Abstract
A formal distributed control methodology to coordinate a team of fixed-wing UAVs (Unmanned Aerial Vehicles) in a three-dimensional workspace is addressed. The complete task to be accomplished is divided in three stages: (i) each UAV tracks a circle parallel to the \(xy\) plane in a given altitude (different altitudes for different UAVs); (ii) the UAVs distribute themselves in such a way that their projection onto the \(xy\) plane are evenly spaced around a circle; (iii) each UAV converges to the same altitude to track the same circle. The main contribution of this work lies in the mathematical proofs of the proposed strategy for a given UAV model. We consider minimum and maximum limits in the forward speed command, maximum limit in the absolute value of the yaw rate, maximum limit in the absolute value of the altitude speed, second-order dynamics, and a non-holonomic constraint. Stability and collision avoidance are guaranteed during the whole task including the stage transitions and without violating the constraints. Simulation results are given to illustrate the proposed approach.
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Notes
Which comes from a vector field that will be presented in the next Section.
\(K_f>0\) and \(K_{\alpha }>0\) chosen as in (23) naturally result in \(R>R_\mathrm{{min}}\).
References
Aguiar, A. P., Hespanha, J. P., & Kokotavić, P. (2008). Performance limitations in reference-tracking and path-following for nonlinear systems. Automatica, 44, 598–610.
Aicardi, M., Casalino, G., Bicchi, A., & Balestrino, A. (1995). Closed loop steering of unicycle-like vehicles via Lyapunov techniques. IEEE Robotics & Automation Magazine, 2(1), 27–35.
Ajorlou, A., Momeni, A. & Aghdam, A. G. (2011). A connectivity preserving containment control strategy for a network of single integrator agents. In Proceedings of the American Control Conference (pp. 499–501).
Bayraktar, S., Fainekos, J. E. & Pappas, G. J. (2004). Experimental cooperative control of fixed-wing unmanned aerial vehicles. In Proceedings of the 43rd IEEE Conference on Decision and Control (pp. 4292–4298).
Bó, A. P. L. & Borges, G. A. (2007). Denvolvimento de um sistema de localização 3D para aplicação em robôs aéreos. In V Simpósio Brasileiro de Engenharia Inercial (SBEIN 2007) (pp. 1–6).
Bussamra, F. L. S., Vilchez, C. M. M., & Santos, J. C. (2009). Experimental determination of unmanned aircraft inertial properties. In Brazilian Symposium on Aerospace Engineering and Applications.
Carlési, N., Michel, F., Jouvencel, B. & Ferber, J. (2011). Generic architecture for multi-AUV cooperation based on a multi-agent reactive organizational approach. In Proceedings of the International Conference on Intelligent Robots and Systems (pp. 5041–5047).
Casbeer, D. W., Kingston, D. B., Beard, R. W., McLain, T. W., Li, S.-M., & Mehra, R. (2006). Cooperative forest fire surveillance using a team of small unmanned air vehicles. International Journal of Systems Science, 37(6), 351–360.
Ceccarelli, N., Marco, M. D., Garulli, A., & Giannitrapani, A. (2008). Collective circular motion of multi-vehicle systems. Automatica, 40, 3025–3035.
Cheah, C. C., Hou, S. P., & Slotine, J. J. E. (2009). Region-based shape control for a swarm of robots. Automatica, 45, 2406–2411.
Costa, F. G., Ueyama, J., Braun, T., Pessin, G., Osório, F. S., & Vargas, P. A. (2012). The use of unmanned aerial vehicles and wireless sensor network in agricultural applications. In IEEE International Geoscience and Remote Sensing Symposium.
Dimarogonas, D. V., & Kyriakopoulos, K. J. (2008). Connectedness preserving distributed swarm aggregation for multiple kinematic robots. IEEE Transactions on Robotics, 24(5), 1213–1223.
Ding, X. C., Rahmani, A. R., & Egerstedt, M. (2010). Multi-UAV convoy protection: An optimal approach to path planning and coordination. IEEE Transactions on Robotics, 26, 256–268.
Franchi, A., Stegagno, P., Rocco, M. D., & Oriolo, G. (2010). Distributed target localization and encircling with a multi-robot system. In Proceedings of the IFAC Symposium on Intelligent Autonomous Vehicles.
Frew, E. W. & Lawrence, D. (2012). Tracking expanding star curves using guidance vector fields. In Proceedings of the American Control Conference (pp. 1749–1754).
Galloway, K. S., Justh, E. W. & Krishnaprasad, P. S. (2010). Cyclic pursuit in three dimensions. In Proceedings of the 49th IEEE Conference on Decision and Control (pp. 7141–7146).
Gan, S. K. & Sukkarieh, S. (2011). Multi-UAV target search using explicit decentralized gradient-based negotiation. In Proceedings of the IEEE International Conference on Robotics and Automation (pp. 751–756).
Gonçalves, M. M., Pimenta, L. C. A., & Pereira, G. A. S. (2011). Coverage of curves in 3D with swarms of nonholonomic aerial robots. Proceedings of the 18th World Congress of the International Federation of Automatic Control (IFAC). (Vol. 18, pp. 10367–10372).
Gonçalves, V. M., Pimenta, L. C. A., Maia, C. A., Dutra, B. C. O., & Pereira, G. A. S. (2010). Vector fields for robot navigation along time-varying curves in n-dimensions. IEEE Transactions on Robotics, 26(4), 647–659.
Hara, S., Kim, T.-H. & Sugie, T. (2008). Distribution formation control for target-enclosing operations based on a cyclic pursuit strategy. In Proceedings of the 17th World Congress of the International Federation of Automatic Control (IFAC) (pp. 6602–6607).
Hsieh, M. A., Kumar, V., & Chaimowicz, L. (2008). Decentralized controllers for shape generation with robotic systems. Robotica, 26, 691–701.
Hsieh, M. A., Loizou, S. & Kumar, R. V. (2007). Stabilization of multiple robots on stable orbits via local sensing. In Proceedings of the IEEE International Conference on Robotics and Automation (pp. 2312–2317).
Iscold, P., Pereira, G. A. S., & Tôrres, L. A. B. (2010). Development of a hand-launched small UAV for ground reconnaissance. IEEE Transactions on Aerospace and Electronic Systems, 46, 335–348.
Jesus, T. A., Pimenta, L. C. A., Tôrres, L. A. B. & Mendes, E. M. A. M. (2012). A vector field approach for controlling a fixed-wing aerial robot with constraints in the inputs and in the state variables. In XIX Congresso Brasileiro de Automática (CBA 2012). Campina Grande, PB.
Kim, T.-H., & Sugie, T. (2007). Cooperative control for target-capturing task based on a cyclic pursuit strategy. Automatica, 43(3), 1426–1431.
Krontiris, A. & Bekris, K. E. (2011). Using minimal communication to improve decentralized conflict for non-holonomic vehicles. In Proceedings of the International Conference on Intelligent Robots and Systems (pp. 3235–3240).
Loizou, S. G., & Kyriakopoulos, K. J. (2008). Navigation of multiple kinematically constrained robots. IEEE Transactions on Robotics, 24(1), 221–231.
Marshall, J. A., Broucke, M. E., & Francis, B. A. (2004). Formations of vehicles in cyclic pursuit. IEEE Transactions on Automatic Control, 49, 1963–1974.
Martins, A. S., Bó, A. P. L., Borges, G. A. & Ishihara, J. Y. (2007). Design and experimental evaluation of rotor speed regulators for model helicopters in a test bench. In Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 1600–1605).
Michael, N., & Kumar, V. (2008). Controlling shapes of ensembles of robots of finite size with nonholonomic constraints. In Proceedings of the Robotics, Science and Systems, Zurich, Switzerland.
Ramirez, J. L., Pavone, M., Frazolli, E. & Miller, D. W. (2009). Distributed control of spacecraft formation via cyclic pursuit: Theory and experiments. In Proceedings of the American Control Conference (pp. 4811–4817).
Ren, W. (2007). On constrained nonlinear tracking control of a small fixed-wing UAV. Journal of Intelligent and Robotic Systems, 48, 525–537.
Sabattini, L., Chopra, N. & Secchi, C. (2011). Distributed control of multi-robot systems with global connectivity maintenance. In Proceedings of the International Conference on Intelligent Robots and Systems (pp. 2321–2326).
Saska, M., Vonasek, V. & Preucil, L. (2011). Roads sweeping by unmanned multi-vehicle formations. In Proceedings of the IEEE International Conference on Robotics and Automation (pp. 631–636).
Slotine, J.-J. E., & Li, W. (1991). Applied nonlinear control. Englewood Cliffs, NJ: Prentice Hall.
Thums, G. D. (2012). Sintonia PID robusta multi-malha para veículos aéreos não tripulados. Master’s thesis, Programa de Pós-Graduação em Engenharia Elétrica (PPGEE), Escola de Engenharia, Universidade Federal de Minas Gerais (UFMG).
Thums, G. D., Tôrres, L. A. B. & Palhares, R. M. (2012). Metodologia de sintonia PID multi-malha para veículos aéreos não tripulados: Dinâmica longitudinal. In XIX Congresso Brasileiro de Automática (CBA 2012). Campina Grande, PB.
Zhang, H., Pothuvila, K., Hui, Q., Yang, R. & Berg, J. M. (2011). Control of synchronization for multi-agent systems in acceleration motion with additional analysis of formation control. In Proceedings of the American Control Conference (pp. 509–514).
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Jesus, T.A., Pimenta, L.C.d.A., Tôrres, L.A.B. et al. On the Coordination of Constrained Fixed-Wing Unmanned Aerial Vehicles. J Control Autom Electr Syst 24, 585–600 (2013). https://doi.org/10.1007/s40313-013-0062-x
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DOI: https://doi.org/10.1007/s40313-013-0062-x