A hierarchical and dynamic method to compute harmonic functions for constrained motion planning

Robot path planning copes with the planning of a collision-free path for the robot from an initial configuration to a goal configuration. The potential field method is one of the main approaches to path planning, and the use of harmonic functions allows the definition of potential fields without local minima and with the ability to be incrementally updated. Constrained motion planning copes with the planning of motions in cluttered environments with low clearances and high uncertainties. The robust, adaptive and reactive behavior of the harmonic functions approach suits the requirements of constrained motion planning. To efficiently compute harmonic functions for this purpose, the paper presents a hierarchical and dynamic method that works on a non-regular grid decomposition of configuration space.