Aiming at the multi-point path planning problem of mobile robots, a path planning algorithm combining ant colony algorithm and bat algorithm is proposed in this paper. The ant colony algorithm is used to establish the shortest path network between nodes. The pointing angle and turning angle are introduced as heuristic information in the traditional ant colony algorithm to reduce the paths' turning times and turning angles. The reward and punishment mechanism is used to optimize the pheromone updating mode and improve the convergence speed of the algorithm. The objective function of multi-point path planning is based on the shortest path network. When solving the optimal node access order, the structure of the bat algorithm is improved, the hierarchical search method and a new local optimization mechanism are introduced, and the bat algorithm's solving accuracy, speed, and stability are improved. The simulation results demonstrate that the proposed algorithm effectively addresses the issue of multi-point path planning. In comparison to existing algorithms, it exhibits lower computational complexity, higher search efficiency, smoother overall paths, and shorter lengths.