Time-optimal control of two-degree of freedom robot arms

Abstract

A dynamics model for a robot arm using state variables based on the Hamiltonian canonical equations is derived. From this model it is shown that the structure of the minimum-time control (MTC) law requires that at least one of the actuators is always saturated. A control algorithm for the MTC of a robot arm 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. A simulation of a two-degree-of-freedom arm is performed to verify the mathematical structure of the MTC law.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>