To address the issues of excessive redundant nodes and path curvature in the paths generated by traditional A* algorithm for mobile robots, this paper proposes a path planning algorithm based on the heuristic function Ax. Firstly, a weighting coefficient is incorporated into the heuristic function to mitigate local optima problems, thereby balancing search speed and accuracy. Simultaneously, three search directions are discarded to reduce computational burden and enhance search speed. Secondly, to mitigate the risk of collisions caused by path curvature, the proposed algorithm employs a key point extraction strategy to reduce the number of turning points and introduces multiple second-order Bézier curves to smooth the resultant path. Lastly, validation and analysis are conducted using the MATLAB simulation platform. Compared to the traditional A* algorithm, Ax demonstrates faster average search speed and fewer nodes, thus validating the effectiveness of the proposed algorithm.