Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T20:33:05.063Z Has data issue: false hasContentIssue false
  • English
  • Français

Spatially-distributed coverage optimization and control with limited-range interactions

Published online by Cambridge University Press:  15 September 2005

Jorge Cortés ,
Sonia Martínez  and
Francesco Bullo
Jorge Cortés
Affiliation:
Department of Applied Mathematics and Statistics, Baskin School of Engineering, University of California, Santa Cruz, 1156 High Street, Santa Cruz, California, 95064, USA; jcortes@ucsc.edu
Sonia Martínez
Affiliation:
Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, Engineering Building II, Santa Barbara, California, 93106, USA; smartine@engr.ucsb.edu; bullo@engr.ucsb.edu
Francesco Bullo
Affiliation:
Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, Engineering Building II, Santa Barbara, California, 93106, USA; smartine@engr.ucsb.edu; bullo@engr.ucsb.edu
Get access

Abstract

This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius.
Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time.
These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.

Keywords

Distributed dynamical systemscoordination and cooperative controlgeometric optimizationnonsmooth analysisVoronoi partitions.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 4 , October 2005 , pp. 691 - 719
Copyright
© EDP Sciences, SMAI, 2005

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

R.C. Arkin, Behavior-Based Robotics. Cambridge, Cambridge University Press (1998).
Y. Asami, A note on the derivation of the first and second derivative of objective functions in geographical optimization problems. J. Faculty Engineering, The University of Tokio (B) XLI (1991) 1–13.
R.G. Bartle, The Elements of Integration and Lebesgue Measure, 1st edn. Wiley-Interscience (1995).
M. de Berg, M. van Kreveld and M. Overmars, Computational Geometry: Algorithms and Applications. New York, Springer-Verlag (1997).
S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge,Cambridge University Press (2004).
A.J. Chorin and J.E. Marsden, A Mathematical Introduction to Fluid Mechanics. 3rd edn., Ser. Texts in Applied Mathematics. New York, Springer-Verlag 4 (1994).
J. Cortés and F. Bullo, Coordination and geometric optimization via distributed dynamical systems. SIAM J. Control Optim. (June 2004), to appear.
Cortés, J., Martínez, S., Karatas, T. and Bullo, F., Coverage control for mobile sensing networks. IEEE Trans. Robotics Automat. 20 (2004) 243–255. CrossRef
R. Diestel, Graph Theory. 2nd edn., Ser. Graduate Texts in Mathematics. New York, Springer-Verlag 173 (2000).
Z. Drezner and H.W. Hamacher, Eds., Facility Location: Applications and Theory. New York, Springer-Verlag (2001).
Du, Q., Faber, V. and Gunzburger, M., Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev. 41 (1999) 637–676. CrossRef
Edelsbrunner, H. and Shah, N.R., Triangulating topological spaces. Internat. J. Comput. Geom. Appl. 7 (1997) 365–378. CrossRef
J. Gao, L.J. Guibas, J. Hershberger, L. Zhang and A. Zhu, Geometric spanner for routing in mobile networks, in ACM International Symposium on Mobile Ad-Hoc Networking & Computing (MobiHoc). Long Beach, CA (Oct. 2001) 45–55.
Gray, R.M. and Neuhoff, D.L., Quantization. IEEE Trans. Inform. Theory 44 (1998) 2325–2383. Commemorative Issue 1948–1998. CrossRef
U. Helmke and J. Moore, Optimization and Dynamical Systems. New York, Springer-Verlag (1994).
Jadbabaie, A., Lin, J. and Morse, A.S., Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Control 48 (2003) 988–1001. CrossRef
Jaromczyk, J.W. and Toussaint, G.T., Relative neighborhood graphs and their relatives. Proc. of the IEEE 80 (1992) 1502–1517. CrossRef
H.K. Khalil, Nonlinear Systems. Englewood Cliffs, Prentice Hall (1995).
J.P. LaSalle, The Stability and Control of Discrete Processes. Ser. Applied Mathematical Sciences. New York, Springer-Verlag 62 (1986).
Algorithmic, X.-Y. Li, geometric and graphs issues in wireless networks. Wireless Communications and Mobile Computing 3 (2003) 119–140.
D.G. Luenberger, Linear and Nonlinear Programming. Reading, Addison-Wesley (1984).
Marshall, J., Broucke, M. and Francis, B., Formations of vehicles in cyclic pursuit. IEEE Trans. Automat. Control 49 (2004) 1963–1974. CrossRef
A. Okabe, B. Boots, K. Sugihara and S.N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. 2nd edn., Ser. Wiley Series in Probability and Statistics. New York, John Wiley & Sons (2000).
Okabe, A. and Suzuki, A., Locational optimization problems solved through Voronoi diagrams. European J. Oper. Res. 98 (1997) 445–56. CrossRef
Okubo, A., Dynamical aspects of animal grouping: swarms, schools, flocks and herds. Adv. Biophysics 22 (1986) 1–94. CrossRef
Olfati-Saber, R. and Murray, R.M., Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control 49 (2004) 1520–1533. CrossRef
K.M. Passino, Biomimicry for Optimization, Control, and Automation. New York, Springer-Verlag (2004).
Reynolds, C.W., Flocks, herds, and schools: A distributed behavioral model. Computer Graphics 21 (1987) 25–34. CrossRef
Rose, K., Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proc. of the IEEE 80 (1998) 2210–2239. CrossRef
A.R. Teel, Nonlinear systems: discrete-time stability analysis. Lecture Notes, University of California at Santa Barbara (2004).