TY - JOUR
T1 - Near-Optimal Multi-Robot Motion Planning with Finite Sampling
AU - Dayan, Dror
AU - Solovey, Kiril
AU - Pavone, Marco
AU - Halperin, Dan
N1 - Publisher Copyright:
© 2004-2012 IEEE.
PY - 2023/10/1
Y1 - 2023/10/1
N2 - An underlying structure in several sampling-based methods for continuous multirobot motion planning (MRMP) is the tensor roadmap, which emerges from combining multiple probabilistic roadmap (PRM) graphs constructed for the individual robots via a tensor product. We study the conditions under which the tensor roadmap encodes a near-optimal solution for MRMP - satisfying these conditions implies near optimality for a variety of popular planners, including dRRT*, and the discrete methods M∗ and conflict-based search, when applied to the continuous domain. We develop the first finite-sample analysis of this kind, which specifies the number of samples, their deterministic distribution, and magnitude of the connection radii that should be used by each individual PRM graph, to guarantee near-optimality using the tensor roadmap. This significantly improves upon a previous asymptotic analysis, wherein the number of samples tends to infinity. Our new finite sample-size analysis supports guaranteed high-quality solutions in practice within finite time. To achieve our new result, we first develop a sampling scheme, which we call the staggered grid, for finite-sample motion planning for individual robots, which requires significantly fewer samples than previous work. We then extend it to the much more involved MRMP setting, which requires to account for interactions among multiple robots. Finally, we report on a few experiments that serve as a verification of our theoretical findings and raise interesting questions for further investigation.
AB - An underlying structure in several sampling-based methods for continuous multirobot motion planning (MRMP) is the tensor roadmap, which emerges from combining multiple probabilistic roadmap (PRM) graphs constructed for the individual robots via a tensor product. We study the conditions under which the tensor roadmap encodes a near-optimal solution for MRMP - satisfying these conditions implies near optimality for a variety of popular planners, including dRRT*, and the discrete methods M∗ and conflict-based search, when applied to the continuous domain. We develop the first finite-sample analysis of this kind, which specifies the number of samples, their deterministic distribution, and magnitude of the connection radii that should be used by each individual PRM graph, to guarantee near-optimality using the tensor roadmap. This significantly improves upon a previous asymptotic analysis, wherein the number of samples tends to infinity. Our new finite sample-size analysis supports guaranteed high-quality solutions in practice within finite time. To achieve our new result, we first develop a sampling scheme, which we call the staggered grid, for finite-sample motion planning for individual robots, which requires significantly fewer samples than previous work. We then extend it to the much more involved MRMP setting, which requires to account for interactions among multiple robots. Finally, we report on a few experiments that serve as a verification of our theoretical findings and raise interesting questions for further investigation.
KW - Motion planning
KW - multi-agent systems
KW - multi-robot systems
KW - sampling methods
UR - http://www.scopus.com/inward/record.url?scp=85163448027&partnerID=8YFLogxK
U2 - 10.1109/TRO.2023.3281152
DO - 10.1109/TRO.2023.3281152
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AN - SCOPUS:85163448027
SN - 1552-3098
VL - 39
SP - 3422
EP - 3436
JO - IEEE Transactions on Robotics
JF - IEEE Transactions on Robotics
IS - 5
ER -