Robust Impedance-Matching of Manipulators Interacting With Uncertain Environments: Application to Task Verification of the Space Station's Dexterous Manipulator

A systematic design method is developed for the identification and control of a simulating robot in order to adjust its contact force and impact dynamics to match those of a reference robot when both robots couple to a similar physical environment with unknown impedance. The control architecture, which is based on closed-loop impedance matching between two robots, is utilized by a hydraulic robot testbed facility for high-fidelity task verification of the space station's dexterous manipulator without requiring contact dynamics modeling. First, the uncertain environment is modeled in terms of parameter uncertainty bounds for a class of environment impedances. Then, the control goal is specifically defined as to minimize the contact-force error between the two robots, where the contact force is caused either by time-varying operator commands or impacts due to a nonzero preimpact velocity. Next, a hierarchical control architecture is formulated in the general framework of linear fractional transformation system by making use of the frequency-domain specifications of the robots together with the environment's parameter uncertainty bounds. It is shown that the overall system uncertainty can be represented by a perturbation block in the feedback form, which can be specified by a block structure array by making use of a unitary transformation. Subsequently, a $\mu$-synthesis-based controller is developed and implemented to achieve the dynamical similarity while maintaining contact stability. Experimental results demonstrate that the simulating robot can generate high-fidelity contact-force profile and impulsive force for different environments without contact dynamics modeling.