Time-optimal extension and retraction of robots: Numerical analysis of the switching structure

The problem of the time-optimal control of robot manipulators is of importance because of its potential for increasing the productivity of assembly lines. This work is part of a series of papers by the authors on this topic using direct and indirect methods of optimization. A cylindrical robot or a spherical polar robot constrained to the horizontal plane is considered, and optimal solutions for radial maneuvers are generated. Indirect methods are employed in order to establish the switching structure of the solutions. The results show that even such apparently simple maneuvers as extension or retraction of a robot with a prismatic joint can produce very complex optimal solutions. Time-optimal retraction can exhibit ten different switching structures with eight switching points and two singular arcs.This research was supported by the Deutsche Forschungsgemeinschaft. The results reported in this paper first appeared in the thesis of the first author and were presented at the 1989 AIAA Guidance, Navigation and Control Conference (Refs. 1 and 2).