Efficient Collision Checking in Sampling-Based Motion Planning

Collision checking is generally considered to be the primary computational bottleneck in sampling-based motion planning algorithms. We show that this does not have to be the case. More specifically, we introduce a novel way of implementing collision checking in the context of sampling-based motion planning, such that the amortized complexity of collision checking is negligible with respect to that of the other components of sampling-based motion planning algorithms. Our method works by storing a lower bound on the distance to the nearest obstacle of each normally collision-checked point. New samples may immediately be determined collision free—without a call to the collision-checking procedure—if they are closer to a previously collision-checked point than the latter is to an obstacle. A similar criterion can also be used to detect points inside of obstacles (i.e., points that are in collision with obstacles). Analysis proves that the expected fraction of points that require a call to the normal (expensive) collision-checking procedure approaches zero as the total number of points increases. Experiments, in which the proposed idea is used in conjunction with the RRT and RRT∗ path planning algorithms, also validate that our method enables significant benefits in practice.