Learning control for robot tasks under geometric endpoint constraints

A learning control scheme for a class of robot manipulators whose endpoint is moving under geometrical constraints on a surface is proposed. In this scheme, the input torque command is composed of two different signals updated separately at every trial by different ways. One is updated by the angular velocity error vector which is projected to the tangent plane of the constraint surface in joint space. The other is updated by the magnitude of contact force error at the manipulator endpoint. Not only the uniform boundedness of position and velocity trajectory errors but also the uniform convergence of position and velocity trajectories to their desired ones with repeating practices are proved theoretically. In addition, it is shown that the contact force itself converges to the desired one in the sense of L²-norm with repeating practices. Computer simulation results by using a 3 DOF manipulator are presented to demonstrate the effectiveness of the proposed method and to examine the speed of convergence of force trajectories besides position and velocity trajectories