In order to solve the problem of joint acceleration mutation in the cubic polynomial trajectory planning algorithm, the algorithm of the quintic polynomial trajectory planning is studied. The results show that the calculation of quintic polynomial trajectory planning algorithm is relatively heavy, and it can ensure the continuity of angular acceleration and stable operation of motor. Trajectory planning is carried out in Cartesian space by using the spatial line and the spatial arc interpolation algorithm. MATLAB robotics toolbox is used to model the motion system and simulate the motion, which verifies the correctness and feasibility of the linear interpolation and circular interpolation algorithm.