A novel path planning proposal based on the combination of deterministic sampling and harmonic functions

The sampling-based approach is currently the most successful and yet more promising approach to path planning problems. Sampling-based methods are demonstrated to be probabilistic complete, being their performance reliant on the generation of samples. To obtain a good set of samples, this paper proposes a new sampling paradigm based on a deterministic sampling sequence guided by an harmonic potential function computed on a hierarchical cell decomposition of C-space. In the proposed method, known as Kautham sampler, samples are not isolated configurations but parts of a whole. As samples are generated they are dynamically grouped into cells that capture the C-space structure. This allows the use of harmonic functions to share information and guide further sampling towards more promising regions of C-space. Finally, using the samples obtained, a roadmap is easily built taking advantage of the known neighborhood relationships.