Optimal trajectory planning of manipulators subject to motion constraints

This paper presents a novel approach to plan an optimal joint trajectory for a manipulator robot performing a compliant motion task. In general, a two-step scheme are deployed to find the optimal robot joint curve. Firstly, we approximate the functional and use Newton´s iteration to numerically calculate the joint trajectory´s intermediate discretized points, instead of solving a corresponding nonlinear, implicit Euler-Lagrange equation. Secondly, we interpolate these points to get the final joint curve in a way such that the motion constraints will always be sustained throughout the movement. An example of motion planning for a 4-degree-of-freedom robot WAM are given at the end of this paper