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

Jorge Cortés; Sonia Martínez; Francesco Bullo

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 11, Issue: 4, page 691-719
- ISSN: 1292-8119

## Access Full Article

top## Abstract

top## How to cite

topCortés, Jorge, Martínez, Sonia, and Bullo, Francesco. "Spatially-distributed coverage optimization and control with limited-range interactions." ESAIM: Control, Optimisation and Calculus of Variations 11.4 (2010): 691-719. <http://eudml.org/doc/90783>.

@article{Cortés2010,

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.
},

author = {Cortés, Jorge, Martínez, Sonia, Bullo, Francesco},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Distributed dynamical systems; coordination and cooperative
control; geometric optimization; nonsmooth analysis; Voronoi partitions.; coordination and cooperative control; Voronoi partitions},

language = {eng},

month = {3},

number = {4},

pages = {691-719},

publisher = {EDP Sciences},

title = {Spatially-distributed coverage optimization and control with limited-range interactions},

url = {http://eudml.org/doc/90783},

volume = {11},

year = {2010},

}

TY - JOUR

AU - Cortés, Jorge

AU - Martínez, Sonia

AU - Bullo, Francesco

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 11

IS - 4

SP - 691

EP - 719

AB -
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.

LA - eng

KW - Distributed dynamical systems; coordination and cooperative
control; geometric optimization; nonsmooth analysis; Voronoi partitions.; coordination and cooperative control; Voronoi partitions

UR - http://eudml.org/doc/90783

ER -

## References

top- 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). Zbl0838.28001
- M. de Berg, M. van Kreveld and M. Overmars, Computational Geometry: Algorithms and Applications. New York, Springer-Verlag (1997). Zbl0939.68134
- S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge,Cambridge University Press (2004). Zbl1058.90049
- 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). Zbl0417.76002
- J. Cortés and F. Bullo, Coordination and geometric optimization via distributed dynamical systems. SIAM J. Control Optim. (June 2004), to appear. Zbl1165.37041
- J. Cortés, S. Martínez, T. Karatas and F. Bullo, Coverage control for mobile sensing networks. IEEE Trans. Robotics Automat.20 (2004) 243–255.
- 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).
- Q. Du, V. Faber and M. Gunzburger, Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev.41 (1999) 637–676. Zbl0983.65021
- H. Edelsbrunner and N.R. Shah, Triangulating topological spaces. Internat. J. Comput. Geom. Appl.7 (1997) 365–378. Zbl0887.57028
- 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.
- R.M. Gray and D.L. Neuhoff, Quantization. IEEE Trans. Inform. Theory44 (1998) 2325–2383. Commemorative Issue 1948–1998.
- U. Helmke and J. Moore, Optimization and Dynamical Systems. New York, Springer-Verlag (1994). Zbl0984.49001
- A. Jadbabaie, J. Lin and A.S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Control48 (2003) 988–1001.
- J.W. Jaromczyk and G.T. Toussaint, Relative neighborhood graphs and their relatives. Proc. of the IEEE80 (1992) 1502–1517.
- 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). Zbl0606.93001
- X.-Y. Li, Algorithmic, geometric and graphs issues in wireless networks. Wireless Communications and Mobile Computing3 (2003) 119–140.
- D.G. Luenberger, Linear and Nonlinear Programming. Reading, Addison-Wesley (1984). Zbl0571.90051
- J. Marshall, M. Broucke and B. Francis, Formations of vehicles in cyclic pursuit. IEEE Trans. Automat. Control49 (2004) 1963–1974.
- 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). Zbl0946.68144
- A. Okabe and A. Suzuki, Locational optimization problems solved through Voronoi diagrams. European J. Oper. Res.98 (1997) 445–56. Zbl0930.90059
- A. Okubo, Dynamical aspects of animal grouping: swarms, schools, flocks and herds. Adv. Biophysics22 (1986) 1–94.
- R. Olfati-Saber and R.M. Murray, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control49 (2004) 1520–1533.
- K.M. Passino, Biomimicry for Optimization, Control, and Automation. New York, Springer-Verlag (2004). Zbl1080.93002
- C.W. Reynolds, Flocks, herds, and schools: A distributed behavioral model. Computer Graphics21 (1987) 25–34.
- K. Rose, Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proc. of the IEEE80 (1998) 2210–2239.
- A.R. Teel, Nonlinear systems: discrete-time stability analysis. Lecture Notes, University of California at Santa Barbara (2004).

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.