A boundary-integral algorithm for adaptive motion planning

An algorithm is developed for adaptively computing the path of an object in a domain with arbitrary geometry in the presence of stationary or arbitrarily moving obstacles. The methodology hinges on an analogy with heat transfer where hard walls and obstacles are cold surfaces while targeted positions such as doorways or laboratory benches are hot surfaces. At any instant, the navigator moves in a direction that maximizes the rate of inward heat transport so as to get warmer. A central part of the algorithm is the fast solution of the heat transfer problem using a boundary-element method. Illustrative examples are provided for stationary and moving obstacles in sample domain geometries.