Path planning plays an essential role in mobile robot navigation, and the A* algorithm is one of the best-known path planning algorithms. However, the conventional A* algorithm and the subsequent improved algorithms still have some limitations in terms of robustness and efficiency. These limitations include slow algorithm efficiency, weak robustness, and collisions when robots are traversing. In this paper, we propose an improved A*-based algorithm called EBHSA* algorithm. The EBHSA* algorithm introduces the expansion distance, bidirectional search, heuristic function optimization and smoothing into path planning. The expansion distance extends a certain distance from obstacles to improve path robustness by avoiding collisions. Bidirectional search is a strategy that searches for a path from the start node and from the goal node at the same time. Heuristic function optimization designs a new heuristic function to replace the traditional heuristic function. Smoothing improves path robustness by reducing the number of right-angle turns. Moreover, we carry out simulation tests with the EBHSA* algorithm, and the test results show that the EBHSA* algorithm has excellent performance in terms of robustness and efficiency. In addition, we transplant the EBHSA* algorithm to a robot to verify its effectiveness in the real world.