This paper presents a novel approach to plan the optimal joint trajectory for a manipulator robot performing constrained motion tasks. In general, a two-step scheme will be deployed to find the optimal robot joint curve. Firstly, instead of solving a nonlinear, implicit Euler-Lagrange equation, we discretize the corresponding cost function and use Newton's iterations to numerically calculate the joint trajectory's intermediate discrete points. Secondly, we interpolate these points to get the final joint trajectory in a way such that the motion constraint will always be sustained throughout the movement. An example of motion planning for a 4-degree-of-freedom robot WAM will be given at the end of this paper.
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