Adaptive Impedance Control: A Contraction Theory Approach

This paper introduces an adaptive impedance control framework tailored for a rigid manipulator with n links, even in scenarios where the precise model is not known apriori. The framework utilizes a contraction theory-based virtual system, ensuring the exponential convergence of the actual trajectory towards the desired one. Within this framework, only the underlying structure of the matrices governing the manipulator's system dynamics is assumed to be known. By ensuring incremental stability of the virtual system dynamics, the framework guarantees exponential convergence of the tracking error. This primarily involves assessing the negative definiteness of the Jacobian, which governs the differential dynamics of the virtual system. To validate this approach, simulation results for a 2-link rigid manipulator are presented, offering empirical validation for the proposed method.