Intercepting a maneuvering target in a multidimensional stationary environment using a wave equation potential field strategy

This paper presents a potential-based technique for intercepting a maneuvering target that is moving amidst known stationary obstacles. The method is a generalization of the Harmonic Potential approach which is used to plan a path to a stationary target. It employs a time dependent potential field that is generated using the linear Wave Equation. It then construct a first order time dependent nonlinear differential equation to generate a trajectory leading from an initial point to the target. Proofs of the ability of the technique to converge to the target as well as its ability to avoid obstacles are supplied. Simulation results and comparisons with other approaches are also provided.