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Parameterized collision region for centralized motion planning of multiagents along specified paths

Published online by Cambridge University Press:  15 April 2011

Jeong S. Choi ,
Younghwan Yoon ,
Myoung H. Choi  and
Beom H. Lee
Jeong S. Choi
Affiliation:
Department of Electrical Engineering, Seoul National University, ASRI, Kwanak-ku, Seoul, Korea. E-mails: Jsforce2@snu.ac.kr, bhlee@snu.ac.kr
Younghwan Yoon*
Affiliation:
Automation R&D Center, LS Industrial Systems, Anyang, Korea. E-mail: lucidite@gmail.com
Myoung H. Choi
Affiliation:
Division of Electrical and Computer Engineering, Kangwon National University, Chuncheon-si, Gangwon-do, Republic of Korea
Beom H. Lee
Affiliation:
Department of Electrical Engineering, Seoul National University, ASRI, Kwanak-ku, Seoul, Korea. E-mails: Jsforce2@snu.ac.kr, bhlee@snu.ac.kr
*
*Corresponding author. E-mail: lucidite@gmail.com
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Summary

This paper presents closed-form analytic solutions for collision detection among multiagents traveling along specified paths. Previous solutions for centralized multiagent systems have mainly used iterative computational approaches for collision detection, which impose a heavy computational burden on the systems. In this paper, we formalize a new mathematical approach to overcoming the difficulty on the basis of simple continuous curvature (SCC) path modeling and a collision representation tool, extended collision map (ECM) method. The formulation permits all the potential collisions to be detected, represented, and parameterized with physical and geometric variables. The proposed parameterized collision region (PCR) method is a simple but precise, computationally efficient tool for describing complicated potential collisions with time traveled. Several simulations are presented to validate the proposed approach for use in centralized collision detectors and to compare the results with those of the iterative computational method and the proximity query package (PQP) method that are available.

Keywords

Multirobot systemsMobile robotsMotion planningCollision detectionCentralized approach
Type
Articles
Information
Robotica , Volume 29 , Issue 7 , December 2011 , pp. 1059 - 1073
Copyright
Copyright © Cambridge University Press 2011

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References

1.Durfee, E. H., Lesser, V. R. and Corkill, D. D., “Trends in cooperative distributed problem solving,” IEEE Trans. Knowl. Data Eng. 1 (1), 63–83 (1989).CrossRefGoogle Scholar
2.Hsu, D., Kavaraki, L. E., Latombe, J. C., Motwani, R. and Sorkin, S., “On Finding Narrow Passage With Probabilistic Roadmap Planners,” Parallel and Distributed Proceedings of IPPS/SPDP, Orlando, FL (1998) pp. 141–153.Google Scholar
3.LaValle, S. M. and Kuffner, J. J., “Randomized kinodynamic planning,” Int. J. Robot. Res. 20 (5), 378–400 (2001).CrossRefGoogle Scholar
4.Sanchez, G. and Latombe, J. C., “On delaying collision checking in PRM planning - Application to multi-robot coordination,” Int. J. Robot. Res. 21 (1), 15–26 (2002).CrossRefGoogle Scholar
5.Peng, J. and Akella, S., “Coordinating multiple robots with kinodynamic constraints along specified paths,” Int. J. Robot. Res. 24 (4), 295–310 (2005).CrossRefGoogle Scholar
6.Peng, J. and Akella, S., “Coordinating Multiple Double Integrator Robots on a Roadmap: Convexity and Global Optimality,” Proceedings of the International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 2751–2758.Google Scholar
7.Lavalle, S. M. and Hutchinson, S. A., “Optimal motion planning for multiple robots having independent goals,” IEEE Trans. Robot. Autom. 14 (6), 912–925 (1998).CrossRefGoogle Scholar
8.Saha, M. and Isto, P., “Multi-Robot Motion Planning by Incremental Coordination,” Proceedings of the International Conference on Intelligent Robotics and Systems, Beijing, China (2006) pp. 5960–5963.Google Scholar
9.Latombe, J. C., Robot Motion Planning (Kluwer Academic Publishers, Boston, 1991).CrossRefGoogle Scholar
10.Fujimura, K., Motion Planning in Dynamic Environment (Springer-Verlag, NewYork, 1991).CrossRefGoogle Scholar
11.Choset, H., Lynch, K. M., Hutchinson, S., Kantor, G., Burgard, W., Kavaraki, L. E. and Thrun, S., Principles of Robot Motion (The MIT Press, Massachusetts, 2005).Google Scholar
12.Lavalle, S. M., Planning Algorithms (Cambridge University Press, Cambridge, 2006).CrossRefGoogle Scholar
13.Akella, S. and Hutchinson, S., “Coordinating the Motions of Multiple Robots with Specified Trajectories,” Proceedings of the International Conference on Robotics and Automation, Washington, DC (May 2002) pp. 624–631.Google Scholar
14.Guizzo, E., “Three engineers, hundreds of robots, one warehouse,” IEEE Spectr. 45 (7), 22–29 (2008).CrossRefGoogle Scholar
15.Kant, K. and Zucker, S. W., “Toward efficient trajectory planning: The path-velocity decomposition,” Int. J. Robot Res. 5 (3), 72–88 (Fall, 1986).CrossRefGoogle Scholar
16.Warren, C. W., “Multiple Robot Path Coordination using Artificial Potential Fields,” Proceedings of IEEE International Conference on Robotics and Automation, Cincinnati, OH (1990) pp. 500–505.CrossRefGoogle Scholar
17.Lee, P. S. and Wang, L. L., “Collision avoidance by fuzzy logic for AGV navigation,” J. Robot. Syst. 11 (8), 743–760 (1994).CrossRefGoogle Scholar
18.Krishna, K. M. and Hexmoor, H., “Reactive Collision Avoidance of Multiple Moving Agents by Cooperation and Conflict Propagation,” Proceedings of the International Conference on Robotics and Automation, New Orleans, LA (2004) pp. 2141–2146.Google Scholar
19.Krishna, K. M. and Hexmoor, H., “Reactive Collision Avoidance of Multiple Moving Agents by Cooperation and Conflict Propagation,” Proceedings of the International Conference on Robotics and Automation, New Orleans, LA (2004) pp. 2141–2146.Google Scholar
20.Azarm, K. and Schmit, G., “Conflict-Free Motion of Multiple Mobile Robots Based on Decentralized Motion Planning and Negotiation,” Proceedings of IEEE International Conference on Robotics and Automation, Albuquerque, NM (Apr. 1997) pp. 3526–3533.CrossRefGoogle Scholar
21.Quottrup, M. M., Bak, T. and Zamanabadi, R. I., “Multi-robot planning: A timed automata approach,” Proceedings of IEEE International Conference on Robotics and Automation, vol. 5, New Orleans, LA (2004) pp. 4417–4422.Google Scholar
22.Fox, D., Burgard, W. and Thrun, S., “The dynamic window approach to collision avoidance,” IEEE Robot. Autom. Mag. 4 (1), 23–33 (1997).CrossRefGoogle Scholar
23.Ma, H., Cannon, D. J. and Kumara, S. R. T., “A Scheme Integrating Neural Networks for Real-Time Robotics Collision Detection,” Proceedings of IEEE International Conference on Robotics and Automation, Nagoya, Japan (1995) pp. 881–886.Google Scholar
24.Luh, J. Y. S. and Campbell, C. E., “Minimum distance collision-free path planning for industrial robots with a prismatic joint,” IEEE Trans. Autom. Control AC-29 (8), 675–680 (Aug 1984).CrossRefGoogle Scholar
25.Gilbert, E. G., Johnson, D. W. and Keerthi, S. S., “A Fast Procedure Computing the Distance between Complex Objects in Three-Dimensional Space,” IEEE J. Robot. Autom. 4 (2), 193–203 (Apr. 1988).CrossRefGoogle Scholar
26.Gill, M. A. and Zomaya, A. Y., Obstacle Avoidance in Multi-Robot Systems (World Scientific, Singapore, 1998).CrossRefGoogle Scholar
27.Freud, E. and Hoyer, H., “Real-Time Path Finding in Multirobot Systems Including Obstacle Avoidance,” Int. J. Robot. Res. 7 (1), 42–70 (1988).CrossRefGoogle Scholar
28.Basta, R. A., Mehrotra, R. and Varanasi, M. R., “Collision Detection for Planning Collision-Free Motion of Two Robot Arms,” Proceedings of IEEE International Conference on Robotics and Automation, Philadelphia, PA (1988) pp. 638–640.Google Scholar
29.Lee, B. H. and Lee, C. S. G., “Collision-free motion planning of two robots,” IEEE Trans. Syst. Main Cybern. 17 (1), 21–31 (Jan./Feb. 1987).CrossRefGoogle Scholar
30.Shin, Y. and Bien, Z., “Collision-free trajectory planning for two robots,” Robotica 7, 205–212 (Jul.–Sep. 1989).CrossRefGoogle Scholar
31.Park, S. H. and Lee, B. H., “Analysis of robot collision characteristics using the concept of the collision map,” Robotica 24, 295–303 (May 2006).CrossRefGoogle Scholar
32.Park, J. B. and Lee, B. H., “Roadmap-Based Collision-Free Motion Planning for Multiple Moving Agents in a Smart Home Environment,” Lecture Notes in Computer Science (Springer-Verlag, Berlin, Jun. 2007) pp. 70–80.Google Scholar
33.Chang, C., Chung, M. J. and Lee, B. H., “Collision avoidance of two general robot manipulators by minimum delay time,” IEEE Trans Syst Main Cybernetics 24 (3), 517–522 (Mar. 1994).CrossRefGoogle Scholar
34.Ji, S. H., Choi, J. S. and Lee, B. H., “A computational interactive approach to multi-agent motion planning,” Int. J. Control Autom. Sys. 5 (3), 295–306 (Jun. 2007).Google Scholar
35.Owen, E. and Montano, L., “A Robocentric Motion Planner for Dynamic Environments using the Velocity Space,” Proceedings in IEEE International Conference on Intelligent Robots and Systems, Beijing, China (2006) pp. 4368–4374.Google Scholar
36.Larsen, E., Gottschalk, S., Lin, M. C. and Manocha, D., “Fast Distance Queries with Rectangular Swept Sphere Volumes,” Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, CA (Apr. 2000) pp. 3719–3726.Google Scholar
37.Bergen, G., “Efficient collision detection of complex deformable models using AABB trees,” J. Graph. Tools 2 (4), 1–14 (1997).CrossRefGoogle Scholar
38.Mirtich, B., “V-clip: Fast and robust polyhedral collision detection,” ACM Trans. Graph. 17 (3), 177–208 (1998).CrossRefGoogle Scholar
39.Cohen, J. D., Lin, M. C., Manocha, D. and Ponamgi, M. K., “I-COLLIDE: An Interactive and Exact Collision Detection System for Large-Scale Environments,” Symposium on Interactive 3D graphics, Nashville, TN, USA (1995) pp. 189–196.Google Scholar
40.Ehmann, A. and Lin, M. C., “Accurate and fast proximity queries between polyhedra using convex surface decomposition,” Comput. Graph. Forum 20, 500–511 (2001).CrossRefGoogle Scholar
41.Nieuwenhuisen, D., “Callisto” January, 2010, Accessed http://www.nieuwenhuisen.nl/callisto/callisto.php, 28 March 2011.Google Scholar
42.Geraerts, R. J., Sampling-Based Motin Planning: Analysis and Path Quality,” Ph.D. Thesis (Utrecht University, Utrecht, Netherlands, 2006).Google Scholar
43.LaValle, S. M., “Rapidly-Exploring Random Trees: A New Tool for Path Planning,” Technical Report No. 98-11 (Computer Science Department, Iowa State University, Iowa, USA, 1998).Google Scholar
44.Peasgood, M., Clark, C. M. and McPhee, J., “A complete and scalable strategy for coordinating multiple robots within roadmaps,” IEEE Trans. Robotics 24 (2), 283–292 (2008).CrossRefGoogle Scholar
45.Berg, J., Snoeyink, J., Lin, M. and Manocha, D., “Centralized Path Planning for Multiple Robots: Optimal Decoupling into Sequential Plans,” Proceedings of Robotics: Science and Systems, Seattle, USA (2009) pp. 1–8.Google Scholar
46.Berg, J. and Overmars, M. H., “Prioritized Motion Planning for Multiple Robots,” Proceedings of the International Conference on Intelligent Robots and Systems, Edmonton, Canada (2005) pp. 2217–2222.Google Scholar
47.Li, Y., Gupta, K. and Payandeh, S., “Motion Planning of Multiple Agents in Virtual Environments using Coordination Graphs,” Proceedings of the International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 378–383.Google Scholar
48.Scheuer, A. and Fraichard, T., “Continuous-Curvature Path Planning for Car-Like Vehicles,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 2, Grenoble, France (Sep. 1997) pp. 997–1003.Google Scholar
49.Esquivel, W. D. and Chiang, L. E., “Nonholonomic path planning among obstacles subject to curvature restrictions,” Robotica 20, 49–55 (2002).CrossRefGoogle Scholar
50.Waheed, I. and Fotouhi, R., “Trajectory and temporal planning of a wheeled mobile robot on an uneven surface,” Robotica 27 (4), 481–498 (2008).CrossRefGoogle Scholar
51.Leroy, S., Laumond, J. P. and Simeon, T., “Multiple Path Coordination for Mobile Robots: A Geometric Algorithm,” Proceedings of the International Joint Conference on Artificial Intelligence, Stockholm, Sweden (1999) pp. 1118–1123.Google Scholar
52.Jiang, R., Tian, X., Xie, L. and Chen, Y., “A Robot Collision Avoidance Scheme Based on the Moving Obstacle Motion Prediction,” Proceedings of International Colloquium on Computing, Communication, Control, and Management, Guangzhou City, China (2008) pp. 341–345.Google Scholar
53.Lin, M. and Gottschalk, S., “Collision Detection Between Geometric Models: A Survey,” Proceedings of IMA Conference on Mathematics of surface, Birmingham, UK (1998).Google Scholar