An Efficient Computation of Time-Optimal Control Trajectory for Robotilc Point-to-Point Motion

Abstract

This paper presents a two-phase computational method for time-optimal control of robotic systems with point-topoint motions. In the first phase, the original time-optimal control (TOC) problem with possible discontinuilies and singular arcs in control is convened into one with continuous and nonsingular control trajectories by adding to the performance index a perturbed energy term. The resultant two-point boundary value problem (TPBVP) can easily be solved for an appropriately large value of the pertwbation parameter. In the second phase, a continuation method is developed to obtain the solution to the original TOC problem by solving a set of initial value probliems sequentially andor in parallel. The proposed two-phase method is computationally eficient since the resulting TPBVP is solved only once and the remaining problem becomes solutions to a set of initial value sub-problems. The proposed algorithm is, therefore, applicable to more complex systems such as multi-am robot systems moving a common object. The practicability of the method is demonstrated by computer simulations on an [cxample robot system with different motion configurations.