Optimal point-to-point motion planning of flexible parallel manipulator with adaptive Gauss pseudo-spectral method

Optimal point-to-point motion planning of flexible parallel manipulator was investigated in this paper. First, the dynamic model of a 3RRR planar parallel manipulator was derived through Kane equation and the improved curvature-based finite element (ICFE) method. Secondly, an optimal point-to-point motion planning problem was constructed with consideration of the flexible dynamic model. Then, an adaptive Gauss Pseudo-spectral Method (GPM) was proposed to transcribe the trajectory optimization problem into Nonlinear Programming (NLP) problem, and the SQP was adopted to solve the NLP problem. At last, the simulation was carried out on a 3RRR flexible parallel manipulator, the result showed residue vibration of the flexible links can be diminished and the predefined accuracy can be satisfied by adding collocation points or refining the mesh interval through the proposed adaptive algorithm.