CVD pulse: lower 5th and upper 95th percentile confidence intervals are
shown for identified Rp calculated using the mean of the Rp power-fitted regression curves for each individual (shown as
the dashed line).
135

The histogram of Figure 44 is included to compare the percent error between all
calculated Rp and Interpolated Rp over the respective means of perceptive stimulation
thresholds (sensation and pain) for the population derived in the psychophysics
experimental section. The histogram shows evidence of a slight positive bias for the Rp
interpolation estimator. Otherwise, the figure illustrates that the error between identified
and interpolated Rp values is small. This result further suggests that the confidence
intervals on the calculated Rp are reliable bounds for the sample population versus
stimulation current if the interpolated Rp is used to calculate the bounds.

Figure 44. Histogram of percent error between the identified Rp and Interpolated Rp
values using square wave CVD pulse (N = 278).
136

Figure 45 displays the scatter plot for CVD square wave amplitude versus the
corresponding RMS measured stimulation current (V-I) irrespective of subject (N=278).
This graph displays two related regression curves for the data for the following two
cases: 1) the logarithmic-fitted regression curve calculated from the V-I scatter plot that
gave the best goodness-of-fit (R2 = 0.6924); 2) the mean of the fitted logarithmic
regression curves to each subject‟s data, which itself is a vector of entries produced
from a logarithmic function (R2 = 1). The motivation for case 2 was to build the lower 5
percent and upper 95 percent confidence intervals for any measured V-I pair. As seen,
this regression curve is qualitatively similar to the scatter-plot regression curve.

The goodness-of-fit for case 2 ranged from R2 = 0.9594 to R2 = 0.9989 with a mean of
R2 = 0.9866 and standard deviation of 0.01165 for the sample population (N=21).
Testing the interpolated voltage amplitudes produced from these curves at a particular
stimulation current for normality was done at 4 different current magnitudes using
Lilliefors (0.113 ≤ K(20) ≤ 0.139, 0.350 ≤ pCalc ≤ 0.703, p < 0.05), Q-Q plot analysis (R2
>0.9523), kurtosis (0.320 ≤ γ2(20) ≤ 0.597, p < 0.05), and skewness ((-0.202 ≤ γ1(20) ≤
0.738, p < 0.05). Testing indicated that the interpolated voltage amplitudes for the
population could not be rejected for normally; hence, the conclusion is that the
confidence intervals represent the lower 5th and upper 95th percentile for the measured
voltage amplitudes referenced to the logarithmic-fitted curve of the second case. As
well, the mean sensation and pain stimulation thresholds at 0.0998 and 0.176 mA
corresponded to 97.12±18.93 volts and 120.92±22.28 volts in amplitude, respectively,
with tolerances at the 5 percent significance level.
137

Figure 45. Scatter plot of measured CVD Vpp for sample population (N = 278) as a
function of stimulation current with log-fitted regression curve using square wave CVD
pulse: lower 5th and upper 95th percentile confidence intervals are shown for measured
CVD Vpp calculated using the mean of the Vpp log-fitted regression curves for each
individual (shown as the dashed line).

Figure 46 gives the histogram included to compare the percent error between all
measured CVD voltage amplitudes and Interpolated values over the mean perceptive
stimulation thresholds for the population derived in the psychophysics experimental
section. The figure illustrates that the error between the measured and corresponding
interpolated CVD voltage amplitude values is small. This result further suggests that
the confidence intervals on the actual CVD amplitude are reliable bounds for the sample
138

population versus stimulation current if the interpolated CVD amplitude is used to
calculate the bounds.

Figure 46. Histogram of percent error between the measured CVD and interpolated
CVD amplitude values using square wave CVD pulse (n = 278).

6.2.8 OUTPUT ESTIMATION UNDER TIME VARIATION STUDY
The experiment carried out was to test how responsive the ELS adjustment model could
be with updating the parameters in the DTC model given in section 5.2 under simulated
time variation of the plant by manipulating the value of its forgetting factor. The
motivation for the experiment originates from notable time variation in human bio-

139

impedance loading on the tactor that increased with increasing stimulation current
amplitude level for the participants. Two different forgetting factor coefficients were used
to see how well the process model could track the measured load current. Namely, λ =
1, where previous data is not exponentially weighted, and λ = 0.99975, where previous
data is exponentially weighted as a function of discrete time. The previous data
becomes less influential in the update model for this latter case. Only one subject was
used for this test. The conditions for the test were administered square wave CVD
pulses to the index fingertip-electrode interface set at 90 volt amplitude.

For each forgetting factor experiment, the fingertip of the subject was placed on the
tactile display with the estimation and measured output results of the stimulation current
recorded for 10 seconds in each case. In the two experiments, the subject simulated his
impedance time variation by scanning his index fingertip slowly across the stimulating
electrode under measurement for the 10 second duration. The motivation for the
experiment was to determine the proper forgetting factor value to use so that applying
the haptic renderer and model estimation algorithm to a sample population gives
accurate results.

Figure 47 shows the real-time results of the output estimation of measured stimulation
current over time with λ = 1. Only the steady state points, taken at the midpoints of the
measured and estimation model output current pulses, for each pulse are plotted for
clarity. The midpoint is a point in the active duty cycle of square wave voltage pulse.
The dashed line is the measured, and the solid line the estimated output current to load,

140

respectively. The measured current changed as a function of time when constant
voltage pulses were applied, as illustrated, when fingertip scanning occurred. The figure
shows that the DTC model output time lags in estimating the output with plant time
variation present when the adaptation law has no forgetting factor set when updating
the model parameters.

141

Figure 47. Output estimation of measured stimulation current for human subject using DTC model in (5.4a): square wave
CVD pulses with λ = 1.0, time = 10 sec, and Vpp = 90V.

142

Figure 48 illustrates the estimation results of the second experiment with the
exponential forgetting factor set slightly less than unity: λ = 0.99975. By setting the
forgetting factor, and repeating the fingertip scanning procedure over the relevant
electrode, the estimated model now estimates the measured current pulses to a high
degree. By using equation (5.23) in section 5, the number of data points that the
algorithm is sensitive to is approximately 8000 of the most recently sampled points. This
corresponded to about 80 milliseconds of estimation time in the continuous domain. The
voltage pulse width at 60 Hz frequency and 11 percent duty cycle for both these
experiments was about 1.83 milliseconds or about 183 sampled points; therefore, it is
reasonable to assume that the adjustment model can update the DTC model in less
than 80 milliseconds of time for it to become valid (accurate).

143

Figure 48. Output estimation of measured stimulation current for human subject using DTC model in (5.4a): square wave
CVD pulses with λ = 0.9975, recording time = 10 sec, and Vpp = 90V.
144

6.2.9 ESTIMATION MODEL OUTPUT AS A FUNCTION OF CVD WAVEFORM TYPE
STUDY
This section examines and illustrates some experimental cases concerning model
uncertainty and model validity in estimation of output current when the haptic renderer
drives a human skin-electrode load as a function of the three CVD waveform pulse
types. For reference, the three types of voltage pulses were shown in Figure 17. The
results that will follow can be compared to the results when the load is a known ideal
LTI impedance network driven by the haptic renderer, which was studied in section 6.1
of this paper. The motivation for the experiments was to empirically assess to what
extent the shapes of the voltage pulses excite differently the underlying non-linear plant
dynamics. For this purpose, the measured output current was estimated in real-time
using the small signal DT-SSC estimation model and the generalized DTC model given
in (5.4a) for applied square wave, saw tooth, and triangle wave pulses. The output
estimation from the CED filter in (5.4a) was also plotted alongside the results to
visualize the magnitude of plant uncertainty that cannot be modeled alone using DTSSC estimation model versus CVD waveform type. Again, the CED filter is the term that
corrects for this plant uncertainty in its output for stimulation current estimation. It should
be noted that the CT-LPBI model given in (5.3) and the DT-SSC model will be assumed
interchangeable for all estimations, whose sufficient conditions for validity rests on the
assumption put forth in (5.1.1); the equivalency relation between these two models is
given by (5.31b) with parameter transformations given by equations (5.34a – 5.34c).

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In this study, the collected data from three subjects were used that accounted for each
of the three applied CVD waveform types. The recorded data was taken at each
subject‟s reported pain threshold in stimulation current amplitude so that the effects of
model uncertainty would be apparent in the time domain plots. Selecting the maximum
stimulation current data also showed the extreme case for the ability of the models to
estimate the load current. The fundamental frequency in the output was 60 Hz with 11
percent duty cycle for all plots, as in previous cases. As well, a forgetting factor of: λ =
0.99975 was used. The total recording time for all the following plots was one second.
In the time domain plots, only one pulse of the resulting 60 is shown for each case.

Figure 49 displays one of the output current pulses in the recording of CVD square
wave voltage pulses delivered to subject #4 for one second. Along with this plot, the
estimated current outputs, ICorrError, ICalcModeled, and ICorrError + ICalcModeled are shown,
which correspond to outputs from: the CED filter, DT-SSC model and the superposition
of the model terms in (5.4a), respectively. Here we see that the measured current
response is approximately first order by examining the transient and steady state
responses. The small-signal DT-SSC model is accurate in estimating the output
response on a small time resolution even at the rising and falling edge of the pulse. The
output from the CED filter is negligible for the entire pulse duration indicating that: 1) the
DT-SSC estimation model and CT-LPBI estimation model derived in section 5.1 are
equivalent for square wave pulses as was argued in section 5; 2) the electrical bioimpedance plant effectively shows linear dynamics under square wave pulses. The
conclusion empirically supports the conditions set forth in (5.1.1). The CED filter output

146

is greatest at the transient response of the pulse as expected, since the curve must
transition over the true non-ohmic I-V relationship to get to steady state (see equation
(5.2) for the general relationship). It should be noted that these results were observed
for all subjects and over all valid stimulation current dynamic ranges. Therefore, the
parameter estimates of the physical bio-impedance parameters, shown in the model
structure in Figure 25, model the lumped effects of the underlying electro-biological
chemistry of the fingertip to a reasonable degree when CVD square wave pulses are
applied to the skin.

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Figure 49. One of 60 square wave pulse of measured and estimated model output current, using models in (5.3) and
(5.4a), for CVD square wave pulse train administered at reported pain threshold for subject #4: Vpp = 125V, λ = 0.99975
and recording time = 1 sec.

148

The parameter estimates for impedance values corresponding to the previous figure are
given in Figure 50. These were the recorded parameters that estimated the dynamics
for the fingertip-electrode interface for the one second square wave pulse application.
The locations of the active duty cycle in the pulse train are apparent by the seen
“spikes” in the parameter estimates because of the exponential rise in the norm of the
covariance P matrix used in the ELS-FF adaptation law during the inactive pulse region,
which is explained in section 5.2.2. Rp is shown to be the parameter most affected by
the time varying plant, as expected.

This graph can be compared to the subsequent saw tooth and triangle wave parameter
estimates over time in Figure 52 and Figure 54. It is seen, that at pain threshold
stimulation for all three subjects, the respective Rp and Rs values are similar. This result
was repeatable. However, Cp does not, in general, take on similar magnitude values
between the different CVD pulse types, as is exemplified by these plots. The likely
reason for this phenomenon is the coupling in estimates of the parameters specific to
the DT-SSC model and CED filter, which should be independent if the load is ideally
linear. However as will be seen in the saw tooth and triangle wave graphs in Figure 51
Figure 53 respectively, the shapes of the CVD pulses violate the assumptions set forth
in (5.1.1) to guarantee minimizing the effects of non-linear dynamics of the electrobiological plant. Hence, the equivalency between the DT-SSC and CT-LPBI model are
not guaranteed when transforming the DT-SSC model parameters from the discrete
time domain to the CT-LPBI model impedance parameters in the continuous time
domain.

149

Figure 50. Estimated Rp, Rs, and Cp as a function of time and square wave CVD pulses for subject #4: Vpp = 125 volts, λ
= 0.99975 and recording time = 1 sec.
150

Figure 51 shows the plot based of the same conditions as the previous case except with
saw tooth CVD pulse trains administered to subject #1. Here the CED filter output
estimation compensated noticeably for the significant estimation error present in the
small-signal DT-SSC output estimation; hence, both DT-SSC and CT-LPBI are no
longer valid for the plant dynamics on such a small time resolution. The generalized
DTC model, however, estimated the load current well. In contrast, the DT-SSC model
first over estimates the measured current output and then underestimates it at higher
current levels. This is likely due to the exponential rise in measured stimulation current
as a function of rising voltage which is visible in the graph over time; equivalently the
underlying physical phenomenon can be viewed as the fall in stratum corneum skin
resistance as the measured stimulation current increases over time, which is related in
equation (5.2). This suggests that (5.2) can be used to model Rp during transition time
and not only in steady state if this in fact the trend. In summary, the phenomenon
becomes apparent over the long duration of I-V transition as a function of time. The
result emphasizes the inadequacy of the CT-LPBI physical model, in the large signal, in
terms of long I-V transition time. Moreover, the results illustrates the need for a more
robust physical model that accounts for the large signal I-V transition times as it relates
to the electro-biological dynamics of the skin. In this respect, the estimation error could
be reduced when only the reformulated model is considered.

151

Figure 51. One of 60 saw tooth wave pulse of measured and estimated model output current, using models in (5.3) and
(5.4a), for CVD saw tooth wave pulse train administered at reported pain threshold for subject #2: Vpp = 135V, λ =
0.99975 and recording time = 1 sec.
152

Figure 52 shows that, at reported pain stimulation threshold for subject #1, Rp and Rs
resistances are the same magnitudes, to their square wave counterparts in Figure 50,
as expected. However, the estimation of Cp confirms that it is an order of magnitude
greater than expected. Rp is shown to be the parameter most influenced by the time
varying process, as expected. It is known that Cp is larger than should be expect
because of the larger than expected recovery time erroneously estimated by the DTSSC model output in Figure 51.

153

Figure 52. Estimated Rp, Rs, and Cp as a function of time and saw tooth wave CVD pulses for subject #2: Vpp = 135
volts, λ = 0.99975 and recording time = 1 sec.
154

The last time domain recording, corresponding to CVD triangle wave pulse trains
administered to subject #20 at recorded pain threshold, is graphed in Figure 53. The
small error in output estimation using the generalized DTC model is in line with the
previous time domain results. As well, the calculated Cp extracted from the DT-SSC
estimated parameters as a function of time is clearly over estimated. As with the saw
tooth current, the bio-impedance model of (5.3) has significant error in estimation as is
apparent by the bowing in the CED filter output correction.

155

Figure 53. One of 60 triangle wave pulses of measured and estimated model output current, using models in (5.3) and
(5.4a), for CVD triangle wave pulse train administered at reported pain threshold for subject #20: Vpp = 142V, λ = 0.99975
and recording time = 1 sec.
156

Figure 54 shows that for subject #20, the calculated capacitance is of the same order as
that of the capacitance value derived from the physical model when saw tooth
waveforms are applied to the skin in the previous results. However, Rp and Rs are of
the same order of magnitude as the previous two cases. This is as expected from the
discussion for the saw tooth wave analysis.

157

Figure 54. Estimated Rp, Rs, and Cp as a function of time and triangle wave CVD pulses for subject #20: Vpp = 142 volts,
λ = 0.99975 and recording time = 1 sec.
158

In conclusion, the DTC model estimates the resulting stimulation current output pulses
regardless of the applied CVD pulse shape extremely well. However, the CT-LPBI
model is valid for the square wave pulses for which the model was originally developed.
As well, Rp and Rs appear accurate for all the cases. The calculated Cp, however, for
the saw tooth and triangle wave pulses is clearly inaccurate.

159

7. ADAPTIVE CONTROL MODELING, SIMULATION AND ANALYSIS

The following sections rely on experimental results from section 6 of this paper.
Stochastic characterization for identified Rp in section 6.2.7 will be generalized to the
instantaneous current case and tested for validity. The motivation will be to have a full
bio-impedance dynamics model for closed-loop adaptive control to track square-wave
voltage pulse induced current. Simulation will be presented to provide evidence for the
proposed model.

7.1 MODEL
The CVD amplifier circuit low pass filter along with the skin bio-impedance model first
presented in Figure 21 is shown in Figure 55. The circuit will be the used as the overall
model for simulation.

160

Figure 55. Illustration of bio-impedance model of skin and frequency model for constant
voltage pulse driver (CVD)

The models for skin bio-conductivity and CVD OpAmp, along with the large signal
stochastic modeling of Rp are stated as:
λ
λ
δ
δ

δ

Coefficients A and B are experimentally determined stochastic parameters that fit the
large-signal characteristic curve of Rp versus RMS output current to a power law
regression curve. It holds for any member in the sample population to a reasonable
degree. The value of λ is the pole location of the low pass filter of the OpAmp
161

determined by its gain-bandwidth product. Va is taken as the input to the system and
Istim the stimulation current output. It is important to note that the relationship in (7.1b) is
derived from average current and not instantaneous. In our system, Istim and the postfiltered output Va, termed VLoad (not shown), are observable via the corresponding
current and voltage sensors measuring signals to an electrode on the display.

7.2 STOCHASTIC PARAMETER IDENTIFICATION FROM POPULATION DATA
Figure 56 illustrates the identified Rp versus RMS stimulation current scatter plot for 21
participants Rp in was identified online using extended least squares and the measured
stimulation current averaged over the sampling interval time. As seen, the data can be
fitted to a power law (R2 = 0.874) , which ranges in value from 450 kΩ to 1550 kΩ near
0.03 mA RMS, and 100 kΩ to 200 kΩ near the maximum RMS current applied. The
variance decreases as function of current. The mean values of A and B coefficients for
the entire sample population are Aavg = 40.903 and Bavg = -0.798. Analysis on the
sample population data for identified Cp indicates that the value over the same RMS
current range increases approximately linearly from 200 pF at the low end of RMS
current to 600 pF at maximum RMS current level. The average value of Cp for the
population over the current range shown in Figure 56 is about 400 pF.

162

Figure 56. Large-signal stochastic representation of Rp and A and B power law
coefficients for sample population (N = 21) versus RMS stimulation current for 60 Hz,
5% duty cycle square wave pulses

Figure 57 shows a box and whiskers plot of the averages for each set of identified
values of Rs for each member of the population (N = 21) identified over the same
current range as in the previous figure. The population mean of the averages equals 63
kΩ. Rs exhibits a small variation in value compared to Rp. In summary, this value is
used as the stochastic representation of Rs in (7.1a).

163

μ (Rs) kΩ

Box and Whiskers Plot for Random
Variable: Average of the Estimated Rs
Values for Each Subject (N = 21) (Square
Wave)
100
90
80
70
q1
60
50
min
40
median
30
20
max
10
q3
0
Square Wave

CVD Pulse Type
Figure 57. The mean of the average values of Rs for each member of the population
(N = 21)

7.3 PROPOSED BIO-IMPEDANCE DYNAMICS MODEL
It is desirable to generalize the model (7.1b) by replacing RMS with instantaneous
current to account for dynamic on Rp. Without prior knowledge and as a first
assessment, (7.1b) is assumed to hold for instantaneous time. The bio-impedance
dynamics model to be studied then becomes:
λ
λ

Ω
Ω
Here, the physical parameters Rp, Cp, and Rs are defined as before. In part 5 of this
work, an online ELS identification algorithm was introduced as a means to estimate
164

these parameters in real-time. Section 6 demonstrated real-time identification for Rp, Cp
and Rs for square wave voltage pulses in addition to other pulse geometries. (7.2b) is
obtained by the graph in Figure 56. In (7.2b), the instantaneous output current term is
normalized by duty cycle and re-dimensioned to amperes. As well, Rp is re-dimensioned
from kilo-ohms to ohms. 5 MΩ is taken as the DC resistance of the skin when no current
is applied and is also the isolation resistance of the actual haptic rendering device from
ground. Now, Istim is defined as the measurable instantaneous current to the skinelectrode interface due to measurable voltage pulses from the driver.

7.4 DERIVATION OF ADAPTIVE CONTROL LAW
Assume that the condition of the skin is slowly changing and the control is for one
electrode on the array; Rp introduces nonlinearity in the system. Neglecting the
dynamics of the OpAmp, which will be assumed to be much quicker than the output
response time, taking (7.2a) in to the time domain and substituting Rp in to the original
model yield the following differential equation:

In this equation, we are assuming that

since it was found experimentally to be

relatively close to unity and will greatly simplify the control law. VLoad ≈ Va is the system
input and Istim is the output, which are both measurable. The parameters Rs and Cp are
estimated online using an extended least squares algorithm and are assumed to be
known for this reason; A is unknown. The system is linearized with nonlinear feedback
165

by canceling out the square term and the coupled term on the original differential
equation using the substitution:

which leaves:

The introduced term u is the input to the new system with coefficients as previously
defined in (7.4).The input will be controlled by using adaptation on the model with the
indirect MRAC law approach. The following is the reference model to be tracked:
π

where T is the period and TD the duty cycle for a train of square wave pulses. The
inequality constraint in (7.7a) is so that output tracking does not exceed the slew rate of
the OpAmp. The virtual control for u will be:

where:

The error is defined as:

An MRAC law with σ-switching modification applied to 7.6 gives:
γ

γ σ
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γ

γ σ

σ

σ
σ

The σ-switching modification is necessary to correct for parameter drift due to model
uncertainty from approximations made in deriving the nonlinear feedback. Using data
collected previously, the constant, A, in (7.4) is substituted by the known sample
population coefficient Aavg computed for the regression analysis in Figure 56 giving:

Once u is updated, the real input Va must be computed to produce the desired output.
There is not direct access to

in (7.5); so instead, taking into consideration the sample

rate of the DAQ card Ts, the implementation is:

Note at the end of the active duty pulse cycle duration, the control is shutoff for reasons
to be explained.

7.5 SIMULATION OF THE BIO-IMPEDANCE MODEL (OPEN-LOOP)
The instantaneous model in (7.2a – 7.2b) will be simulated in Matlab using filled in
parameters found experimentally for subject #2 which are given in

167

Table 7. One instance of the measured and ELS-estimated current pulses
corresponding to the identified parameters is shown in Figure 58 for the subject. The
first order zero and pole in the impedance model are clearly evident in the transient
response; As well the addition in Rp and Rs values at the voltage amplitude predict the
steady state current component accurately. The effects of current nonlinearity versus R p
are not apparent because of the fast rise and fall times in the pulse. If the model is a
reflection of the dynamics of skin under electronic stimulation, then the simulated output
should replicate the actual output to a reasonable extent. The simulated CVD pulses
should also account for the low-pass filter characteristics of the OpAmp or the
simulation could result in large error in the transient response. The low pass filter corner
frequency of the driver OpAmp is based on its data sheet and observed time differences
between voltage rise and fall times under known resistive load. The low pass filter is:
λ
λ

λ

π

λ

π

Table 7. Experimentally estimated bio-impedance parameters for subject #2 with square
wave voltage pulse amplitude conditions shown
168 kΩ; Vpp = 150 Volts
430 pF; Vpp = 150 Volts
65 kΩ; Vpp = 150 Volts
0.63 mA; Vpp = 150 Volts
IstimSS
A
61.613; Vpp = 30…150 Volts
B
0.741; Vpp = 30…150 Volts
Rp
Cp
Rs

168

Figure 58. Measured and estimated output current pulse shape to subject #2 at 150 volt square wave pulse; measured
and estimated Istim at steady state equals 0.63 mA

169

A simulated current pulse is shown in Figure 59 for a train of simulated voltage pulses
inputted in to the dynamics model with parameters taken from
Table 7. In addition, Figure 60 illustrates the simulated value of Rp. The absolute error
between experimental and simulated steady state current is 0.13 milliamps. The error
may be attributed to the imperfect and statistical power law approximation between
current and Rp that is nonetheless assumed in the dynamical model. The value of R p
drops to 231 kΩ during the simulated steady state current. Comparing this to R p from
experiment, the SC resistance for the subject was 168 kΩ. The transient response
between experiment and simulation agree well during the rise time and could be
improved with better dynamical modeling of the driver circuitry and additional modeling
of measurement sensors. The discrepancy seen during the fall-time of the simulated
current pulse is likely due to the need of a larger time constant than was used since the
ELS estimate of current matches with experimental measurement. The simulation
makes apparent that the SC skin resistance drops quickly for square wave pulses;
hence, the effects of Rp nonlinearity are negligible during such a short transient
response time. In summary, the results are promising for generalizing the stochastic
model presented in (7.1a – 7.1b) to the instantaneous current impedance model given
in (7.2a – 7.2b). However, the model affords improvement as seen in the steady state
current discrepancy.

170

Figure 59. Simulated current pulse from square wave voltage pulses inputted into equations 7.2a- 7.2b using experimental
data in
Table 7 for one subject; Istim steady state equals 0.5 mA

171

Figure 60. Simulated value of Rp stratum corneum resistance (Ohms) using equation 7.2b during the current pulse time in
Figure 59; the minimum of Rp equals 231 kΩ

172

7.6. SIMULATION ON CLOSED LOOP STIMULATION CURRENT CONTROL
The following simulations use values from
Table 7. Figure 61 shows the desired reference current. Reference current is designed
with the pole at 2000 KHz so that rise and fall time are at 175 μs. The frequency is at
60Hz, amplitude at 0.63mA and with 11 percent duty cycle.

173

Figure 61: Reference Current

174

Figure 62 shows the simulation result on the stimulation current output of the closed
loop control system. It displays that the designed stimulation current control system was
able to track the reference current plotted in Figure 61 very well at the beginning of
every pulse. There is a spike at the end of every pulse. This spike is the result of
abruptly turning off the voltage control of the system. This is a result of the capacitive
effects of the skin. This is a necessary step to ensure correct tracking of the current.
Given the behavior of Rp, when the current is low, it increases dramatically as seen in
Figure 63. This results in a dramatic increase in the time constant of the system and so
there is very slow convergence.

Figure 62. Simulation results: Tracked stimulation current.

175

Figure 63. Simulation results: behavior of Rp.

Figure 64 plots the simulated closed loop CVD voltage pulses. In the figure, the voltage
output Va approximates to VLoad. This agrees with our assumption in simplification of
the dynamic model.

176

Figure 64. Simulation Results: Voltage output of closed loop CVD.

177

8. CONCLUSIONS AND FUTURE WORK

This paper presents development of a complete electrotactile haptic renderer using a
constant voltage driver (CVD) method with closed loop design. The hardware for
powering the driver as well as measurement circuitry to monitor voltage and current
output were developed that must operate under high voltage conditions were
successfully developed. The CVD output driver as well as the measurement circuitry
was also proven to be able to operate under typical human fingertip bio-impedance
loading. In addition, the on-line identification algorithm of fingertip skin bio-impedance
and associated models are presented. The algorithm is based on a discrete-time
extended least squares (ELS) iterative approach with forgetting factor, which serves as
an adaptive law to estimate parameters of the first-order bio impedance model of the
fingertip. Experimental results demonstrate the performance of the developed CVD
based electrotactile haptic renderer, as well the effectiveness of the algorithm for oneline identification of parameters of human fingertip skin bioimpedance. This work will
greatly improve the tactile/haptic rendering performance of electrical stimulation
(electrotactile) systems and facilitate the development of electrotactile based haptic
rendering devices and applications.

The purpose of this work is also to establish a generalized dynamic model of the
electronic bio-impedance of the fingertip skin, based on experimental research for which
closed-loop MRAC control could be applied using the direct method. The goal of the
control is to regulate stimulation current to the reference current. The model is

178

presented to instantaneous stimulation current, which is necessitated by the type of
input our electrotactile driver used to deliver sensory content to the skin, namely
constant voltage pulses. This is in contrast to drivers that use constant current pulses
whose outputs are mainly independent of the current state of the electronic bioimpedance of the skin. The results of this work will be used to develop the advanced
controller in an application where an electrotactile haptic renderer adapts the stimulation
output current from changing electro-bioimpedance conditions of the skin. This will allow
reduced driver complexity design and increased power efficiency. The tradeoff will be in
the complexity of sensor design to monitor the output, external DAQ hardware, and
software complexity necessary for implementing the adaptive control and estimation
law. The modeling of the dynamics for the generalized model was shown to be
preliminarily valid from simulation when compared to experimental results.

179

REFERENCES

180

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