Robotic navigation using harmonic function-based probabilistic roadmaps

This paper presents a new hybrid motion planning technique based on harmonic functions (HF) and probabilistic roadmaps (PRM). The proposed harmonic function based probabilistic roadmap (HFPRM) method comprises three phases: in phase one, the Laplace's equation, pertinent to potential flow, in an environment cluttered with obstacles is solved. In phase two, a probabilistic roadmap with a novel sampling scheme is constructed based on information obtained about the environment topology through the HF technique developed in phase one. The roadmap is then searched for the shortest path in phase three. Simulation results presented in this paper show that the combination of the HF and the PRM works better than each individual in terms of finding a collision free path in environments where narrow passages exist. The proposed HFPRM method can be extended to sensor-based motion planning problem in environments not known a priori.