Avoiding collisions in flocks

IEEE Transactions on Automatic Control

Volumn 55, Issue 5, 2010, Pages 1238-1243

  Cucker, Felipe ^a   Dong, Jiu Gang ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b Suzhou Institute for Advanced Study   (China)

Author keywords

Collision avoidance; Convergence to consensus; Particle systems

Indexed keywords

CONVERGENCE TO CONSENSUS; INITIAL STATE; INTERACTING PARTICLES; MINIMAL DISTANCE; MODIFIED MODEL; PARTICLE SYSTEMS;

MATHEMATICAL MODELS;

COLLISION AVOIDANCE;

EID: 77952158023     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2042355     Document Type: Article

References (23)

1. C. M. Breder, "Equations descriptive of fish schools and other animal aggregations," Ecology, vol.35, pp. 361-370, 1954.
2. J. Cortés, S. Martínez, and F. Bullo, "Spatially- distributed coverage optimization and control with limited-range interactions," ESAIM Control Optim. Calc. Var., vol.11, pp. 691-719, 2005.
3. F. Cucker and C. Huepe, "Flocking with informed agents," Math. in Action, vol.1, pp. 1-25, 2008.
4. F. Cucker and E. Mordecki, "Flocking in noisy environments," J. Math. Pures Appl., vol.89, pp. 278-296, 2008.
5. F. Cucker and S. Smale, "Emergent behavior in flocks," IEEE Trans. Autom. Control, vol.52, no.5, pp. 852-862, May 2007.
6. J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formation," IEEE Trans. Autom. Contr., vol.49, no.9, pp. 1465-1476, Sep. 2004.
7. G. Flierl, D. Grünbaum, S. Levin, and D. Olson, "From individuals to aggregations: The interplay between behavior and physics," J. Theor. Biol., vol.196, pp. 397-454, 1999.
8. V. Gazi and K. M. Passino, "Stability analysis of swarms," IEEE Trans. Autom. Control, vol.48, no.4, pp. 692-697, Apr. 2003.
9. G. Gómez, M. Marcote, J. J. Masdemont, and J. M. Mondelo, "Zero relative radial acceleration cones and controlled motions suitable for formation flying," J. Astronaut. Sci., vol.53, pp. 413-431, 2005.
10. D. Grunbaum and A. Okubo,Modeling Social Animal Aggregations. Berlin, Germany: Springer-Verlag, 1994, vol.100, Lecture Notes in Biomathematics, pp. 296-325.
11. S.-Y. Ha and J.-G. Liu, "A simple proof of the Cucker-Smale flocking dynamics and mean-field limit," Commun. Math. Sci., vol.7, pp. 297-325, 2009.
12. S.-Y. Ha and E. Tadmor, "From particle to kinetic and hydrodynamic descriptions of flocking," Kinetic and Related Models, vol.1, pp. 415-435, 2008.
13. A. Jadbabaie, J. Lin, and A. S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Trans. Autom. Control, vol.48, no.6, pp. 988-1001, Jun. 2003.
14. E. W. Justh and P. S. Krishnaprasad, "Equilibria and steering laws for planar formations," Syst. Control Lett., vol.52, pp. 25-38, 2004.
15. P. Ogren, E. Fiorelli, and N. E. Leonard, "Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment," IEEE Trans. Autom. Control, vol.49, no.8, pp. 1292-1302, Aug. 2004.
16. A. Okubo, "Dynamical aspects of animal grouping: Swarms, schools, flocks, and herds," Adv. Biophys, vol.22, pp. 1-94, 1986.
17. L. Perea, P. Elosegui, and G. Gómez, "Extension of the Cucker-Smale control law to space flight formations," J. Guid., Control, Dynam., vol.32, pp. 526-536, 2009.
18. J. Shen, "Cucker-Smale flocking under hierarchical leadership," SIAM J. Appl. Math, vol.68, pp. 694-719, 2007.
19. I. Suzuki and M. Yamashita, "Distributed anonymous mobile robots: Formation of geometric patterns," SIAM J. Comput., vol.28, pp. 1347-1363, 1999.
20. J. N. Tsitsiklis, "Problems in Decentralized Decision Making and Computation," PhD thesis, Dept. Elect. Eng. Comput. Sci., MIT, Cambridge, MA, 1984.
21. J. N. Tsitsiklis, D. P. Bertsekas, and M. Athans, "Distributed asynchronous deterministic and stochastic gradient optimization algorithms," IEEE Trans. Autom. Control, vol.AC-31, no.9, pp. 803-812, Sep. 1986.
22. T. Vicsek, A. Czirók, E. Ben-Jacob, and O. Shochet, "Novel type of phase transition in a system of self-driven particles," Phys. Rev. Lett., vol.75, pp. 1226-1229, 1995.
23. K.Warburton and J. Lazarus, "Tendency-distance models of social cohesion in animal groups," J. Theoret. Biol., vol.150, pp. 473-488, 1991.