Optimal Motion Planning Passing Through Kinematic Singularities for Robot Arms

Path-constrained optimal trajectory planning for serial-link robot arms has been extensively studied in the past decades. As an interesting topic in the robot motion planning and control, the kinematic singularity problem also attracted much attention in the literatures. In this paper, we present a systematic approach to plan an optimal trajectory passing though kinematic singularities with the end-effector precisely tracking the desired path. The method follows two steps. In the first step, the desired path is parameterized with a geometric variable q₀. The robot motion can then be represented as a spatial curve in the joint space augmented by q₀. The spatial curve, called augmented path, is obtained by numeric method as a function of another parameter s, which represents the arc-length of the augmented path. In the second step, the optimal trajectory with respect to time can be solved by optimally assigning s(t) along the augmented path. Dynamic programming is adopted in this paper to fulfill the optimal computation. Numerical simulations are carried out to verify the presented approach