Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-15T23:19:02.246Z Has data issue: false hasContentIssue false

Distributed coverage with mobile robots on a graph: locational optimization and equal-mass partitioning

Published online by Cambridge University Press:  18 December 2013

Seung-kook Yun*
Affiliation:
SRI International, Menlo Park, CA 94025, USA
Daniela Rus
Affiliation:
Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
*Corresponding author. E-mail: seungkook.yun@sri.com

Summary

This paper presents decentralized algorithms for coverage with mobile robots on a graph. Coverage is an important capability of multi-robot systems engaged in a number of different applications, including placement for environmental modeling, deployment for maximal quality surveillance, and even coordinated construction. We use distributed vertex substitution for locational optimization and equal mass partitioning, and the controllers minimize the corresponding cost functions. We prove that the proposed controller with two-hop communication guarantees convergence to the locally optimal configuration. We evaluate the algorithms in simulations and also using four mobile robots.

Type
Articles
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Cortes, J., Martinez, S., Karatas, T. and Bullo, F., “Coverage control for mobile sensing networks,” IEEE Trans. Robot. Autom. 20 (2), 243255 (2004).Google Scholar
2.Schwager, M., Rus, D. and Slotine, J.-J. E., “Decentralized, adaptive control for coverage with networked robots,” Int. J. Robot. Res. 28 (3), 357375 (Mar. 2009).Google Scholar
3.Pavone, M., Frazzoli, E. and Bullo, F., “Distributed Algorithms for Equitable Partitioning Policies: Theory and Applications,” IEEE Conference on Decision and Control, Cancun, Mexico (Dec. 2008), pp. 41914197.Google Scholar
4.Yun, S.-kook, Schwager, M. and Rus, D., “Coordinating Construction of Truss Structures Using Distributed Equal-Mass Partitioning,” Proceedings of the 14th International Symposium on Robotics Research, Lucern, Switzerland (Aug. 2009).Google Scholar
5.Choset, H., “Coverage for robotics – a survey of recent results,” Ann. Math. Arti. Intell. 31, 113126 (2001).Google Scholar
6.Choset, H. and Pignon, P., “Coverage Path Planning: The Boustrophedon Cellular Decomposition,” Proceedings of the International Conference on Field and Service Robotics (1997).Google Scholar
7.Hert, S. and Lumelsky, V., “Polygon area decomposition for multiple-robot workspace division,” Int. J. Comput. Geom. Appl. 8, 437466 (1998).Google Scholar
8.Pimenta, L. C. A., Kumar, V., Mesquita, R. C. and Pereira, G. A. S., “Sensing and Coverage for a Network of Heterogeneous Robots,” IEEE Conference on Decision and Control, Cancun, Mexico (Dec. 2008), pp. 39473952.Google Scholar
9.Kwok, A. and Martínez, S., “Energy-Balancing Cooperative Strategies for Sensor Deployment,” IEEE International Conference on Decision and Control, New Orleans, LA (Dec. 2007) pp. 61366141.Google Scholar
10.Ganguli, A., Cortes, J. and Bullo, F., “Distributed Deployment of Asynchronous Guards in Art Galleries,” American Control Conference, Minneapolis, MN (Jun. 2006), pp. 14161421.Google Scholar
11.Caicedo-Nunez, C. H. and Zefran, M., “A Coverage Algorithm for a Class of Non-Convex Regions,” IEEE International Conference on Decision and Control, Cancun, Mexico (Dec. 2008) pp. 42444249.Google Scholar
12.Ayanian, N. and Kumar, V., “Decentralized Feedback Controllers for Multi-Agent Teams in Environments with Obstacles,” IEEE International Conference on Robotics and Automation, Pasadena, CA (May 2008) pp. 19361941.Google Scholar
13.Bhattacharya, S., Michael, N. and Kumar, V., “Distributed Coverage and Exploration in Unknown Non-Convex Environments,” 10th International Symposium on Distributed Autonomous Robots, Nov. 1–3 (Springer, New York, NY, 2010).Google Scholar
14.Teitz, M. B. and Bart, P., “Heuristic methods for estimating the generalized vertex median of a weighted graph,” Oper. Res. 16, 955961 (1968).Google Scholar
15.Reese, J., “Solution methods for the p-median problem: An annotated bibliography,” Networks 48, 125142 (2006).Google Scholar
16.Fjallstrom, P.-O., “Algorithms for graph partitioning: A survey,” Linkoping Electronic Articles in Computer and Information Science, Vol. 3, article no. 10, available at http://www.ep.liu.se/ea/cis/1998/010/ (1998), online.Google Scholar
17.Gabriely, Y. and Rimon, E., “Spanning-tree based coverage of continuous areas by a mobile robot,” Ann. Math. Arti. Intell. 31 (1–4), 7798 (2001).Google Scholar
18.Durham, J. W., Carli, R., Frasca, P. and Bullo, F., “Discrete Partitioning and Coverage Control with Gossip Communication,” ASME Dynamic Systems and Control Conference, Hollywood, CA (Oct. 2009) pp. 225232.Google Scholar
19.Durham, J., Carli, R., Frasca, P. and Bullo, F., “Discrete partitioning and coverage control for gossiping robots,” IEEE Trans. Robot. 28 (2), 364378 (2012).Google Scholar
20.Beasley, J. E., “OR-library: Distributing test problems by electronic mail,” J. Oper. Res. Soc. 41 (11), 10691072 (1990).Google Scholar
21.Bolger, A., Faulkner, M., Stein, D., White, L., Yun, S.-kook and Rus, D., “Experiments in Decentralized Robot Construction with Tool Delivery and Assembly Robots,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, China (Oct. 2010) pp. 50855092.Google Scholar
22.Erwig, M. and Hagen, F., “The graph voronoi diagram with applications,” Networks 36, 156163 (2000).3.0.CO;2-L>CrossRefGoogle Scholar
23.Floyd, R. W., “Algorithm 97: Shortest path,” Commun. ACM 5 (6), 345 (1962).Google Scholar
24.Garey, M. R. and Johnson, D. S., Computers and Intractability: A Guide to the Theory of NP-Completeness (Series of Books in the Mathematical Sciences). (Freeman, W. H., New York, NY, Jan. 1979).Google Scholar
25.Julian, B. J., Schwager, M., Angermann, M. and Rus, D., “A Location-Based Algorithm for Multi-Hopping State Estimates within a Distributed Robot Team,” Proceedings of the International Conference on Field and Service Robotics (FSR 09), Cambridge, MA (Jul. 2009).Google Scholar
26.Beasley, J., “Lagrangean heuristics for location problems,” Eur. J. Oper. Res. 65 (3), 383399 (1993).Google Scholar
27.Baron, O., Berman, O., Krass, D. and Wang, Q., “The equitable location problem on the plane,” Eur. J. Oper. Res. 183 (2), 578590 (Dec. 2007).Google Scholar
28.Garey, M. R., Johnson, D. S. and Stockmeyer, L., “Some Simplified Np-Complete Problems,” Proceedings of the Sixth Annual ACM Symposium on Theory of Computing (STOC '74) (ACM, New York, NY, 1974) pp. 4763.Google Scholar
29.Berger, M. J. and Bokhari, S. H., “A partitioning strategy for nonuniform problems on multiprocessors,” IEEE Trans. Comput. 36 (5), 570580 (1987).Google Scholar
30.Leland, R. and Hendrickson, B., “An Empirical Study of Static Load Balancing Algorithms,” Proceedings of the Scalable High-Performance Computing Conference (1994) pp. 682–685.Google Scholar
31.Vidwans, A., Kallinderis, Y. and Venkatakrishnan, V., “A parallel dynamic load balancing algorithm for 3D adaptive unstructured grids,” AIAA J. 32, 497505 (1993).Google Scholar
32.Ozturan, C., deCougny, H. L., Shephard, M. S. and Flaherty, J. E., “Parallel adaptive mesh refinement and redistribution on distributed memory computers,” Comput. Methods Appl. Mech. Engrg, Tech. Rep. 119, 123137 (1993).Google Scholar
33.Babuška, I., Banerjee, U. and Osborn, J. E., “Survey of meshless and generalized finite element methods: A unified approach,” Acta Numerica 12, 1125 (2003).Google Scholar