自适应Radau伪谱法自由漂浮空间机器人轨迹规划

Free-floating space manipulator trajectory optimization based on adaptive Radau pseudospectral method

为解决Gauss伪谱法(GPM)计算速度和求解精度之间的矛盾,在多段Radau伪谱法的基础上,提出了求解自由漂浮空间机器人(FFSM)最优路径规划问题的hp自适应Radau伪谱法(hp-RPM).与传统的Gauss伪谱法不同,该方法并不是单纯通过增加节点数量来提高精度,而是在每次迭代的过程中对整个路径分段个数和各个路径子区间的宽度进行合理的分配,并能配置每个子区间内节点的数量.通过增加分段个数可以减小子区间内所需节点个数,以此降低多项式阶数、提高计算速度.基于上述理论,首先建立了多臂FFSM系统动力学模型,并给出了运动过程中系统模型更新方法;然后将连续最优轨迹规划问题离散化,完成了hp自适应Radau伪谱法的设计;最后利用hp-RPM解决两连杆FFSM系统轨迹规划问题并进行了仿真实验.结果表明:在初始条件相同的情况下,两种方法得到的位置、速度规划曲线相似,但hp-RPM在各个节点处的误差明显低于GPM计算误差;在精度要求较高,初始节点较多的情况下,hp-RPM可以在保证精度的同时有效的提高计算速度.

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 hpRPM 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.