Error-Summation Enhanced Newton Algorithm for Model Predictive Control of Redundant Manipulators

Abstract

Redundant manipulators have been investigated and employed in various fields, and its trajectory tracking is of much importance in the field of robotic control. In this article, a model predictive control (MPC) scheme for the trajectory tracking of redundant manipulators is constructed, which minimizes the tracking error, velocity norm, and acceleration norm simultaneously. The commonly used trajectory tracking schemes for redundant manipulators, such as the minimum-velocity-norm scheme and minimum-acceleration-norm scheme, handle joint limits at different levels by introducing additional parameters, which reduces the feasible region of decision variables. In contrast, the proposed scheme directly considers these limits at three different levels, without reducing the feasible region of decision variables. In addition, to compensate for the deficiencies of most existing algorithms in noise environments, an error-summation enhanced Newton (ESEN) algorithm is proposed for solving the MPC scheme. Through theoretical analysis, it is determined that the proposed ESEN algorithm has a small steady-state error under noise conditions. Finally, in contrast with the comparative trajectory tracking schemes, as determined through computer simulations and experiments, the proposed MPC scheme solved by the ESEN algorithm not only enables the redundant manipulator to perform the trajectory tracking task in excellent fashion, but also offers advantages of high efficiency, fast responsiveness, and strong noise tolerance.