Harmonic functions and collision probabilities

Abstract

This paper describes a relationship between harmonic functions (used for path planning) and work on randomization and learning in robotics. In short, the hitting probabilities for random walks can be cast as a Dirichlet problem for harmonic functions, in much the same way as in path planning. This equivalence has implications both for uncertainty in motion planning and in some robot learning problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>