Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
The complexity of the two dimensional curvature-constrained shortest-path problem
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Feasible Trajectories for Mobile Robots with Kinematic and Environment Constraints
Intelligent Autonomous Systems, An International Conference
Nonholonomic Modeling of Needle Steering
International Journal of Robotics Research
Toward Reliable Off Road Autonomous Vehicles Operating in Challenging Environments
International Journal of Robotics Research
Action-space partitioning for planning
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Path diversity is only part of the problem
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Real-time informed path sampling for motion planning search
International Journal of Robotics Research
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Many problems in robot motion planning involve collision testing a set of local paths. In this paper we propose a novel solution to this problem by exploiting the structure of paths and the outcome of previous collision tests. Our approach circumvents expensive collision tests on a given path by detecting that the entire geometry of the path has effectively already been tested on a combination of other paths. We define a homotopy-like equivalence relation among local paths to detect this condition, and we provide algorithms that (1) classify paths based on equivalence, and (2) circumvent collision testing on up to 90% of them. We then prove both correctness and completeness of these algorithms and provide experimental results demonstrating a performance increase up to 300% in the rate of path tests. Additionally, we apply our equivalence relation to the navigation problem in a planning algorithm that takes advantage of information gained from equivalence relationships among collision-free paths. Finally, we explore applications of path equivalence to several other mechanisms, including kinematic chains and medical steerable needles.