Learning control for robot tasks under geometric endpoint constraints

A theory of training-based learning control is developed for a class of robotic tasks under geometric endpoint constraints. An algorithm for updating the control input which makes the next input consist of the previous input plus modified terms of previous velocity and force errors at the robot endpoint constrained on a surface is proposed. Simulation results are presented to demonstrate the convergence of position and force tracking to a desired path with force specified on the surface. It is shown that the robot dynamics satisfies the passivity condition regarding the joint torque input vector versus the joint velocity vector, even in the case of geometric constraints. A theoretical proof of the convergence of position and force errors is given. In the proof, a relaxed concept of passivity of error dynamics of robot arms plays a crucial role