Abstract
In this work, we consider a group of differential-wheeled robots endowed with noisy relative positioning capabilities. We develop a decentralized approach based on a receding horizon controller to generate, in real-time, trajectories that guarantee the convergence of our robots to a common location (i.e. rendezvous).Our receding horizon controller is tailored around two numerical optimization methods: the hybrid-state A* and trust-region algorithms. To validate both methods and test their robustness to computational delays, we perform exhaustive experiments on a team of four real mobile robots equipped with relative positioning hardware.
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References
Beard, R., McLain, T., Nelson, D., Kingston, D., Johanson, D.: Decentralized cooperative aerial surveillance using fixed-wing miniature UAVs. Proceedings of the IEEE 94(7), 1306–1324 (2006)
Branch, M., Coleman, T., Li, Y.: A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems. SIAM Journal on Scientific Computing 21, 1–23 (1999)
Byrd, R., Schnabel, R., Shultz, G.: Approximate solution of the trust region problem by minimization over two-dimensional subspaces. Mathematical Programming 40, 247–263 (1988)
Chyung, D.H.: Time optimal rendezvous of three linear systems. Journal of Optimization Theory and Applications 12, 242–247 (1973)
Dimarogonas, D., Johansson, K.: Further results on the stability of distance-based multi-robot formations. In: American Control Conference, pp. 2972–2977 (2009)
Dimarogonas, D., Kyriakopoulos, K.: On the rendezvous problem for multiple nonholonomic agents. IEEE Transactions on Automatic Control 52(5), 916–922 (2007)
Dimarogonas, D.V., Loizou, S.G., Kyriakopoulos, K.J., Zavlanos, M.M.: A feedback stabilization and collision avoidance scheme for multiple independent non-point agents. Automatica 42(2), 229–243 (2006)
Dolgov, D., Thrun, S., Montemerlo, M., Diebel, J.: Path planning for autonomous driving in unknown environments. In: Khatib, O., Kumar, V., Pappas, G.J. (eds.) Experimental Robotics. STAR, vol. 54, pp. 55–64. Springer, Heidelberg (2009)
Eisenberg, E., Gale, D.: Consensus of subjective probabilities: The pari-mutuel method. The Annals of Mathematical Statistics 30(1), 165–168 (1959)
Falconi, R., Sabattini, L., Secchi, C., Fantuzzi, C., Melchiorri, C.: A graph–based collision–free distributed formation control strategy. In: 18th IFAC World Congress (2011), doi:10.3182/20110828-6-IT-1002.02450
Fax, J., Murray, R.: Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control 49(9), 1465–1476 (2004)
Findeisen, F., Allgöwer, F.: An introduction to nonlinear model predictive control. In: Benelux Meeting on Systems and Control, pp. 119–141 (2002)
Gowal, S., Martinoli, A.: Bayesian rendezvous for distributed robotic systems. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2765–2771 (2011)
Gowal, S., Martinoli, A.: Real-time optimization of trajectories that guarantee the rendezvous of mobile robots. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (2012) (to appear)
Hestenes, M.R., Stiefel, E.: Methods of Conjugate Gradients for Solving Linear Systems. Journal of Research of the National Bureau of Standards 49, 409–436 (1952)
Lawton, J., Beard, R., Young, B.: A decentralized approach to formation maneuvers. IEEE Transactions on Robotics and Automation 19(6), 933–941 (2003)
Lochmatter, T., Roduit, P., Cianci, C., Correll, N., Jacot, J., Martinoli, A.: Swistrack - a flexible open source tracking software for multi-agent systems. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4004–4010 (2008)
McLain, T., Chandler, P., Rasmussen, S., Pachter, M.: Cooperative control of UAV rendezvous. In: Proceedings of the American Control Conference, vol. 3, pp. 2309–2314 (2001)
Meschler, P.: Time-optimal rendezvous strategies. IEEE Transactions on Automatic Control 8(4), 279–283 (1963)
Miele, A., Weeks, M., Ciarcià, M.: Optimal trajectories for spacecraft rendezvous. Journal of Optimization Theory and Applications 132, 353–376 (2007)
Milam, M., Franz, R., Hauser, J., Murray, R.: Receding horizon control of vectored thrust flight experiment. IEE Proceedings on Control Theory and Applications 152(3), 340–348 (2005)
Moré, J., Sorensen, D.: Computing a trust region step. SIAM Journal on Scientific and Statistical Computing 3, 553–572 (1983)
Olfati-Saber, R., Fax, J., Murray, R.: Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE 95(1), 215–233 (2007)
Prorok, A., Arfire, A., Bahr, A., Farserotu, J., Martinoli, A.: Indoor navigation research with the Khepera III mobile robot: An experimental baseline with a case-study on ultra-wideband positioning. In: 2010 International Conference on Indoor Positioning and Indoor Navigation (2010), doi:10.1109/IPIN.2010.5647880
Ren, W.: Distributed attitude consensus among multiple networked spacecraft. In: American Control Conference (2006), doi:10.1109/ACC.2006.1656474
Ren, W., Beard, R.: Distributed Consensus in Multi-vehicle Cooperative Control: Theory and Applications. Springer Publishing Company, Incorporated (2007)
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Gowal, S., Martinoli, A. (2013). Real-Time Optimized Rendezvous on Nonholonomic Resource-Constrained Robots. In: Desai, J., Dudek, G., Khatib, O., Kumar, V. (eds) Experimental Robotics. Springer Tracts in Advanced Robotics, vol 88. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00065-7_25
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DOI: https://doi.org/10.1007/978-3-319-00065-7_25
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