×

Controlling anonymous mobile agents with unidirectional locomotion to form formations on a circle. (English) Zbl 1298.93038

Summary: We study the circle forming problem in which a group of anonymous mobile agents are required to form a formation when moving on a given circle. The agents are constrained to move in the one-dimensional space of the circle only in the counterclockwise direction, but not the opposite way. Distributed, cooperative, sampled-data control strategies are designed that only take nonnegative values. We prove that the multi-agent system under such constrained control input can be guided to reach the prescribed circle formation asymptotically with the additional guarantee that no collision between agents ever takes place. The theoretical analysis is further validated through simulations.

MSC:

93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93C57 Sampled-data control/observation systems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bullo, F.; Cortes, J.; Martinez, S., Distributed control of robotic networks, (2009), Princeton University Press Princeton
[2] Cao, M.; Morse, A. S.; Anderson, B. D.O., Reaching a consensus in a dynamically changing environment: a graphical approach, SIAM Journal on Control and Optimization, 47, 575-600, (2008) · Zbl 1157.93514
[3] Chatzigiannakis, I.; Markou, M.; Nikoletseas, S., Distributed circle formation for anonymous oblivious robots, (Experimental and efficient algorithms, Vol. 3059, (2004), Springer Berlin, Heidelberg), 159-174, (Chapter 12)
[4] Chen, T.; Francis, B., Optimal sampled-data control systems, (1995), Springer-Verlag New York, Inc., Secaucus, NJ, USA · Zbl 0847.93040
[5] Défago, X.; Konagaya, A., Circle formation for oblivious anonymous mobile robots with no common sense of orientation, (Proceedings of the second ACM international workshop on principles of mobile computing, (2002), ACM Press), 97-104
[6] Défago, X.; Souissi, S., Non-uniform circle formation algorithm for oblivious mobile robots with convergence toward uniformity, Theoretical Computer Science, 396, 1-3, 97-112, (2008) · Zbl 1146.68462
[7] Dhariwal, A., Sukhatme, G. S., & Requicha, A. A. G. (2004). Bacterium-inspired robots for environmental monitoring. In Proc. of the IEEE international conference on robotics and automation (ICRA ’04) (pp. 1436-1443).
[8] Diestel, R., Graph theory, (1997), Springer-Verlag New York, Inc.
[9] Dubins, L. E., On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents, American Journal of Mathematics, 79, 497C516, (1957) · Zbl 0098.35401
[10] Elor, Y.; Bruckstein, A. M., Uniform multi-agent deployment on a ring, Theoretical Computer Science, 412, 783-795, (2011) · Zbl 1206.68311
[11] Flocchini, P.; Prencipe, G.; Santoro, N., Self-deployment of mobile sensors on a ring, Theoretical Computer Science, 402, 1, 67-80, (2008) · Zbl 1156.68594
[12] Horn, R. A.; Johnson, C. R., Matrix analysis, (1985), Cambridge University Press Cambridge, U.K. · Zbl 0576.15001
[13] Ijspeert, A. J.; Crespi, A.; Ryczko, D.; Cabelguen, J. M., From swimming to walking with a salamander robot driven by a spinal cord model, Science, 315, 1416-1420, (2007)
[14] Krick, L.; Broucke, M. E.; Francis, B. A., Stabilisation of infinitesimally rigid formations of multi-robot networks, International Journal of Control, 82, 423-439, (2009) · Zbl 1168.93306
[15] Leonard, N. E.; Paley, D. A.; Davis, R. E.; Fratantoni, D. M.; Lekien, F.; Zhang, F., Coordinated control of an underwater glider fleet in an adaptive Ocean sampling field experiment in monterey bay, Journal of Field Robotics, 27, 718-740, (2010)
[16] 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 IEEE, 95, 48-74, (2007)
[17] Marshall, J. A.; Broucke, M. E.; Francis, B. A., Formations of vehicles in cyclic pursuit, IEEE Transactions on Automatic Control, 49, 11, 1963-1974, (2004) · Zbl 1366.91027
[18] Roy, N.; Dudek, G., Collaborative robot exploration and rendezvous: algorithms, performance bounds and observations, Autonomous Robots, 11, 2, 117-136, (2001) · Zbl 0987.68547
[19] Suzuki, I.; Yamashita, M., Distributed anonymous mobile robots: formation of geometric patterns, SIAM Journal on Computing, 28, 4, 1347-1363, (1999) · Zbl 0940.68145
[20] Wang, C.; Xie, G.; Cao, M., Forming circle formations of anonymous mobile agents with order preservation, IEEE Transactions on Automatic Control, 58, 12, 3248-3254, (2013)
[21] Wang, C.; Xie, G.; Wang, L.; Cao, M., CPG-based locomotion control of a robotic fish: using linear oscillators and reducing control parameters via PSO, International Journal of Innovative Computing, Information and Control, 7, 4237-4249, (2011)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.