Potential Fields

The potential fields method is a technique used in motion planning that models the environment as a scalar field of forces. Each object in the environment exerts an attractive force towards the goal and repulsive forces away from obstacles. The resultant force acting on a robot is derived from the superposition of these attractive and repulsive fields, guiding the robot towards the goal while avoiding collisions. Mathematically, the potential function U can be expressed as U = U_attractive + U_repulsive, where U_attractive decreases as the robot approaches the goal, and U_repulsive increases as the robot nears obstacles. This method is particularly effective for real-time applications due to its simplicity and computational efficiency. However, it can suffer from local minima, where the robot may get stuck in a position that is not optimal. Potential fields are foundational in robotics and are often integrated with other planning techniques to enhance performance.