Abstract
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.
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Bialkowski, J., Karaman, S., Otte, M., Frazzoli, E. (2013). Efficient Collision Checking in Sampling-Based Motion Planning. In: Frazzoli, E., Lozano-Perez, T., Roy, N., Rus, D. (eds) Algorithmic Foundations of Robotics X. Springer Tracts in Advanced Robotics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36279-8_22
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DOI: https://doi.org/10.1007/978-3-642-36279-8_22
Publisher Name: Springer, Berlin, Heidelberg
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