An analytically tractable potential field model of free space and its application in obstacle avoidance

An analytically tractable potential field model of free space is presented in this paper. The model assumes that the border of every two-dimensional (2-D) region is uniformly charged. It is shown that the potential and the resulting repulsion (force and torque) between polygonal regions can be calculated in closed form. By using the Newtonian potential function, collision avoidance between object and obstacle thus modeled is guaranteed in a path planning problem. A local planner is developed for finding object paths going through narrow areas of free space where the obstacle avoidance is most important. Simulation results show that not only does individual object configuration of a path obtained with the proposed approach avoid obstacles effectively, the configurations also connect smoothly into a path.