A Random Sampling Scheme for Path Planning

Abstract

Several randomized p ath planners have been proposed during the last few years. Their attractiveness stems from their applicability to virtually any type o f r obots, and their empirically observed s u c cess. In this paper we attempt to present a unifying view of these planners and to theoretically explain their success. First, we introduce a general planning scheme that consists of randomly sampling the robot's con guration space. We then describe t w o p r eviously developed planners as instances of planners based on this scheme, but applying very di erent sampling strategies. These planners are p r obabilistically complete: if a path exists, they will nd one with high probability, if we let them run long enough. Next, for one of the planners, we analyze the relation between the probability of failure and the running time. Under assumptions characterizing the \goodness" of the robot's free s p ace, we show that the running time only grows as the absolute value of the logarithm of the probability of failure t h a t w e a r e willing to tolerate. We also show that it increases at a reasonable ra t e a s t h e s p ace g o odness degrades. In the last section we suggest directions for future r esearch.

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