A proof of the structure of the minimum-time control law of robotic manipulators using a Hamiltonian formulation

Abstract

A Hamiltonian canonical formulation that yields a new and straightforward proof of the structure of the minimum-time control (MTC) law for m-link robotic manipulators is used. It is shown that the structure of the MTC law requires that at least one of the actuators always be in saturation. A numerical algorithm is presented. The algorithm converts the original problem, possibly a partially singular one, into a totally nonsingular optimal control problem by introducing a perturbed energy term in the performance index. It is shown that the solution to the perturbed problem converges to that of the MTC problem in the sense of the performance index as the perturbation parameter approaches zero. The control algorithm is used in a simulation to verify the MTC law structure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>