Optimal Time Trajectory Planning and Control of Space Cable Robot based on " Brachistochrone " Theory

Abstract

This paper presents optimal-time trajectory planning of Samen cable robot using optimal control theory. The optimal-time trajectory planning solution method is based on the calculus of variations method. This issue can be solved by the Pontryagin’s Minimum Principle using the Bang-Bang control. To do so, a time-cost function is considered. By turning optimal-time trajectory planning into a problem-solving procedure with a two-point boundary value problem, the solving stages begin. In addition, the beginning and the end of the path are certain, which can be solved with numerical algorithms. One of the most important and effective methods of minimum time trajectory planning is the brachistochrone method. In this study, the brachistochrone curve is introduced and solved by both brachistochrone method and minimum time trajectory planning using optimal control. First, the path generation for the robot is described using optimization methods; subsequently, with respect to appropriate cost functions, a proportional-integral-derivative controller (PID) and a sliding mode for tracking generated paths are presented. By testing the algorithms in the simulation environment, good and acceptable results are obtained. Simulation results demonstrate proper performance of the proposed method.