Potential-Based Modeling of Three Dimensional Workspace for Obstacle Avoidance

A potential-based model of three-dimensional (3D) workspace is proposed in this paper for ensuring obstacle avoidance in path planning. It is assumed that the workspace boundary is uniformly distributed with generalized charges. The potential due to a point charge is inversely proportional to the distance to the power of an integer, the order of the potential function. It is shown that such potential functions and their gradients due to polyhedral surfaces can be derived analytically, and thus can facilitate efficient collision avoidance. Intuitively, the potential fields and their effects on object paths should be spatially continuous and smooth. The continuity and differentiability properties of a particular potential function are investigated. In theory, by minimizing the repulsion between object and obstacles, the approach completely eliminates the possibility of a collision between them if the dynamics of the moving object is ignored.