Robot manipulator tracking control with conquering joint physical limits at angle and velocity layers based on different-layer equivalency technique

Abstract

The study of manipulator physical limits is a very important direction in the field of robotics. Most traditional approaches to addressing physical limits are typically within the framework of optimization, treating physical limits as constraints to be addressed. However, this approach has a limitation in that it may not be real-time responsive. In order to improve real-time performance, latest study in literature formulated physical limits and tracking task as different-layer time-varying problems. This approach effectively enhances real-time performance via obtaining calculated control variables in advance. Nevertheless, this study only considers joint angle limits, without taking into account the higher-layer joint velocity limits. This work conquers physical limits at angle and velocity layers simultaneously by a three-layer time-varying system. Two different ways are used to solve the system based on different-layer equivalency technique, and two differential equations are obtained. The equations are discretized by using a discretization formula, and then two discrete models are proposed. The robot tracking control conquers physical limits at angle and velocity layers simultaneously by using discrete models. Theoretical convergence of the discrete models is demonstrated. Furthermore, the effectiveness and superiority of models are also verified through numerical experiments.