Impedance Control and Admittance Control are two different implementation methods that are used to achieve the same control objective of producing a desired relationship between applied force and displacement of a robotic system interacting with an environment. Due to the difference in implementation method, impedance control and admittance control have complementary performance and stability characteristics. Impedance control is stable for all contact environment stiffness and has good performance for stiff environments, but results in poor performance during interaction with soft environments. Admittance control results in good performance during interaction with soft environments but results in either poor performance and or unstable behavior during interaction with stiff environments. We use a hybrid system framework to propose a family of controllers that attempt to interpolate the stability and performance characteristics of impedance control and admittance control. The advantages of this approach are first demonstrated through analysis and simulations of a single degree-of-freedom rigid linear model. The methodology is thenextended to multi degree-of-freedom linear and non-linear models and single degree-of-freedom system with flexibility. Experimental results with a lightweight robotic arm are presented to demonstrate the usefulness of the approach.
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