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.