Adaptive control of kinematically redundant robots

It is shown through careful problem formulation that the adaptive control of redundant robots can be addressed as a reference velocity tracking problem in the joint space. A control law which ensures the bounded estimation of the unknown dynamic parameters of the robot and the convergence to zero of the velocity tracking error is derived. In order to ensure that the joint motion on the self-motion manifold (SMM) remains bounded, a homeomorphic transformation is found. This transformation decomposes the velocity tracking error dynamics into a cascade system consisting of the dynamics in the end-effector error coordinates and the dynamics on the SMM. The dynamics on the SMM is directly shown to be related to the concept of zero-dynamics. It is shown that if the reference joint trajectory is selected to optimize a certain type of objective function, then stable dynamics on the SMM results. This ensures the overall stability of the adaptive system. Detailed simulations are given to verify the theoretical developments. The proposed adaptive scheme does not require measurements of the joint accelerations or the inversion of the inertia matrix of the robot