Learning Control for Robot Manipulators Under Geometric Endpoint Constraint

Abstract

A learning control scheme for a class of robot manipulators whose end point is geometrically constrained is proposed. This scheme is based on only PD feedback control and composed of a simple recursive update law, which makes the next actuator input torque consist of the vector of previous angular velocity errors and the force error at the manipulator endpoint constrained on a surface.
A theoretical proof of the uniform boundedness of velocity and position trajectory errors and the convergence to their given desired trajectories is presented. Simulation results by using a 3 DOF manipulator whose end point constrained on a vertical surface in the gravity field are presented to demonstrate the efficiency of the proposed method and the convergence of trajectories.
In these simulations, it is observed that the force trajectories at the end point converge to the desired one simultaneously together with the convergence of position and velocity trajectories. However, a theoretical proof on the convergence of force trajectories remains unsolved.