自适应Radau伪谱法自由漂浮空间机器人轨迹规划

To solve the contradiction between calculation speed and accuracy of Gauss Pseudo-spectral Method(GPM), a novel hp-adaptive Radau Pseudo-spectral Method(hp-RPM) is proposed for the Optimal Trajectory Planning issue in Free-Floating Space Manipulator(FFSM). Based on the multi-segment Radau Pseudo-spectral Method, the proposed method can allocate segment-numbers of total paths and the width of each sub-interval during iteration process, and configure the number of nodes in each sub-interval. By increasing the number of segment, the number of nodes and the order of polynomial can be reduced, saving the calculation speed as well. Based on the above theory, this paper first establishes the dynamic model of multi-arm FFSM system and develops a method for updating this model. Then, the continuous optimal trajectory planning problem is discretized and the design of hp-RPM is described. Finally, the hp-RPM is used to solve the trajectory planning problem of two-link FFSM system and the simulation is conducted. The result shows that the position and velocity planning curves of the two methods are similar under the same initial condition, but the error of hp-RPM at each node is obviously lower than that of the GPM. In the case of higher precision and more initial nodes, hp-RPM can effectively improve the computation speed and guarantee the accuracy simultaneously.