Reachability-based analysis for Probabilistic Roadmap planners

In the last fifteen years, sampling-based planners like the Probabilistic Roadmap Method (prm) have proved to be successful in solving complex motion planning problems. While theoretically, the complexity of the motion planning problem is exponential in the number of degrees of freedom, sampling-based planners can successfully handle this curse of dimensionality in practice. We give a reachability-based analysis for these planners which leads to a better understanding of the success of the approach. This analysis compares the techniques based on coverage and connectivity of the free configuration space. The experiments show, contrary to general belief, that the main challenge is not getting the free space covered but getting the nodes connected, especially when the problems get more complicated, e.g. when a narrow passage is present. By using this knowledge, we can tackle the narrow passage problem by incorporating a refined neighbor selection strategy, a hybrid sampling strategy, and a more powerful local planner, leading to a considerable speed-up.