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Several randomized path planners have been proposed dur ing the last few years. Their attractiveness stems from their applicability to virtually any type of robots, and their empir ically observed success. In this article, 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 configuration space. We then describe two previously developed planners as instances of planners based on this scheme, but applying very different sampling strategies. These planners are probabilis tically complete: if a path exists, they will find 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 characteriz ing the "goodness" of the robot's free space, we show that the
Barraquand et al. (Mon,) studied this question.