TY - GEN
T1 - Multi-agent path planning and network flow
AU - Yu, Jingjin
AU - Lavalle, Steven M.
N1 - Funding Information:
The authors thank Max Katsev for double checking the proofs and the anonymous reviewers for their constructive suggestions. This work was supported in part by NSF grants 0904501 (IIS Robotics) and 1035345 (Cyberphysical Systems), DARPA SToMP grant HR0011-05-1-0008, and MURI/ONR grant N00014-09-1-1052.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2013.
PY - 2013
Y1 - 2013
N2 - This paper connects multi-agent path planning on graphs (roadmaps) to network flow problems, showing that the former can be reduced to the latter, therefore enabling the application of combinatorial network flow algorithms, as well as general linear program techniques, tomulti-agent path planning problems on graphs. Exploiting this connection, we show that when the goals are permutation invariant, the problem always has a feasible solution path set with a longest finish time of no more than n+V −1 steps, in which n is the number of agents and V is the number of vertices of the underlying graph.We then give a complete algorithm that finds such a solution in O(nVE) time, with E being the number of edges of the graph. Taking a further step, we study time and distance optimality of the feasible solutions, show that they have a pairwise Pareto optimal structure, and again provide efficient algorithms for optimizing two of these practical objectives.
AB - This paper connects multi-agent path planning on graphs (roadmaps) to network flow problems, showing that the former can be reduced to the latter, therefore enabling the application of combinatorial network flow algorithms, as well as general linear program techniques, tomulti-agent path planning problems on graphs. Exploiting this connection, we show that when the goals are permutation invariant, the problem always has a feasible solution path set with a longest finish time of no more than n+V −1 steps, in which n is the number of agents and V is the number of vertices of the underlying graph.We then give a complete algorithm that finds such a solution in O(nVE) time, with E being the number of edges of the graph. Taking a further step, we study time and distance optimality of the feasible solutions, show that they have a pairwise Pareto optimal structure, and again provide efficient algorithms for optimizing two of these practical objectives.
UR - http://www.scopus.com/inward/record.url?scp=85009433889&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85009433889&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-36279-8_10
DO - 10.1007/978-3-642-36279-8_10
M3 - Conference contribution
AN - SCOPUS:85009433889
SN - 9783642362781
T3 - Springer Tracts in Advanced Robotics
SP - 157
EP - 173
BT - Springer Tracts in Advanced Robotics
A2 - Frazzoli, Emilio
A2 - Roy, Nicholas
A2 - Lozano-Perez, Tomas
A2 - Rus, Daniela
PB - Springer Verlag
T2 - 10th International Workshop on the Algorithmic Foundations of Robotics, WAFR 2012
Y2 - 13 June 2012 through 15 June 2012
ER -