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. This minor disadvantage, however, can be remedied by a two-stage strategy, in which the solution with the Neumann condition is used to generate the Dirichlet boundary conditions for the second stage of solution.
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