DDM: Fast Near-Optimal Multi-Robot Path Planning Using Diversified-Path and Optimal Sub-Problem Solution Database Heuristics

We propose a novel centralized and decoupled algorithm, DDM, for solving multi-robot path planning problems in grid graphs, targeting on-demand and automated warehouse-like settings. Two settings are studied: a traditional one whose objective is to move a set of robots from their respective initial...

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Published inIEEE robotics and automation letters Vol. 5; no. 2; pp. 1349 - 1356
Main Authors Han, Shuai D., Yu, Jingjin
Format Journal Article
LanguageEnglish
Published Piscataway IEEE 01.04.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
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ISSN2377-3766
2377-3766
DOI10.1109/LRA.2020.2967326

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Abstract We propose a novel centralized and decoupled algorithm, DDM, for solving multi-robot path planning problems in grid graphs, targeting on-demand and automated warehouse-like settings. Two settings are studied: a traditional one whose objective is to move a set of robots from their respective initial vertices to the goal vertices as quickly as possible, and a dynamic one which requires frequent re-planning to accommodate for goal configuration adjustments. Among other techniques, DDM is mainly enabled through exploiting two innovative heuristics: path diversification and optimal sub-problem solution databases. The two heuristics attack two distinct phases of a decoupling-based planner: while path diversification allows the more effective use of the entire workspace for robot travel, optimal sub-problem solution databases facilitate the fast resolution of local path conflicts. Extensive evaluation demonstrates that DDM achieves high levels of scalability and solution quality close to the optimum.
AbstractList We propose a novel centralized and decoupled algorithm, DDM , for solving multi-robot path planning problems in grid graphs, targeting on-demand and automated warehouse-like settings. Two settings are studied: a traditional one whose objective is to move a set of robots from their respective initial vertices to the goal vertices as quickly as possible, and a dynamic one which requires frequent re-planning to accommodate for goal configuration adjustments. Among other techniques, DDM is mainly enabled through exploiting two innovative heuristics: path diversification and optimal sub-problem solution databases. The two heuristics attack two distinct phases of a decoupling-based planner: while path diversification allows the more effective use of the entire workspace for robot travel, optimal sub-problem solution databases facilitate the fast resolution of local path conflicts. Extensive evaluation demonstrates that DDM achieves high levels of scalability and solution quality close to the optimum.
Author Han, Shuai D.
Yu, Jingjin
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Cites_doi 10.1109/IROS.2006.282536
10.15607/RSS.2009.V.003
10.1109/IROS.2005.1545306
10.1109/LRA.2016.2524067
10.1109/ROBOT.2010.5509502
10.1109/ROBOT.2002.1014852
10.1613/jair.2241
10.15607/RSS.2018.XIV.013
10.1007/s11036-009-0153-x
10.1016/j.artint.2014.11.001
10.1109/LRA.2019.2894217
10.1109/CDC.2012.6426233
10.15607/RSS.2009.V.018
10.1177/0278364913515307
10.1177/0278364913506268
10.1007/978-3-642-22670-0_1
10.1109/ROBOT.2004.1307146
10.1109/TRO.2016.2593448
10.1109/ROBOT.2008.4543489
10.24963/ijcai.2019/76
10.1109/ROBOT.2009.5152773
10.1109/MRS.2019.8901065
10.1109/ROBOT.2009.5152696
10.1016/S0921-8890(02)00256-7
10.1177/0278364905059067
10.1109/ROMAN.2012.6343737
10.1007/11527862_18
10.1109/TRO.2011.2120810
10.1109/70.736775
10.15607/RSS.2015.XI.011
10.1109/ICAR.1997.620182
10.1007/978-3-642-32695-0_50
10.1023/A:1008937911390
10.1109/ROBOT.2008.4543392
10.21236/ADA196213
10.1109/IROS.1995.525802
10.1007/978-3-319-16595-0_1
10.1109/TRO.2016.2623345
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References ref13
ref12
ref15
stern (ref21) 2019
ref14
barer (ref48) 0
ref52
ref54
ref10
ref17
ref16
ref19
ref18
wurman (ref2) 2008; 29
ref51
ref50
ref46
ref45
ref47
sigurdson (ref32) 2019
ref42
ref44
ref43
ref49
han (ref55) 2019
ref8
ref7
cohen (ref27) 0
ref9
ref4
ref3
ref6
erdem (ref23) 0
ref5
ma (ref33) 0
ref40
ref35
pereira (ref53) 0
ref34
wurman (ref20) 0
ref37
ref36
ref30
wang (ref28) 2011; 42
guo (ref11) 0
ref39
ref38
boyarski (ref26) 0
chinta (ref41) 0
standley (ref24) 0
ref25
ref22
yu (ref1) 0
ref29
vedder (ref31) 0
References_xml – ident: ref29
  doi: 10.1109/IROS.2006.282536
– year: 0
  ident: ref41
  article-title: Coordinating the motion of labeled discs with optimality guarantees under extreme density
  publication-title: Proc Int Worksh Algorithm Found Robot
– ident: ref49
  doi: 10.15607/RSS.2009.V.003
– ident: ref6
  doi: 10.1109/IROS.2005.1545306
– start-page: 837
  year: 0
  ident: ref33
  article-title: Lifelong multi-agent path finding for online pickup and delivery tasks
  publication-title: Proc 16th Conf Auton Agents MultiAgent Syst
– ident: ref47
  doi: 10.1109/LRA.2016.2524067
– start-page: 1444
  year: 0
  ident: ref1
  article-title: Structure and intractability of optimal multi-robot path planning on graphs
  publication-title: Proc AAAI Nat Conf Artif Intell
– start-page: 3067
  year: 0
  ident: ref27
  article-title: Improved Solvers for Bounded-Suboptimal Multi-Agent Path Finding
  publication-title: Proc Int Joint Conf Artif Intell
– ident: ref12
  doi: 10.1109/ROBOT.2010.5509502
– ident: ref4
  doi: 10.1109/ROBOT.2002.1014852
– ident: ref52
  doi: 10.1613/jair.2241
– start-page: 2612
  year: 0
  ident: ref11
  article-title: A distributed and optimal motion planning approach for multiple mobile robots
  publication-title: Proc IEEE Int Conf Robot Autom
– ident: ref30
  doi: 10.15607/RSS.2018.XIV.013
– ident: ref14
  doi: 10.1007/s11036-009-0153-x
– ident: ref25
  doi: 10.1016/j.artint.2014.11.001
– ident: ref34
  doi: 10.1109/LRA.2019.2894217
– start-page: 740
  year: 0
  ident: ref26
  publication-title: Proc 8th Annu Symp Comb Search
– ident: ref37
  doi: 10.1109/CDC.2012.6426233
– ident: ref7
  doi: 10.15607/RSS.2009.V.018
– ident: ref36
  doi: 10.1177/0278364913515307
– ident: ref38
  doi: 10.1177/0278364913506268
– ident: ref9
  doi: 10.1007/978-3-642-22670-0_1
– year: 2019
  ident: ref32
  article-title: Automatic algorithm selection in multi-agent pathfinding
  publication-title: arXiv 1906 03992
– ident: ref13
  doi: 10.1109/ROBOT.2004.1307146
– ident: ref8
  doi: 10.1109/TRO.2016.2593448
– ident: ref39
  doi: 10.1109/ROBOT.2008.4543489
– ident: ref35
  doi: 10.24963/ijcai.2019/76
– ident: ref45
  doi: 10.1109/ROBOT.2009.5152773
– start-page: 141
  year: 0
  ident: ref53
  article-title: Finding optimal solutions to sokoban using instance dependent pattern databases
  publication-title: Proc 6th Ann Symp Combinator Search (SoCS)
– ident: ref54
  doi: 10.1109/MRS.2019.8901065
– ident: ref46
  doi: 10.1109/ROBOT.2009.5152696
– start-page: 19
  year: 0
  ident: ref48
  article-title: Suboptimal variants of the conflict-based search algorithm for the multi-agent pathfinding problem
  publication-title: the 7th Annual Symposium on Combinatorial Search
– ident: ref5
  doi: 10.1016/S0921-8890(02)00256-7
– start-page: 668
  year: 0
  ident: ref24
  article-title: Complete algorithms for cooperative pathfinding problems
  publication-title: Proc Int Joint Conf Artif Intell
– ident: ref16
  doi: 10.1177/0278364905059067
– ident: ref19
  doi: 10.1109/ROMAN.2012.6343737
– start-page: 1752
  year: 0
  ident: ref20
  article-title: Coordinating hundreds of cooperative, autonomous vehicles in warehouses
  publication-title: Proc 19th Innov Appl Artif Intell Conf
– volume: 42
  start-page: 55
  year: 2011
  ident: ref28
  article-title: Mapp: a scalable multi-agent path planning algorithm with tractability and completeness guarantees
  publication-title: J Artif Intell Res
– ident: ref51
  doi: 10.1007/11527862_18
– ident: ref40
  doi: 10.1109/TRO.2011.2120810
– ident: ref10
  doi: 10.1109/70.736775
– ident: ref43
  doi: 10.15607/RSS.2015.XI.011
– ident: ref18
  doi: 10.1109/ICAR.1997.620182
– year: 2019
  ident: ref21
  article-title: Multi-agent pathfinding: Definitions, variants, and benchmarks
  publication-title: 12th Ann Symp Combinatorial
– ident: ref22
  doi: 10.1007/978-3-642-32695-0_50
– year: 2019
  ident: ref55
  article-title: Ddm: Fast near-optimal multi-robot path planning using diversified-path and optimal sub-problem solution database heuristics
  publication-title: arXiv 1904 02598
– start-page: 2247
  year: 0
  ident: ref31
  article-title: X*: Anytime multiagent planning with bounded search
  publication-title: Proc 8th Int Conf Auton Agents Multiagent Syst
– ident: ref15
  doi: 10.1023/A:1008937911390
– ident: ref44
  doi: 10.1109/ROBOT.2008.4543392
– start-page: 290
  year: 0
  ident: ref23
  article-title: A general formal framework for pathfinding problems with multiple agents
  publication-title: Proc 27th AAAI Conf Artif Intell
– ident: ref3
  doi: 10.21236/ADA196213
– ident: ref17
  doi: 10.1109/IROS.1995.525802
– ident: ref42
  doi: 10.1007/978-3-319-16595-0_1
– volume: 29
  start-page: 9
  year: 2008
  ident: ref2
  article-title: Coordinating hundreds of cooperative, autonomous vehicles in warehouses
  publication-title: AI Mag
– ident: ref50
  doi: 10.1109/TRO.2016.2623345
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Snippet We propose a novel centralized and decoupled algorithm, DDM, for solving multi-robot path planning problems in grid graphs, targeting on-demand and automated...
We propose a novel centralized and decoupled algorithm, DDM , for solving multi-robot path planning problems in grid graphs, targeting on-demand and automated...
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SubjectTerms Algorithms
Apexes
Collision avoidance
Decoupling
Heuristic
Heuristic algorithms
multi-robot systems
Multiple robots
Optimization
Path planning
Path planning for multiple mobile robots or agents
Planning
Robot kinematics
Robots
scheduling and coordination
Warehouses
Title DDM: Fast Near-Optimal Multi-Robot Path Planning Using Diversified-Path and Optimal Sub-Problem Solution Database Heuristics
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