Joint Trajectory Optimization for Redundant Manipulators with Constant Path Speed

Abstract

In this work, we present an approach to minimizing the time necessary for the end-effector of a redundant robot manipulator to traverse a given trajectory by optimizing the trajectory of its joints, under a number of restrictions. Each joint has limits in the ranges of position, velocity and acceleration, the latter making jerks in joint space undesirable. Furthermore, for the applications involved, the end-effector must traverse the path with high accuracy and at constant path velocity, i.e. the tip of the manipulator must cover equal distances in equal amounts of time. The proposed approach takes this nonlinear optimization problem that has two variables (path speed and joint trajectory) and solves it in two steps - First, we solve an inner subproblem that considers a fixed joint trajectory and maximizes path speed, for which we obtain a closed form solution that considers all joint velocity and acceleration restrictions. Moreover, we establish that the value of the inner subproblem is convex. Then, we solve an outer subproblem that takes a subgradient of the inner subproblem's value to update the trajectory with a Primal-Dual optimization method that considers all path accuracy and joint position restrictions. We show the efficacy of our proposed approach with simulations.