TY - JOUR
T1 - Probabilistic Completeness of RRT for Geometric and Kinodynamic Planning with Forward Propagation
AU - Kleinbort, Michal
AU - Solovey, Kiril
AU - Littlefield, Zakary
AU - Bekris, Kostas E.
AU - Halperin, Dan
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2019/4
Y1 - 2019/4
N2 - The rapidly exploring random tree (RRT) algorithm has been one of the most prevalent and popular motion-planning techniques for two decades now. Surprisingly, in spite of its centrality, there has been an active debate under which conditions RRT is probabilistically complete. We provide two new proofs of probabilistic completeness (PC) of RRT with a reduced set of assumptions. The first one for the purely geometric setting, where we only require that the solution path has a certain clearance from the obstacles. For the kinodynamic case with forward propagation of random controls and duration, we only consider in addition mild Lipschitz-continuity conditions.These proofs fill a gap in the study of RRT itself. They also lay sound foundations for a variety of more recent and alternative sampling based methods, whose PC property relies on that of RRT.
AB - The rapidly exploring random tree (RRT) algorithm has been one of the most prevalent and popular motion-planning techniques for two decades now. Surprisingly, in spite of its centrality, there has been an active debate under which conditions RRT is probabilistically complete. We provide two new proofs of probabilistic completeness (PC) of RRT with a reduced set of assumptions. The first one for the purely geometric setting, where we only require that the solution path has a certain clearance from the obstacles. For the kinodynamic case with forward propagation of random controls and duration, we only consider in addition mild Lipschitz-continuity conditions.These proofs fill a gap in the study of RRT itself. They also lay sound foundations for a variety of more recent and alternative sampling based methods, whose PC property relies on that of RRT.
KW - Motion and path planning
KW - nonholonomic motion planning
UR - http://www.scopus.com/inward/record.url?scp=85063306551&partnerID=8YFLogxK
U2 - 10.1109/LRA.2018.2888947
DO - 10.1109/LRA.2018.2888947
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AN - SCOPUS:85063306551
SN - 2377-3766
VL - 4
SP - 277
EP - 283
JO - IEEE Robotics and Automation Letters
JF - IEEE Robotics and Automation Letters
IS - 2
M1 - 8584061
ER -