Performance Comparison of A* and Dijkstra Algorithms with Bézier Curve in 2D Grid and OpenStreetMap Scenarios

This paper presents a comparative study of the A* and Dijkstra algorithms for path planning in both 2D grid maps and real-world OpenStreetMap (OSM) environments. The evaluation focused on three key performance metrics: computational efficiency, path smoothness, and the number of turns. Both algorithms were tested under varying obstacle densities, and Bézier curve smoothing was applied to enhance path quality. In 2D grid maps, A* consistently generated smoother paths with fewer turns, especially in complex environments. Its heuristic-based search allowed it to expand fewer nodes, resulting in faster computation times compared to Dijkstra. On the other hand, Dijkstra's algorithm, though robust and optimal, exhibited longer runtimes and produced paths with more turns due to its exhaustive search approach. In the OSM-based scenarios, both algorithms yielded paths of identical length. However, A* significantly outperformed Dijkstra in terms of runtime across most test cases, further demonstrating its computational advantage. These findings validate A*’s practical advantage of real-time applications where both efficiency and path quality are crucial. While Dijkstra remains a reliable benchmark, A* offers a balanced trade-off between speed and path quality, making it more suitable for real-world path planning applications in both structured and unstructured environments.