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Free-configuration biased sampling for motion planning

In sampling-based motion planning algorithms the initial step at every iteration is to generate a new sample from the obstacle-free portion of the configuration space. This is usually accomplished via rejection sampling, i.e., repeatedly drawing points from the entire space until an obstacle-free point is found. This strategy is rarely questioned because the extra work associated with sampling (and then rejecting) useless points contributes at most a constant factor to the planning algorithm's asymptotic runtime complexity. However, this constant factor can be quite large in practice. We propose an alternative approach that enables sampling from a distribution that provably converges to a uniform distribution over only the obstacle-free space. Our method works by storing empirically observed estimates of obstacle-free space in a point-proximity data structure, and then using this information to generate future samples. Both theoretical and experimental results validate our approach.