Abstract
Accounting for wind perturbations while controlling a formation of unmanned aerial vehicles (UAVs) is of a particular interest for researchers: it helps confirm the operability of algorithms in realistic non-laboratory conditions and increases the efficiency of these algorithms. This approach, however, becomes a problem for a decentralized formation due to its interconnected structure. This research work focuses on the problem of accounting for wind perturbations for a fixed-wing UAV formation controlled using the vector field path following method in cooperative or collective circumnavigation. We only study the control based on the local data about nearby UAVs as we consider the consensus-based control. The suggested solution is an adaptive control algorithm studied with Lyapunov functions. At the same time, we conduct computer simulation using complete non-linear UAV models, as well as the comparison with an algorithm that does not account for wind perturbations. As a result, we theoretically demonstrate uniform ultimate boundedness (UUB) of the trajectories of the system in question. Simulation shows that, although the algorithm that does not account for wind perturbations can control a formation with reduced accuracy, the suggested algorithm can improve its efficiency. Therefore, the solution considered in this article helps develop the applicability of consensus-based UAV formation control methods under more realistic conditions and wind impacts.
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References
Price, E., Black, M.J., Ahmad, A.: Viewpoint-Driven Formation Control of Airships for Cooperative Target Tracking. IEEE Robot. Autom. Lett. 8(6), 3653–3660 (2023)
Gong, X., Liu, L., Peng, Z., Wang, D., Zhang, W.: Resource-aware synchronized path following of multiple unmanned surface vehicles with experiments: A cooperative vector field approach. Control. Eng. Pract. 124, 105184 (2022)
Tan, G., Sun, H., Du, L., Zhuang, J., Zou, J., Wan, L.: Coordinated control of the heterogeneous unmanned surface vehicle swarm based on the distributed null-space-based behavioral approach. Ocean Eng. 266, 112928 (2022)
Jain, R.P., de Sousa, J.B., Aguiar, A.P.: Three dimensional moving path following control for robotic vehicles with minimum positive forward speed. IEEE ControlSyst. Lett. 6, 79–84 (2022)
Mechali, O., Xu, L., Xie, X., Iqbal, J.: Theory and practice for autonomous formation flight of quadrotors via distributed robust sliding mode control protocol with fixed-time stability guarantee. Control. Eng. Pract. 123, 105150 (2022)
Rekabi, F., Shirazi, F.A., Sadigh, M.J., Saadat, M.: Distributed output feedback nonlinear H∞ formation control algorithm for heterogeneous aerial robotic teams. Rob. Auton. Syst. 136, 103689 (2021)
Li, J., Fang, Y., Cheng, H., Wang, Z., Wu, Z., Zeng, M.: Large-scale fixed-wing UAV swarm system control with collision avoidance and formation maneuver. IEEE Syst. J. 17, 744–755 (2023)
Heintz, C., Bailey, S.C., Hoagg, J. B.: Formation control of fixed-wing unmanned aircraft: Theory and experiments. In: AIAA Scitech 2019 Forum (2019)
Sharma, B.N., Raj, J., Vanualailai, J.: Navigation of carlike robots in an extended dynamic environment with swarm avoidance. Int. J. Robust Nonlinear Control 28(2), 678–698 (2018)
Roza, A., Maggiore, M., Scardovi, L.: A Smooth Distributed Feedback for Formation Control of Unicycles. IEEE Trans. Autom. Control 64(12), 4998–5011 (2019)
Kotov, K.Y., Nesterov, A.A., Filippov, M.N., Yan, A.P.: Method of quadrotor flight control in the target tracking problem. Optoelectron. Instrum. Data Process. 53(4), 309–315 (2017)
Litimein, H., Huang, Z.Y., Hamza, A.: A Survey on Techniques in the Circular Formation of Multi-Agent Systems. Electron 10(23), 2959 (2021)
Kim, S., Cho, H., Jung, D.: Circular Formation Guidance of Fixed-Wing UAVs Using Mesh Network. IEEE Access 10, 115295–115306 (2022)
Ghommam, J., Saad, M., Mnif, F.: Finite-time circular formation around a moving target with multiple underactuated ODIN vehicles. Math. Comput. Simul 180, 230–250 (2021)
El-Hawwary, M.I., Maggiore, M.: Distributed circular formation stabilization for dynamic unicycles. IEEE Trans. Automat. Contr. 58(1), 149–162 (2013)
Briñón-Arranz, L., Seuret, A., Pascoal, A.: Circular formation control for cooperative target tracking with limited information. J. Franklin Inst. 356(4), 1771–1788 (2019)
González-Sierra, J., Flores-Montes, D., Hernandez-Martinez, E.G., Fernández-Anaya, G., Paniagua-Contro, P.: Robust circumnavigation of a heterogeneous multi-agent system. Auton. Robots 45(2), 265–281 (2021)
Lu, H., Yao, W., Chen, L.: Distributed Multi-robot Circumnavigation with Dynamic Spacing and Time Delay. J. Intell. Robot. Syst. Theory Appl. 99(1), 165–182 (2020)
Zhang, M., Jia, J., Mei, J.: A composite system theory-based guidance law for cooperative target circumnavigation of UAVs. Aerosp. Sci. Technol. 118, 107034 (2021)
Fonseca, J., Wei, J., Johansen, T.A., Johansson, K.H.: Cooperative Circumnavigation for a Mobile Target Using Adaptive Estimation. In: Gonçalves, J.A., Braz-César, M., Coelho, J.P. (eds.) CONTROLO 2020. Lecture Notes in Electrical Engineering, vol. 695, pp. 33–48. Springer, Cham (2021)
Matveev, A.S., Magerkin, V.V.: Communication-free autonomous cooperative circumnavigation of unpredictable dynamic objects. Robotica 40(3), 520–543 (2022)
Cui, L., Chen, S., Wang, L.: Distributed control for multi-target circumnavigation by a group of agents. Int. J. Syst. Sci. 48(12), 2565–2574 (2017)
Zhang, C., Li, Y., Qi, G., Sheng, A.: Distributed finite-time control for coordinated circumnavigation with multiple agents under directed topology. J. Franklin Inst. 357(16), 11710–11729 (2020)
Chen, K., Qi, G., Li, Y., Sheng, A.: Cooperative localization and circumnavigation ofmultiple targets with bearing-only measurements. J. Franklin Inst. 360, 9159–9179 (2023)
Dong, F., You, K., Xie, L., Hu, Q.: Coordinate-Free Circumnavigation of a Moving Target Via a PD-Like Controller. IEEE Trans. Aerosp. Electron. Syst. 58(3), 2012–2025 (2022)
Zhang, M., Lin, Y., Hao, H., Mei, J.: Range-only control for cooperative target circumnavigation of unmanned aerial vehicles. Adv. Control Appl. Eng. Ind. Syst. 2(4) (2020)
Yu, Y., Li, Z., Wang, X., Shen, L.: Bearing-only circumnavigation control of the multi-agent system around a moving target. IET Control Theory Appl. 13(17), 2747–2757 (2019)
Ma, J., Lu, H., Xiao, J., Zeng, Z., Zheng, Z.: Multi-robot Target Encirclement Control with Collision Avoidance via Deep Reinforcement Learning. J. Intell. Robot. Syst. Theory Appl. 99(2), 371–386 (2020)
Jain, P., Peterson, C.K., Beard, R.W.: Encirclement of Moving Targets Using Noisy Range and Bearing Measurements. J. Guid. Control. Dyn. 45(8), 1399–1414 (2022)
Wang, W., Chen, X., Jia, J., Fu, Z.: Target localization and encirclement control formulti-UAVs with limited information. IET Control Theory Appl. 16, 1396–1404 (2022)
Olavo, J.L.G., Thums, G.D., Jesus, T.A., De AraujoPimenta, L.C., Torres, L.A.B., Palhares, R.M.: Robust Guidance Strategy for Target Circulation by Controlled UAV. IEEE Trans Aerosp Electron Syst 54(3), 1415–1431 (2018)
Rezaee, H., Abdollahi, F.: A cyclic pursuit framework for networked mobile agents based on vector field approach. J. Franklin Inst. 356(2), 1113–1130 (2019)
Daingade, S., Sinha, A., Borkar, A.V., Arya, H.: A variant of cyclic pursuit for target tracking applications: theory and implementation. Auton. Robots 40(4), 669–686 (2016)
Kokolakis, N.-M.T., Koussoulas, N.T.: Robust Standoff Target Tracking with Finite-TimePhase Separation Under Unknown Wind. J. Guid. Control. Dyn. 44, 1183–1198 (2021)
Lin, C., Shi, J., Lyu, Y., Wang, Y.: Over-flight and standoff tracking of a ground target with a fixed-wing unmanned aerial vehicle based on a unified sliding mode guidance law. Trans. Inst. Meas. Control. 44(2), 410–423 (2022)
Yoon, S., Park, S., Kim, Y.: Circular motion guidance law for coordinated standoff tracking of a moving target. IEEE Trans. Aerosp. Electron. Syst. 49(4), 2440–2462 (2013)
Srinivasu, N., Ratnoo, A.: Standoff Target Tracking Using Line-of-Sight Distance Bifurcation. J. Guid. Control. Dyn. 45(10), 1934–1945 (2022)
Kou, L., Huang, Y., Chen, Z., He, S., Xiang, J.: Cooperative fencing control ofmultiple second-order vehicles for a moving target with and without velocitymeasurements. Int. J. Robust Nonlinear Control. 31, 4602–4615 (2021)
Lawrence, D.A., Frew, E.W., Pisano, W.J.: Lyapunov Vector Fields for Autonomous Unmanned Aircraft Flight Control. J. Guid. Control. Dyn. 31(5), 1220–1229 (2008)
Nelson, D.R., Barber, D.B., McLain, T.W., Beard, R.W.: Vector Field Path Following forMiniature Air Vehicles. IEEE Trans. Robot. 23, 519–529 (2007)
Harinarayana, T., Hota, S., Kushwaha, R.: Vector field guidance for standoff target tracking. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 236, 2963–2973 (2022)
Lin, C., Shi, J., Zhang, W., Lyu, Y.: Standoff tracking of a ground target based oncoordinated turning guidance law. ISA Trans. 119, 118–134 (2022)
Chen, H., Cong, Y., Wang, X., Xu, X., Shen, L.: Coordinated path-following control of fixed-wing unmanned aerial vehicles. IEEE Trans. Syst. Man, Cybern. Syst. 52, 2540–2554 (2022)
Takahashi, Y., Tanaka, M., Tanaka, K.: Coordinated flight path generation and fuzzymodel-based control of multiple unmanned aerial vehicles in windy environments. Int. J. Fuzzy Syst. 25, 1–14 (2023)
Borkar, A.V., Borkar, V.S., Sinha, A.: Aerial monitoring of slow moving convoys using elliptical orbits. Eur. J. Control. 46, 90–102 (2019)
Muslimov, T.Z., Munasypov, R.A.: Consensus-based cooperative circular formation control Strategy for multi-UAV system. In: 2019 international Russian automation conference (RusAutoCon). pp. 1–8. IEEE (2019). https://doi.org/10.1109/RusAutoCon.2019.8867733
Muslimov, T.Z., Munasypov, R.A.: Adaptive decentralized flocking control of multi-UAV circular formations based on vector fields and backstepping. ISA Trans. 107, 143–159 (2020)
Zhou, B., Satyavada, H., Baldi, S.: Adaptive path following for Unmanned Aerial Vehicles in time-varying unknown wind environments. In: Proceedings of the American Control Conference, pp. 1127–1132 (2017)
Fari, S., Wang, X., Roy, S., Baldi, S.: Addressing unmodelled path-following dynamics via adaptive vector field: a UAV test case. IEEE Trans. Aerosp. Electron. Syst. 56, 1613–1622 (2019)
Wang, X., Roy, S., Farì, S., Baldi, S.: The problem of reliable design of vector-field path following in the presence of uncertain course dynamics. IFAC-PapersOnLine. 53, 9399–9404 (2020)
Popov, A.M., Kostrygin, D.G., Shevchik, A.A., Andrievsky, B.: Speed-Gradient Adaptive Control for Parametrically Uncertain UAVs in Formation. Electron. 11(24), 4187 (2022)
Wang, X., Baldi, S., Feng, X., Wu, C., Xie, H., De Schutter, B.: A Fixed-Wing UAV Formation Algorithm Based on Vector Field Guidance. IEEE Trans. Autom. Sci. Eng. 20(1), 179–192 (2023)
Beard, R.W., McLain, T.W.: Small unmanned aircraft: Theory and practice. Princeton University Press, Princeton and Oxford (2012)
Muslimov, T.Z., Munasypov, R.A.: Multi-UAV cooperative target tracking via consensus-based guidance vector fields and fuzzy MRAC. Aircr. Eng. Aerosp. Technol. 93(7), 1204–1212 (2021)
Acknowledgements
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (Agreement No. 075-15-2021-1016).
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The Ministry of Science and Higher Education of the Russian Federation (Agreement No. 075–15-2021–1016).
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Tagir Muslimov did all the research and wrote this manuscript.
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Muslimov, T. Cooperative Circumnavigation with Robust Vector Field Guidance for Multiple UAVs in Unknown Wind Environments. J Intell Robot Syst 109, 84 (2023). https://doi.org/10.1007/s10846-023-02000-3
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DOI: https://doi.org/10.1007/s10846-023-02000-3