Minimum-time control laws for robotic manipulators

Abstract

This work addresses the problem of minimum-time control (MTC) for rigid robotic manipulators with point-to-point motion subject to 'hard' constraints on the control torques. A hamiltonian canonical formulation of the robot dynamic equations is used. A perturbation-based transformation algorithm is applied to solve this category of the MTC problem. In this algorithm, the original MTC problem, possibly a partially singular one, is converted into a totally non-singular optimal control problem by introducing a perturbed energy term into the original objective functional. It is shown that in the limiting case the solution to the transformed problem is convergent to that of the original MTC problem. The numerical solutions to several example manipulators are presented to verify the theoretical result on the structure of the MTC law. Some of the characteristics of the resulting optimal trajectories are analyzed by using a dynamic scaling approach. The result provides new insight into the dynamic characteristics of robot arms, pertaining to both path planning and design specifications.