Optimization Method Based on the Minimum Action Principle for Trajectory Length of Articulated Manipulators

In addition to the performance parameters of a mechanical manipulator—such as precision, repeatability, payload and maximum speed—path optimization can bring significant improvements in terms of cycle time and energy consumption. In this paper, a method is proposed for post-processing trajectories initially generated by spline interpolation in joint space (cubic or quintic interpolation), so that the distances traveled are shorter. The principle of least action is used as a theoretical foundation trying to find the best cost function in terms of trajectory lengths using. In the pursuit of minimizing this cost function, an iterative method is applied. Initial trajectories are split into multiple internal nodes that are displaced little by little from their initial positions, recomposing trajectories that pass through these displaced nodes at every iteration. The purpose of this paper is to demonstrate that by post-processing trajectories initially generated by the usual spline interpolation in joint space, alternative, shorter variants can be obtained.