A frequent problem in the use of potential functions for robot path planning is that local minima often occur. These local minima may be eliminated by judicious selection of potential functions for goals and obstacles. Specifically, harmonic functions may be used without introducing such minima. While there are analytic, easily superposed solutions for impenetrable point obstacles, this is not the case for impenetrable obstacles with finite, nonzero extent (e.g., walls). Instead, numerical methods that are well suited to massively parallel computation can be used.
C. I. Connolly,
J. B. Burns,
"Harmonic Functions for Robot Path Construction", Proc. SPIE 1196, Intelligent Control and Adaptive Systems, (1 February 1990); doi: 10.1117/12.969910; https://doi.org/10.1117/12.969910