Harmonic Functions and Collision Probabilities

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Harmonic Functions and Collision Probabilities
There is a close relationship between harmonic functions { which have recently been proposed for path planning { and hitting probabilities for random processes. 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 the application of machine learning techniques to some robot problems. In particular, Erdmann's method can directly incorporate such hitting probabilities. In addition, the value functions obtained by reinforcement learning algorithms can be rapidly reconstructed by relaxation or resistive networks, once the extrema for such functions are known.
Christopher I. Connolly
Added 08 Aug 2010
Updated 08 Aug 2010
Type Conference
Year 1994
Where ICRA
Authors Christopher I. Connolly
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