With the rapid development of robotics technology, path planning is a crucial aspect of autonomous robot systems. Among them, planning paths involves using the A* algorithm, which is a common method. However, traditional A* algorithm has several limitations in path planning, such as poor real-time performance, large amount of computation per node, long computation time, low algorithmic search efficiency. Based on this, two improved approaches for the A* algorithm are proposed. The first is expanding the obstacles in the map by increasing their expansion radius. The second is the Hybrid A* algorithm, which optimizes the A* algorithm by modifying its heuristic function. Specifically, the Hybrid A* algorithm combines two heuristic functions: one based on non-holonomic constraints and the other based on dynamic programming. Experimental tests are conducted under various map expansions and branching parameters to compare the performance of these two algorithms in terms of path length, execution time, and path smoothness at corners. The results demonstrate that, with smaller branching parameters, the Hybrid A* algorithm generates shorter paths. However, in highly complex mazes, the path length of the Hybrid A* algorithm may be longer, but it exhibits smoother movements at corners.