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