The complexity of elementary algebra and geometry
Journal of Computer and System Sciences
The complexity of robot motion planning
The complexity of robot motion planning
A random sampling scheme for path planning
International Journal of Robotics Research
OBPRM: an obstacle-based PRM for 3D workspaces
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Robot Motion Planning
Collision Detection
Mathematical and Computer Modelling: An International Journal
An unsupervised adaptive strategy for constructing probabilistic roadmaps
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
A Connectivity-Based Method for Enhancing Sampling in Probabilistic Roadmap Planners
Journal of Intelligent and Robotic Systems
A configuration deactivation algorithm for boosting probabilistic roadmap planning of robots
International Journal of Automation and Computing
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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.