Efficient algorithm for time-optimal control of a two-link manipulator

Abstract

A class of optimization problems of interest in the field of robotics is one that seeks to minimize the time required to force a manipulator to travel a specified distance. Robots employ multiple, bounded control inputs. This work describes a new, very fast algorithm for determining minimum-time trajectories for such systems. We have modified the steepest descent method of optimal programming to find time-optimal switch times for bang-bang control systems. The Switch Time Optimization (STO) program has been applied to a two-link manipulator with two control inputs. To find the minimum time for a robot end-effector to travel between two points in its workspace, one must establish the optimal position of the robot with respect to the work station. The algorithm accomplishes this by allowing optimal initial states to be determined along with the time history of the controls. Exact control switch times and optimal initial conditions have been found for minimum-time repositioning maneuvers in which the robot was required to travel a specified distance. The STO algorithm is not limited to use with manipulators; it is applicable to any bang-bang system.