Definition of the Subject
Multi-robot path planning and motion coordinationaddresses the problem of how teams of autonomous mobile robotscan share the same workspace while avoiding interference with each other, and/or while achieving group motion objectives. Nearly all applications ofmultiple autonomous mobile robots must address this issue of motion coordination, either explicitly or implicitly. Multi-robot path planning and teaminghas been extensively studied since the 1980s. While many techniques have been developed to address this challenge, the general centralized multi-robotpath planning problem is known to be intractable, meaning that optimal solutions cannot be found in polynomial time. Thus, alternative techniques thatdecouple aspects of the motion planning and coordination problem have been proposed that trade off optimality for efficiency. A wide variety ofapplications can benefit from teams of robots that can coordinate...
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Abbreviations
- Autonomous robot:
-
An autonomous robot is a robot that can perform tasks in unstructured environments with minimal human guidance.
- Planned path:
-
A planned path is a pre-determined, obstacle-free, trajectory that a robot can follow to reach its goal position from its starting position.
- Complete path planner:
-
A complete path planner is an algorithm that is guaranteed to find a path, if one exists.
- Deadlocked path planning:
-
A deadlock is a situation in path planning in which a solution cannot be found, even though one exists. Typically, this is caused by robots blocking each other’s paths, and the planner being unable to find a solution in which robots move out of each other’s way.
Bibliography
Primary Literature
Alami R, Robert F, Ingrand F, Suzuki S (1995) Multi-robot cooperation through incremental plan-merging. In: Proceedings of the IEEE International Conference on Robotics and Automation, Nagoya, Aichi, 21–27 May 1995, pp 2573–2578
Alami R, Fleury S, Herrb M, Ingrand F, Robert F (1998) Multi-robot cooperation in the MARTHA project. IEEE Robot Autom Mag 5(1):36–47
Antonelli G, Chiaverini S (2006) Kinematic control of platoons of autonomous vehicles. IEEE Trans Robot 22(6):1285–1292
Arkin (1992) Cooperation without communication: multiagent schema-based robot navigation. J Robot Syst 9:351–364
Asama H, Ozaki K, Itakura H, Matsumoto A, Ishida Y, Endo I (1991) Collision avoidance among multiple mobile robots based on rules and communication. In: Proceedings of IEEE/RJS International Conference on Intelligent Robots and Systems, Osaka, 3–5 Nov 1991
Azarm K, Schmidt G (1997) Conflict-free motion of multiple mobile robots based on decentralized motion planning and negotiation. In: Proceedings of IEEE International Conference on Robotics and Automation, 20–25 April 1997, pp 3526–3533
Balch T (1999) The impact of diversity on performance in robot foraging. In: Proceedings of the Third Annual Conference on Autonomous Agents, 1–5 May 1999. ACM Press, Seattle, pp 92–99
Balch T, Arkin R (1998) Behavior-based formation control for multi-robot teams. IEEE Trans Robot Autom 14(6):926–939
Barraquand J, Latombe JC (1991) Robot motion planning: A distributed representation approach. Int J Robot Res 20(6):628–649
Barraquand J, Langlois B, Latombe JC (1992) Numerical potential field techniques for robot motion planning. IEEE Trans Syst Man Cybern 22:224–241
Barraquand J, Langlois B, Latombe JC (1997) Numerical potential field techniques for robot path planning. Int J Robot Res 16(6):759–774
Beard RW, McLain TW, Goodrich M (2002) Coordinated target assignment and intercept for unmanned air vehicles. In: Proceedings of IEEE International Conference on Robotics and Automation, 11–15 May 2002. IEEE, Washington DC
Beckers R, Holland O, Deneubourg J (1994) From local actions to global tasks: Stigmergy and collective robotics. In: Brooks R, Maes P (eds) Proceedings of the 4th International Workshop on Synthesis and Simulation of Living Systems. MIT Press, Cambridge, pp 181–189
Belta C, Kumar V (2004) Abstraction and control for groups of robots. IEEE Trans Robot 20(5):865–875
Bennewitz M, Burgard W, Thrun S (2001) Optimizing schedules for prioritized path planning of multi-robot systems. In: Proceedings of IEEE International Conference on Robotics and Automation, Seoul, 21–26 May 2001, pp 271–276
Bennewitz M, Burgard W, Thrun S (2002) Finding and optimizing solvable priority schemes for decoupled path planning techniques for teams of mobiel robots. Robot Auton Syst 41(2):89–99
Bien Z, Lee J (1992) A minimum-time trajectory planning method for two robots. IEEE Trans Robot Autom 8:414–418
Bobrow JE (1988) Optimal robot path planning using the minimum-time criterion. IEEE Trans Robot Autom 4(4):443–450
Browning B, Bruce J, Bowling M, Veloso M (2005) STP: Skills, tactics and plays for multi-robot control in adversarial environments. IEEE J Control Syst Eng 219:33–52
Buckley SJ (1989) Fast motion planning for multiple moving robots. In: Proceedings of IEEE International Conference on Robotics and Automation, Scottsdale, 14–19 May 1989, pp 322–326
Butler ZJ, Rizzi AA, Hollis RL (2000) Cooperative coverage of rectilinear environments. In: Proceedings of IEEE International Conference on Robotics and Automation, San Francisco, 24–28 April 2000. IEEE
Carpin S, Pagello E (2001) AÂ distributed algorithm for multi-robot motion planning. In: Proceedings of the Fourth European Workshop on Advanced Mobile Robotics, Lund 2001
Chang C, Chung MJ, Lee BH (1994) Collision avoidance of two general robot manipulators by minimum delay time. IEEE Trans Robot Autom 24(3):517–522
Choset H, Lynch K, Hutchinson S, Kantor G, Burgard W, Kavraki L, Thrun S (2005) Principles of robot motion: theory, algorithms, and implementation. MIT Press, Cambridge
Chun L, Zheng Z, Chang W (1999) A decentralized approach to the conflict-free motion planning for multiple mobile robots. In: Proceedings of IEEE International Conference on Robotics and Automation, Detroit, 10–15 May 1999, pp 1544–1549
Clark CM, Rock SM, Latombe JC (2003) Motion planning for multiple mobile robot systems using dynamic networks. In: Proceedings of IEEE International Conference on Robotics and Automation, Taipai, 14–19 Sept 2003, pp 4222–4227
Dimarogonas DV, Loizou SG, Kyriakopoulos KJ, Zavlanos MM (2006) A feedback stabilization adn collision avoidance scheme for multiple independent non-point agents. Automatica 42(2):229–243
Drogoul A, Ferber J (1992) From Tom Thumb to the Dockers: Some experiments with foraging robots. In: Proceedings of the Second International Conference on Simulation of Adaptive Behavior, Honolulu, 2–16 Dec 1992, pp 451–459
Erdmann M, Lozano-Perez T (1987) On multiple moving objects. Algorithmica 2:477–521
Everett HR, Laird RT, Carroll DM, Gilbreath GA, Heath-Pastore TA, Inderieden RS, Tran T, Grant KJ, Jaffee DM (2000) Multiple Resource Host Architecture (MRHA) for the Mobile Detection Assessment Response System (MDARS). In: SPAWAR Systems Technical Document 3026, Revision A. San Diego
Fax JA, Murray RM (2004) Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control 49(9)
Ferrari C, Pagello E, Ota J, Arai T (1998) Multirobot motion coordination in space and time. Robot Auton Syst 25:219–229
Fontan M, Mataric M (1998) Territorial multi-robot task division. IEEE Trans Robot Autom 15(5):815–822
Fujimori A, Teramoto M, Nikiforuk P, Gupta M (2000) Cooperative collision avoidance between multiple mobile robots. J Robot Syst 17(7):347–363
Fujimura K (1991) Motion planning in dynamic environment. Computer Science Workbench. Springer, Tokyo
Gage D (1993) Randomized search strategies with imperfect sensors. In: Proceedings of SPIE Mobile Robots VIII. SPIE, Boston, pp 270–279
Gazi V (2005) Swarm aggregations using artificial potentials and sliding-mode control. IEEE Trans Robot 21(6):1208–1214
Ge SS, Fua CH (2005) Queues and artificial potential trenches for multirobot formations. IEEE Trans Robot 21(4):646–656
Ghrist R, O’Kane JM, LaValle SM (2004) Pareto optimal coordination on roadmaps. In: Proceedings of the Workshop on Algorithmic Foundations of Robotics, Utrecht, 11–13 May 2004, pp 185–200
Gonzalez-Banos HH, Hsu D, Latombe JC (2006) Chapter: Autonomous mobile robots: Sensing, control, decision-making, and applications. In: Motion Planning: Recent Developments. CRC, New York
Griswold NC, Eem J (1990) Control for mobile robots in the presence of moving objects. IEEE Trans Robot Autom 6(2):263–268
Grossman DD (1988) Traffic control of multiple robot vehicles. IEEE Trans Robot Autom 5(5):491–497
Guo Y, Parker LE (2002) A distributed and optimal motion planning approach for multiple mobile robots. In: Proceedings of IEEE International Conference on Robotics and Automation, Washington DC, 11–15 May 2002
Guo Y, Parker LE, Madhavan R (2004) Towards collaborative robots for infrastructure security applications. In: Proceedings of International Symposium on Collaborative Technologies and Systems, San Diego, 18–23 Jan 2004, pp 235–240
Hart EE, Nilsson NJ, Raphael B (1968) A formal basis for the heuristic determination of minimum cost paths. IEEE Trans Syst Sci Cybern SSC-4(2):100–107
Hazard C, Wurman PR, D’Andrea R (2006) Alphabet soup: A testbed for studying resource allocation in multi-vehicle systems. In: Proceedings of AAAI Workshop on Auction Mechanisms for Robot Coordination, Boston, 16–20 July 2006, pp 23–30
Hopcroft JE, Schwartz JT, Sharir M (1984) On the complexity of motion planning for multiple independent objects; PSPACE-Hardness of the Warehouseman’s Problem. Int J Robot Res 3(4):76–88
Hwang Y, Ahuja N (1992) Gross motion planning – a survey. ACM Comput Surv 24(3):219–291
Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001
Jennings JS, Whelan G, Evans WF (1997) Cooperative search and rescue with a team of mobile robots. In: Proceedings of the 8th International Conference on Advanced Robotics, Monterey, 7–9 July 1992, pp 193–200
Jung B, Sukhatme G (2002) Tracking targets using multiple mobile robots: The effect of environment occlusion. Auton Robot 13(3):191–205
Kant K, Zucker SW (1986) Toward efficient trajectory planning: the path-velocity decomposition. Int J Robot Res 5(3):72–89
Kato S, Nishiyama S, Takeno J (1992) Coordinating mobile robots by applying traffic rules. In: Proceedings of the 1992 IEEE/RSJ International Conference on Intelligent Robots and Systems, Raleigh, 7–17 July 1992, pp 1535–1541
Kavraki LE, Svestka P, Latombe JC, Overmars MH (1996) Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans Robot Autom 12(4):566–580
Khatib O (1986) Real-time obstacle avoidance for manipulators and mobile robots. Int J Robot Res 5(1):90–98
Kloder S, Hutchinson S (2006) Path planning for permutation-invariant multirobot formations. IEEE Trans Robot 22(4):650–665
Kolling A, Carpin S (2006) Multirobot cooperation for surveillance of multiple moving targets – a new behavioral approach. In: Proceedings of the IEEE International Conference on Robotics and Automation, Orlando, 15–19 May 2006. IEEE, pp 1311–1316
Latombe JC (1991) Robot motion planning. Kluwer Academic, Boston
LaValle SM (2006) Planning algorithms. Cambridge University Press, Cambridge, New York
LaValle SM, Hutchinson SA (1998) Optimal motion planning for multiple robots having independent goals. IEEE Trans Robot Autom 14:912–925
LaValle SM, Gonzalez-Banos HH, Becker C, Latombe JC (1997) Motion strategies for maintaining visibility of a moving target. In: Proceedings of the 1997 IEEE International Conference on Robotics and Automation, 20–25 April 1997. IEEE, pp 731–736
Lee BH, Lee CS (1987) Collision-free motion planning of two robots. IEEE Trans Syst Man Cybern 17(1):21–32
Lee BJ, Lee SO, Park GT (1999) Trajectory generation and motion tracking for the robot soccer game. In: Proceedings of IEEE International Conference on Intelligent Robots and Systems, 17–21 Oct 1999, pp 1149–1154
Lee J, Bien Z (1990) Collision-free trajectory control for multiple robots based on neural optimization network. Robotica 8:185–194
Lin CF, Tsai WH (1991) Motion planning for multiple robots with multi-mode operations via disjunctive graphs. Robotica 9:393–408
Luke S, Sullivan K, Panait L, Balan G (2005) Tunably decentralized algorithms for cooperative target observation. In: Proceedings of the fourth international joint conference on Autonomous Agents and Multiagent Systems, Utrecht, 25–29 July 2005. ACM Press, pp 911–917
Lumelsky VJ, Harinarayan KR (1997) Decentralized motion planning for multiple mobile robots: The cocktail party model. Auton Robot 4(1):121–135
Marshall JA, Broucke ME, Francis BR (2004) Formations of vehicles in cyclic pursuit. IEEE Trans Autom Control 49(11):1963–1974
Mataric M (1997) Behavior-based control: Examples from navigation, learning, and group behavior. J Exp Theor Artif Intell 19(2–3):323–336
Mataric MJ (1992) Designing emergent behaviors: From local interactions to collective intelligence. In: Meyer J, Roitblat H, Wilson S (eds) Proceedings of the 2nd international conference on simulation of adaptive behavior. MIT Press, Honolulu, pp 432–441
Mourikis AI, Roumeliotis SI (2006) Optimal sensor scheduling for resource-constrained localization of mobile robot formations. IEEE Trans Robot 22(5):917–931
Mourikis AI, Roumeliotis SI (2006) Performance analysis of multirobot cooperative localization. IEEE Trans Robot 22(4):666–681
Nilsson N (1982) Principles of artificial intelligence. Springer, Berlin
O’Donnell PA, Lozano-Perez T (1989) Deadlock-free and collision-free coordination of two robot manipulators. In: Proceedings of IEEE International Conference on Robotics and Automation, Scottsdale, 14–19 May 1989, pp 484–489
O’Dunlaing C, Yap CK (1982) A retraction method for planning the motion of a disc. J Algorithm 6:104–111
Pallottino L, Scordio VG, Bicchi A, Frazzoli E (2007) Decentralized cooperative policy for conflict resolution in multivehicle systems. IEEE Trans Robot 23(6):1170–1183
Pan TJ, Luo RC (1990) Motion panning for mobile robots in a dynamic environment. In: Proceedings of IEEE International Conference on Robotics and Automation, 13–18 May 1990, pp 578–583
Park S, Lee B (2006) A new analytical representation to robot path generation with collision avoidance through the use of the collision map. Int J Control Autom Syst 4(1):77–86
Parker LE (1988) A robot navigation algorithm for moving obstacles. Master’s thesis, The University of Tennessee
Parker LE (1993) Designing control laws for cooperative agent teams. In: Proceedings of the IEEE Robotics and Automation Conference, Atlanta, 2–6 May 1993. IEEE, pp 582–587
Parker LE (1998) Alliance: An architecture for fault-tolerant multi-robot cooperation. IEEE Trans Robot Autom 14(2):220–240
Parker LE (1999) Cooperative robotics for multi-target observation. Intell Autom Soft Comput 5(1):5–19
Parker LE (2008) Chapter 40: Multiple mobile robot systems. In: Siciliano B, Khatib O (eds) Springer handbook of robotics. Springer, New York
Parker LE, Draper J (1999) Robotics applications in maintenance and repair. In: Nof S (ed) Handbook of industrial robotics, 2nd edn. Wiley, New York, pp 1023–1036
Parsons D, Canny J (1990) A motion planner for multiple mobile robots. In: Proceedings of IEEE International Conference on Robotics and Automation, 13–18 May 1990, pp 8–13
Passino K (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Mag 22(3):52–67
Peasgood M, Clark C, McPhee J (2008) A complete and scalable strategy for coordinating multiple robots within roadmaps. IEEE Trans Robot, 24(2):283–292
Peng J, Akella S (2005) Coordinating multiple robots with kinodynamic constraints along specified paths. Int J Robot Res 24(4):295–310
Pilarski T, Happold M, Pangels H, Ollis M, Fitzpatrick K, Stentz A (1999) The demeter system for automated harvesting. In: Proceedings of the 8th International Topical Meeting on Robotics and Remote Systems, Pittsburgh, 25–29 April 1999
Preparata F, Shamos M (1985) Computational geometry. Springer, New York
Reynolds CW (1987) Flocks, herds and schools: A distributed behavioral model. ACM SIGGRAPH Comput Graph 21:25–34
Rude M (1997) Collision avoidance by using space-time representations of motion processes. Auton Robot 4:101–119
Ryan MRK (2007) Graph decomposition for efficient multi-robot path planning. In: Proceedings of the International Joint Conference on Artificial Intelligence, Hyderabad, 6–12 Jan 2007, pp 2003–2008
Rybski P, Stoeter S, Wyman C, Gini M (1997) AÂ cooperative multi-robot approach to the mapping and exploration of mars. In: Proceedings of AAAI/IAAI-97. AAAI, Providence
Sanchez G, Latombe JC (2002) On delaying collision checking in PRM planning: application to multi-robot coordination. Int J Robot Res 21(1):5–26
Schwartz JT, Sharir M (1983) On the ‘piano movers’ problem: Iii. coordinating the motion of several independent bodies: The special case of circular bodies moving amidst polygonal obstacles. Int J Robot Res 2(3):46–75
Schwartz JT, Sharir M (1988) A survey of motion planning and related geometric algorithms. Artif Intell J 37:157–169
Shaffer G, Stentz A (1992) A robotic system for underground coal mining. In: Proceedings of IEEE International Conference on Robotics and Automation, 12–14 May 1992, pp 633–638
Shan L, Hasegawa T (1996) Space reasoning from action observation for motion planning of multiple robots: mutual collision avoidance in a narrow passage. J Robot Soc Jpn 14:1003–1009
Sharir M (2004) Algorithmic motion planning. In: Goodman JE, O’Rourke J (eds) Handbook of discrete and computational geometry, 2nd edn. Chapman Hall/CRC, New York
Shiller Z, Lu HH (1990) Robust computation of path constrained time optimal motions. In: Proceedings of IEEE International Conference on Robotics and Automation, 13–18 May 1990, pp 144–149
Simeon T, Leroy S, Laumond J (2002) Path coordination for multiple mobile robots: a resolution-complete algorithm. IEEE Trans Robot Autom 24(1):42–49
Simmons R, Singh S, Hershberger D, Ramos J, Smith T (2000) First results in the coordination of heterogeneous robots for large-scale assembly. In: Proc. of the ISER Seventh International Symposium on Experimental Robotics, Honolulu, 10–13 Dec 2000. Springer
Stone P, Veloso M (1999) Task decomposition, dynamic role assignment, and low-bandwidth communication for real-time strategic teamwork. Artif Intell 110(2):241–273
Stroupe A, Okon A, Robinson M, Huntsberger T, Aghazarian H, Baumgartner E (2006) Sustainable cooperative robotic technologies for human and robotic outpost infrastructure construction and maintenance. Auton Robot 20(2):113–123
Sugawara K, Sano M (2002) Cooperative behavior of interacting simple robots in a clockface arranged foraging field. In: Asama H, Arai T, Fukuda T, Hasegawa T (eds) Distributed Autonomous Robotic Systems. Springer, Fukjoka, pp 331–339
Sugihara K, Suzuki I (1996) Distributed algorithms for formation of goemetric patterns with many mobile robots. J Robot Syst 13(3):127–139
Sun S, Lee D, Sim K (2001) Artificial immune-based swarm behaviors of distributed autonomous robotic systems. In: Proceedings of IEEE International Conference on Robotics and Automation Seoul 21–26 May 2001. IEEE, pp 3993–3998
Svestka P, Overmars M (1998) Coordinated path planning for multiple robots. Robot Auton Syst 23:125–152
Tabuada P, Pappas G, Lima P (2005) Motion feasibility of multi-agent formations. IEEE Trans Robot 21(3):387–392
Tang Z, Ozguner U (2005) Motion planning for multitarget surveillance with mobile sensor agents. IEEE Trans Robot 21(5):898–908
Thorpe C, Jochem T, Pomerleau D (1997) The 1997 automated highway free agent demonstration. In: Proceedings of IEEE Conference on Intelligent Transportation System, Boston, 9–12 Nov 1997, pp 496–501
Topaz CM, Bertozzi AL (2004) Swarming patterns in two-dimensional kinematic model for biological groups. SIAM J Appl Math 65(1):152–174
Tournassoud P (1986) A strategy for obstacle avoidance and its application to multi-robot systems. In: Proceedings of IEEE International Conference on Robotics and Automation, San Francisco, pp 1224–1229
Veloso M, Stone P, Han K (1999) The CMUnited-97 robotic soccer team: Perception and multiagent control. Robot Auton Syst 29(2–3):133–143
Wagner I, Lindenbaum M, Bruckstein AM (2000) Mac vs. PC – determinism and randomness as complementary approaches to robotic exploration of continuous unknown domains. Int J Robot Res 19(1):12–31
Wang J (1991) Fully distributed traffic control strategies for many-AGV systems. In: Proceedings of the IEEE International Workshop on Intelligent Robots and Systems, Osaka 2–5 Nov 1991, pp 1199–1204
Wang J, Beni G (1990) Distributed computing problems in cellular robotic systems. In: Proceedings of the IEEE International Workshop on Intelligent Robots and Systems, pp 819–826
Wang PKC (1989) Interaction dynamics of multiple autonomous mobile robots in bounded spatial domains. Int J Control 50(6):2109–2124
Wang PKC (1989) Interaction dynamics of multiple mobile robots with simple navigation strategies. J Robot Syst 6(1):77–101
Warren CW (1990) Multiple robot path coordination using artificial potential fields. In: Proceedings of IEEE International Conference on Robotics and Automation, 13–18 May 1990, pp 500–505
Weigel T, Gutmann JS, Dietl M, Kleiner A, Nebel B (2002) CS Freiburg: coordinating robots for successful soccer playing. IEEE Trans Robot Autom 5(18):685–699
Werger BB, Mataric MJ (2000) Broadcast of local eligibility for multi-target observation. In: Parker LE, Bekey G, Barhen J (eds) Distributed autonomous robotic systems 4. Springer, New York, pp 347–356
Yannakakis MZ, Papadimitriou CH, Kung HT (1979) Locking policies: Safety and freedom for deadlock. In: Proceedings of the 20th Annual Symposium on Foundations of Computer Science, San Juan, 29–31 Oct 1979, pp 286–297
Yuta S, Premvuti S (1992) Coordinating autonomous and centralized decision making to achieve cooperative behaviors between multiple mobile robots. In: Proceedings of the 1992 IEEE/RSJ International Conference on Intelligent robots and systems, Raleigh, 7–10 July 1992, pp 1566–1574
Books and Reviews
Arai T, Ota J (1992) Motion planning of multiple mobile robots. In: Proceedings of the 1992 IEEE/RSJ International Conference on Intelligent robots and systems, Raleigh, 7–10 July 1992, pp 1761–1768
Arai T, Pagello E, Parker LE (2002) Editorial: Advances in multi-robot systems. IEEE Trans Robot Autom 18(5):655–661
Cao Y, Fukunaga A, Kahng A (1997) Cooperative mobile robotics: Antecedents and directions. Auton Robot 4:1–23
Canny J (1988) The complexity of robot motion planning. MIT Press, Cambridge
Choset H (2001) Coverage for robotics – A survey of recent results. Ann Math Artif Intell 31(1–4):113–126
Nardi D, Farinelli A, Iocchi L (2004) Multirobot systems: a classification focused on coordination. IEEE Trans Syst Man Cybern Part B 34(5):2015–2028
Parker LE (2005) Current research in multirobot teams. Artif Life Robot 7(2–3):1–5
Thrun S, Burgard W, Fox D (2005) Probabilistic robotics. MIT Press, Cambridge
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Parker, L.E. (2009). Multiple Mobile Robot Teams, Path Planning and Motion Coordination in. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_344
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