Adaptive Control of Kinematically Redundant Robots

A redundant robot has more degrees of freedom than what is needed to uniquely position the robot end-effector. In a usual robotic task, only the end-effector position tr'ajectory is specified. The joint position trajectory is unknown, and it must be selected from a self-motion manifold for a specified end-effector. In many situations the robot dynamic parameters such as link mass, inertia and joint viscous friction are unknown. The lack of knowledge of the joint trajectory and the dynamic parameters make i t difficult to control redundant robots. In this paper, we show 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 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 self-motion manifold. The dynamics on the self-motion manifold is directly shown to be related to the concept of zero-dynamics. It is shown that if the reference joint trajectory is selected t o optimize a certain type of objective functions, then stable dynamics on the self-motion manifold 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.