Adaptive perturbation control with feedforward compensation for robot manipulators

Abstract

An adaptive perturbation control can track a time-based joint trajectory as closely as possible for all times over a wide range of manipulator motion and payloads. The adaptive control is based on the linearized perturbation equations in the vicinity of a nominal trajectory. The highly coupled nonlinear dynamic equations of a manipulator are expanded in the vicinity of a nominal trajectory to obtain the perturbation equations. The controlled system is characterized by feedforward and feedback components which can be computed separately and simulta neously. Given the joint trajectory set points, the feedforward component computes the corresponding nominal torques from the Newton-Euler equations of motion to compensate for all the interactions between joints. The feedback component, consisting of recursive least square identification and an optimal adaptive self-tuning control algorithm for the linearized system, computes the perturbation torques which reduce the position and veloc ity errors of the manipulator along the nominal trajectory. Because of the parallel structure, computations of the adaptive control may be implemented in low-cost microprocessors. This adaptive control strategy reduces the manipulator control prob lem from a nonlinear control to controlling a linear control system about a desired trajectory. Computer simulation results demonstrated its applicability to a three-joint PUMA robot arm.