In order to achieve the fastest fire-fighting purpose, warehouse autonomous mobile fire-fighting robots need to make an overall optimal planning based on the principle of the shortest time for their traveling path. A∗ algorithm is considered as a very ideal shortest path planning algorithm, but the shortest path is not necessarily the optimal path for robots. Furthermore, the conventional A∗ algorithm is affected by the search neighborhood restriction and the theoretical characteristics, so there are many problems, which are closing to obstacles, more inflection points, more redundant points, larger total turning angle, etc. Therefore, A∗ algorithm is improved in eight ways, and the inflection point prior strategy is adopted to compromise Floyd algorithm and A∗ algorithm in this paper. According to the criterion of the inflection point in this paper, the path inflection point arrays are constructed and traveling all path nodes are replaced by traveling path inflection points for the conventional Floyd algorithm backtracking, so it greatly reduces the backtracking time of the smooth path. In addition, this paper adopts the method of the extended grid map obstacle space in path planning safety distance. According to the relationship between the actual scale of the warehouse grid map and the size of the robot body, the different safe distance between the planning path and the obstacles is obtained, so that the algorithm can be applied to the safe path planning of the different size robots in any map environments. Finally, compared with the conventional A∗ algorithm, the improved algorithm reduces by 7.846% for the path length, reduces by 71.429% for the number of the cumulative turns, and reduces by 75% for the cumulative turning angle through the experiment. The proposed method can ensure robots to move fast on the planning path and ultimately achieve the goal of reducing the number of inflection points, reducing the cumulative turning angle, and reducing the path planning time.