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Distributed control of triangular formations with angle-only constraints. (English) Zbl 1186.93003

Summary: This paper considers the coupled, bearing-only formation control of three mobile agents moving in the plane. Each agent has only local inter-agent bearing knowledge and is required to maintain a specified angular separation relative to both neighbor agents. Assuming that the desired angular separation of each agent relative to the group is feasible, a triangle is generated. The control law is distributed and accordingly each agent can determine their own control law using only the locally measured bearings. A convergence result is established in this paper which guarantees global asymptotic convergence of the formation to the desired formation shape.

MSC:

93A14 Decentralized systems
93B51 Design techniques (robust design, computer-aided design, etc.)
93B35 Sensitivity (robustness)
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[1] A.N. Bishop, B. Fidan, B.D.O. Anderson, K. Dogancay, P.N. Pathirana, Optimality analysis of sensor-target geometries in passive localization: Part 1 - Bearing-only localization., in: Proc. of the 3rd International Conference on Intelligent Sensors, Sensor Networks, and Information Processing, Melbourne, Australia, December 2007 · Zbl 1194.93216
[2] A.N. Bishop, B. Fidan, B.D.O. Anderson, P.N. Pathirana, K. Dogancay, Optimality analysis of sensor-target geometries in passive localization: Part 2 - Time-of-arrival based localization, in: Proc. of the 3rd International Conference on Intelligent Sensors, Sensor Networks, and Information Processing, Melbourne, Australia, December 2007 · Zbl 1194.93216
[3] Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control, 48, 6, 988-1001, (2003) · Zbl 1364.93514
[4] Savkin, A.V., Coordinated collective motion of groups of autonomous mobile robots: analysis of vicsek’s model, IEEE transactions on automatic control, 49, 6, 981-983, (2004) · Zbl 1365.93327
[5] Fax, J.A.; Murray, R.M., Information flow and cooperative control of vehicle formations, IEEE transactions on automatic control, 49, 9, 1464-1476, (2004) · Zbl 1365.90056
[6] Moreau, L., Stability of multiagent systems with time-dependent communication links, IEEE transactions on automatic control, 50, 2, 169-182, (2005) · Zbl 1365.93268
[7] Olfati-Saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE transactions on automatic control, 51, 3, 401-420, (2006) · Zbl 1366.93391
[8] Moshtagh, N.; Jadbabaie, A., Distributed geodesic control laws for flocking of nonoholonomic agents, IEEE transactions on automatic control, 52, 4, 681-686, (2007) · Zbl 1366.93390
[9] Gazi, V., Stability analysis of swarms, IEEE transactions on automatic control, 48, 4, 692-697, (2003) · Zbl 1365.92143
[10] Rimon, E.; Koditschek, D.E., Exact robot navigation using artificial potential functions, IEEE transactions on robotics and automation, 8, 5, 501-518, (1992)
[11] R.O. Saber, R.M. Murray, Distributed cooperative control of multiple vehicle formations using structural potential functions, in: Proceedings of the 15th IFAC World Congress, Barcelona, Spain, July 2002, pp. 1-7
[12] Belta, C.; Kumar, V., Abstractions and control policies for a swarm of robots, IEEE transactions on robotics, 20, 5, 865-875, (2004)
[13] Lin, Z.; Broucke, M.E.; Francis, B.A., Local control strategies for groups of mobile autonomous agents, IEEE transactions on automatic control, 49, 4, 622-629, (2004) · Zbl 1365.93208
[14] Gazi, V., Swarm aggregations using artificial potentials and sliding-mode control, IEEE transactions on robotics, 21, 6, 1208-1214, (2005)
[15] ()
[16] Ren, W.; Beard, R.W., A decentralized scheme for spacecraft formation flying via the virtual structure approach, AIAA journal of guidance, control and dynamics, 27, 1, 73-82, (2004)
[17] Ogren, P.; Fiorelli, E.; Leonard, N.E., Cooperative control of mobile sensor networks: adaptive gradient climbing in a distributed environment, IEEE transactions on automatic control, 49, 8, 1292-1302, (2004) · Zbl 1365.93243
[18] Cortes, J.; Martinez, S.; Karatas, T.; Bullo, F., Coverage control for mobile sensing networks, IEEE transactions on robotics, 20, 2, 243-255, (2004)
[19] Fiorelli, E.; Leonard, N.E.; Bhatta, P.; Paley, D.A.; Bachmayer, R.; Fratantoni, D.M., Multi-AUV control and adaptive sampling in monterey bay, IEEE transactions on oceanic engineering, 31, 4, 935-948, (2006)
[20] Leonard, N.E.; Paley, D.A.; Lekien, F.; Sepulchre, R.; Fratantoni, D.M.; Davis, R.E., Collective motion, sensor networks and Ocean sampling, Proceedings of the IEEE, 95, 1, 48-74, (2007)
[21] R.O. Saber, R.M. Murray, Graph rigidity and distributed formation stabilization of multi-vehicle systems, in: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevade, USA, 2002, pp. 2965-2971
[22] J. Baillieul, A. Suri, Information patterns and hedging Brockett’s theorem controlling vehicle formations, in: Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, USA, December 2003, pp. 556-563
[23] Lin, Z.; Francis, B.A.; Maggiore, M., Necessary and sufficient graphical conditions for formation control of unicycles, IEEE transactions on automatic control, 50, 1, 121-127, (2005) · Zbl 1365.93324
[24] Anderson, B.D.O; Yu, C.; Dasgupta, S.; Morse, A.S., Control of a three-coleader formation in the plane, Systems and control letters, 56, 573-578, (2007) · Zbl 1155.93366
[25] T. Eren, D.K. Goldenberg, W. Whiteley, Y.R. Yang, A.S. Morse, B.D.O. Anderson, P.N. Belhumeur, Rigidity, computation, and randomization in network localization, in: Proceedings of the International Joint Conference of the IEEE Computer and Communications Societies, Hong Kong, March 2004, pp. 2673-2684
[26] Hendrickx, J.M.; Anderson, B.D.O.; Delvenne, J-C.; Blondel, V.D., Directed graphs for the analysis of rigidity and persistence in autonomous agents systems, International journal of robust and nonlinear control, 17, 10-11, 960-981, (2006)
[27] Yu, C.; Hendrickx, J.M.; Fidan, B.; Anderson, B.D.O; Blondel, V.D., Three and higher dimensional autonomous formations: rigidity, persistence and structural persistence, Automatica, 43, 3, 387-402, (2007) · Zbl 1137.93309
[28] T. Eren, W. Whiteley, P.N. Belhumeur, Using angle of arrival (bearing) information in network localizationn, in: Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, California, USA, December 2006
[29] Lindgren, A.G.; Gong, K.F., Position and velocity estimation via bearing observations, IEEE transactions on aerospace and electronic systems, 14, 4, 564-577, (1978)
[30] Nardone, S.C.; Lindgren, A.G.; Gong, K.F., Fundamental properties and performance of conventional bearings-only target motion analysis, IEEE transactions on automatic control, 29, 9, 775-787, (1984)
[31] Gavish, M.; Weiss, A.J., Performance analysis of bearing-only target location algorithms, IEEE transactions on aerospace and electronic systems, 28, 3, 817-827, (1992)
[32] S.G. Loizou, V. Kumar, Biologically inspired bearing-only navigation and tracking, in: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, December 2007, pp. 1386-1391
[33] Moshtagh, N.; Michael, N.; Jadbabaie, A.; Daniilidis, K., Vision-based, distributed control for motion coordination of nonholonomic robots, IEEE transactions on robotics, 25, 4, 851-860, (2009)
[34] Wiggins, S., Introduction to applied nonlinear dynamical systems and chaos, (1990), Springer-Verlag New York, NY · Zbl 0701.58001
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