An application of optimal control theory to the trajectory tracking of rigid robot manipulators

Abstract

Abstract In this paper optimal control theory is applied to the trajectory tracking problem for a rigid robot manipulator. First a stability result is developed showing the relationship between optimal control theory and the global exponential stability of a class of second‐order non‐linear systems. Next this class of nonlinear systems is shown to contain the trajectory tracking error dynamics for a rigid robot manipulator when using a modified computed torque controller with an auxiliary input. Finally the stability result is applied to the tracking error dynamics to determine the auxiliary input to the robot controller. The result is a non‐linear feedback control law which provides exponentially stable position and velocity tracking for a rigid robot manipulator without complete feedback linearization of the robot dynamics.