Boundary value problem formulation of pursuit-evasion in a known stationary environment: a potential field approach

In this paper, pursuit-evasion in a known cluttered stationary environment is formulated as a Boundary Value Problem. The devised approach is a generalization of the Harmonic Potential approach 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 constructs a first order time dependent nonlinear differential equation to generate a trajectory leading from an initial point to the target. The planning process enjoys an objectivity that enables it to guarantee interception regardless of the intelligence of the maneuver that the target may employ to avoid being captured (a complete planner). It also has a causal implementation making it possible to lay a course for interception without apriori knowing the path of 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 are also provided.