A comparative study of dirichlet and neumann conditions for path planning through harmonic functions

Abstract

Harmonic functions, by virtue of their extrema appearing only on the domain boundary, are known to have an advantage as a global potential function in the potential field based approach for robot path planning. However, a wide range of possibilities exist for the global harmonic function for a particular situation, depending on the boundary conditions. This paper conducts a comparison of two major classes of boundary conditions, namely Dirichlet and Neumann conditions, and attempts to discover their relative merits and demerits. It is found that the Neumann conditions offer a surer and faster approach to the path planning problem, though suffering from the disadvantage of occasional tendency of the planned path to graze along the domain boundary. Keywords: Harmonic function, Motion planning, Global potential. © Springer-Verlag Berlin Heidelberg 2002.