Robot trajectory planning is a focus area of robot motion control research, relating directly to the working efficiency of robots. To keep robots moving at a continuously angular velocity and angular acceleration, a cubic spline interpolation function was used for robot motion trajectory planning in this paper. Considering that an excessively fast angular velocity and excessively high angular acceleration would bring about vibrations and shocks to the robot system, the particle swarm optimization algorithm was used to optimize robot motion time under the constraints of angular velocity and angular acceleration to enable robots to move smoothly in time-optimal conditions. Finally, the MATLAB robotics toolbox was used to conduct a simulation experiment. The experimental results proved the practical applicability of this method to robot trajectory planning.