Complete trajectory planning includes path planning, inverse solution solving and trajectory optimization. In this paper, a highly smooth and time-saving approach to trajectory planning is obtained by improving the kinematic and optimization algorithms for the time-optimal trajectory planning problem. By partitioning the joint space, the paper obtains an inverse solution calculation based on the partitioning of the joint space, saving 40% of the inverse kinematics solution time. This means that a large number of computational resources can be saved in trajectory planning. In addition, an improved sparrow search algorithm (SSA) is proposed to complete the solution of the time-optimal trajectory. A Tent chaotic mapping was used to optimize the way of generating initial populations. The algorithm was further improved by combining it with an adaptive step factor. The experiments demonstrated the performance of the improved SSA. The robot's trajectory is further optimized in time by an improved sparrow search algorithm. Experimental results show that the method can improve convergence speed and global search capability and ensure smooth trajectories.