Robotic Path Planning Using Artificial Potential Field Method

To determine the shortest path within a potential field, it is essential to model both repulsive forces from obstacles and attractive forces toward the target. This simulation typically involves calculating potential values across the configuration space, where obstacles generate high-potential regions (repulsive fields) and the target creates low-potential regions (attractive fields). The artificial potential field method implements this through gradient descent navigation, where the robot follows the negative gradient of the combined potential field. Key implementation steps include defining attraction potential using quadratic functions (e.g., U_att(q) = ½k‖q - q_goal‖²) and repulsion potential using inverse-distance functions (e.g., U_rep(q) = ½η(1/d(q) - 1/d₀)² when d(q) ≤ d₀). Path optimization can be enhanced through integration with search algorithms like A* or Dijkstra's algorithm, which operate on discretized grid representations of the potential field. The A* algorithm particularly excels here by combining actual path cost (g-score) with heuristic estimates (h-score) derived from potential field gradients. This hybrid approach enables efficient obstacle avoidance while guaranteeing optimal path convergence when admissible heuristics are used. Through proper tuning of potential field parameters and algorithm integration, the system achieves minimum-time path planning with robust collision avoidance capabilities.