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Three-dimensional robust nonlinear cooperative guidance law for spatiotemporal coordination under stringent input constraint

Published online by Cambridge University Press:  19 March 2025

K. Zhao Open the ORCID record for K. Zhao [Opens in a new window] ,
J. Song Open the ORCID record for J. Song [Opens in a new window] ,
J. Yu  and
Y. Liu
K. Zhao
Affiliation:
School of Astronautics, Beihang University (BUAA), Beijing, China
J. Song*
Affiliation:
School of Astronautics, Beihang University (BUAA), Beijing, China
J. Yu
Affiliation:
School of Astronautics, Beihang University (BUAA), Beijing, China
Y. Liu
Affiliation:
School of Automation Science and Electrical Engineering, Beihang University (BUAA), Beijing, China
*
Corresponding author: J. Song; Email: songjia@buaa.edu.cn
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Abstract

A three-dimensional robust nonlinear cooperative guidance law is proposed to address the challenge of multiple missiles intercepting manoeuvering targets under stringent input constraints and thruster failure. The finite-time convergence theory is used to design a distributed nonlinear sliding mode guidance law, ensuring that the system converges in finite time, with the upper limit of convergence time related to the initial state. A nonlinear sliding surface is adopted to mitigate actuator saturation issues. Then, considering thruster failure, a robust cooperative guidance law is further introduced, ensuring mission completion through the reconstruction of the guidance law. The closed-loop system is proven to be stable using Lyapunov theory, and the influence of hyperparameters on the cooperative guidance law is analysed. Additionally, the results of numerical simulations and hardware-in-the-loop experiments demonstrate the effectiveness and robustness of the proposed algorithm in dealing with stringent input saturation and various disturbances.

Keywords

robust cooperative guidance lawfinite-time convergence theorynonlinear sliding mode guidance lawhardware-in-the-loop
Type
Research Article
Information
The Aeronautical Journal , First View , pp. 1 - 18
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Royal Aeronautical Society

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References

Zhang, J. and Jiahao, X. Cooperative task assignment of multi-uav system, Chin. J. Aeronaut., 2020, 33, pp 2825–2827.CrossRefGoogle Scholar
Jeon, I.-S., Lee, J.-I. and Tahk, M.-J. Homing guidance law for cooperative attack of multiple missiles, J. Guid. Control Dyn., 2010, 33, pp 275–280.CrossRefGoogle Scholar
Zhou, J. and Yang, J. Distributed guidance law design for cooperative simultaneous attacks with multiple missiles, J. Guid. Control Dyn., 2016, 39, pp 2439–2447.CrossRefGoogle Scholar
Li, Z. and Ding, Z. Robust cooperative guidance law for simultaneous arrival, IEEE Trans. Control Syst. Technol., 2018, 27, pp 1360–1367.CrossRefGoogle Scholar
Wang, C., Ding, X., Wang, J. and Shan, J. A robust three-dimensional cooperative guidance law against vering target, J. Franklin Inst., 2020, 357, pp 5735–5752.CrossRefGoogle Scholar
Chen, Z., Chen, W., Liu, X. and Cheng, J. Three-dimensional fixed-time robust cooperative guidance law for simultaneous attack with impact angle constraint, Aerospace Sci. Technol., 2021, 110, p 106523.CrossRefGoogle Scholar
Dong, W., Wang, C., Liu, J., Wang, J. and Xin, M. Three-dimensional vector guidance law with impact time and angle constraints, J. Franklin Inst., 2023, 360, pp 693–718.CrossRefGoogle Scholar
Sinha, A., Kumar, S.R. and Mukherjee, D. Cooperative integrated guidance and control design for simultaneous interception, Aerospace Sci. Technol., 2022, 120, p 107262.CrossRefGoogle Scholar
Dong, W., Wang, C., Wang, J., Zuo, Z. and Shan, J. Fixed-time terminal angle-constrained cooperative guidance law against maneuvering target, IEEE Trans. Aerospace Electron. Syst., 2021, 58, pp 1352–1366.CrossRefGoogle Scholar
Lyu, T., Guo, Y., Li, C., Ma, G. and Zhang, H. Multiple missiles cooperative guidance with simultaneous attack requirement under directed topologies, Aerospace Sci. Technol., 2019, 89, pp 100–110.CrossRefGoogle Scholar
Kim, H.-G., Cho, D. and Kim, H.J. Sliding mode guidance law for impact time control without explicit time-to-go estimation, IEEE Trans. Aerospace Electron. Syst., 2018, 55, pp 236–250.CrossRefGoogle Scholar
Yu, H., Dai, K., Li, H., Zou, Y., Ma, X., Ma, S. and Zhang, H. Distributed cooperative guidance law for multiple missiles with input delay and topology switching, J. Franklin Inst., 2021, 358, pp 9061–9085.CrossRefGoogle Scholar
Huang, A., Yu, J., Dong, X., Li, Q. and Ren, Z. Finite-time and fault-tolerant cooperative guidance against maneuvering target with time and angle constraints, International Conference on Guidance, Navigation and Control, Springer, 2022, pp 1985–1994.CrossRefGoogle Scholar
Hou, Z., Lan, X., Chen, H. and Zhuang, X. Finite-time cooperative guidance law for multiple missiles with impact angle constraints and switching communication topologies, J. Intell. Rob. Syst., 2023, 108, p 85.CrossRefGoogle Scholar
Chen, Y., Huang, J., Wang, Z., Jiang, B., Cheng, Y. and Yang, H. Influences of drone swarm failure based on directed graph, Acta Aeronaut. Astronaut. Sinica, 2020, 41, pp 115–121.Google Scholar
Yu, Z., Zhang, Y., Qu, Y., Su, C.-Y., Zhang, Y. and Xing, Z. Fault-tolerant adaptive neural control of multi-uavs against actuator faults, 2019 International Conference on unmanned aircraft Systems (ICUAS), IEEE, 2019, pp 421–426.CrossRefGoogle Scholar
Zhao, K., Song, J., Ai, S., Xu, X. and Liu, Y. Active fault-tolerant control for near-space hypersonic vehicles, Aerospace, 2022, 9, p 237.CrossRefGoogle Scholar
Yang, H., Jiang, B., Yang, H. and Liu, H.H. Synchronization of multiple 3-dof helicopters under actuator faults and saturations with prescribed performance, ISA Trans., 2018, 75, pp 118–126.CrossRefGoogle ScholarPubMed
Kamel, M.A., Ghamry, K.A. and Zhang, Y. Real-time fault-tolerant cooperative control of multiple uavs-ugvs in the presence of actuator faults, J. Intell. Rob. Syst., 2017, 88, pp 469–480.CrossRefGoogle Scholar
Yu, X., Liu, Z. and Zhang, Y. Fault-tolerant formation control of multiple uavs in the presence of actuator faults, Int. J. Robust Nonlinear Control, 2016, 26, pp 2668–2685.CrossRefGoogle Scholar
Li, G., Wu, Y. and Xu, P. Adaptive fault-tolerant cooperative guidance law for simultaneous arrival, Aerospace Sci. Technol., 2018, 82, pp 243–251.CrossRefGoogle Scholar
Liu, W., Zhang, K., Jiang, B. and Yan, X. Adaptive fault-tolerant formation control for quadrotors with actuator faults, Asian J. Control, 2020, 22, pp 1317–1326.CrossRefGoogle Scholar
Yu, Z., Zhang, Y., Jiang, B., Su, C.-Y., Fu, J., Jin, Y. and Chai, T., Fractional order pid-based adaptive fault-tolerant cooperative control of networked unmanned aerial vehicles against actuator faults and wind effects with hardware-in-the-loop experimental validation, Control Eng. Pract., 2021, 114, p 104861.CrossRefGoogle Scholar
Liu, D., Liu, H. and Xi, J. Fully distributed adaptive fault-tolerant formation control for octorotors subject to multiple actuator faults, Aerospace Sci. Technol., 2021, 108, p 106366.CrossRefGoogle Scholar
Yu, Z., Qu, Y. and Zhang, Y. Distributed fault-tolerant cooperative control for multi-uavs under actuator fault and input saturation, IEEE Trans. Control Syst. Technol., 2018, 27, pp 2417–2429.CrossRefGoogle Scholar
Ziquan, Y., Zhang, Y., Jiang, B., Jun, F. and Ying, J. A review on fault-tolerant cooperative control of multiple unmanned aerial vehicles, Chin. J. Aeronaut., 2022, 35, pp 1–18.Google Scholar
Yang, X. and Song, S. Three-dimensional consensus algorithm for nonsingular distributed cooperative guidance strategy, Aerospace Sci. Technol., 2021, 118, p 106958.CrossRefGoogle Scholar
Yu, H., Dai, K., Li, H., Zou, Y., Ma, X., Ma, S. and Zhang, H. Cooperative guidance law for multiple missiles simultaneous attacks with fixed-time convergence, Int. J. Control, 2023, 96, pp 2167–2180.CrossRefGoogle Scholar
Song, J., Song, S. and Xu, S. Three-dimensional cooperative guidance law for multiple missiles with finite-time convergence, Aerospace Sci. Technol., 2017, 67, pp 193–205.CrossRefGoogle Scholar
Hu, J., Niu, H., Carrasco, J., Lennox, B. and Arvin, F. Fault-tolerant cooperative navigation of networked uav swarms for forest fire monitoring, Aerospace Sci. Technol., 2022, 123, p 107494.CrossRefGoogle Scholar
Utkin, V. Variable structure systems with sliding modes, IEEE Trans. Autom. Control, 1977, 22, pp 212–222.CrossRefGoogle Scholar
Bhat, S.P. and Bernstein, D.S. Finite-time stability of continuous autonomous systems, SIAM J. Control Optim., 2000, 38, pp 751–766.CrossRefGoogle Scholar
Orlov, Y. Finite time stability and robust control synthesis of uncertain switched systems, SIAM J. Control Optim., 2004, 43, pp 1253–1271.CrossRefGoogle Scholar
Wang, L. and Xiao, F. Finite-time consensus problems for networks of dynamic agents, IEEE Trans. Autom. Control, 2010, 55, pp 950–955.CrossRefGoogle Scholar
Hölder, O. Ueber die eigenschaft der gammafunction keiner algebraischen differentialgleichung zu genügen, Math. Ann., 1886, 28, pp 1–13.CrossRefGoogle Scholar
He, S., Liu, X., Lu, P., Liu, H. and Du, C. Leader-follower finite-time consensus of multiagent systems with nonlinear dynamics by intermittent protocol, J. Franklin Inst., 2022, 359, pp 2646–2662.CrossRefGoogle Scholar
Akmal, M., Yusoff, M. and Arshad, M. Active fault tolerant control of a remotely operated vehicle propulsion system, Procedia Eng., 2012, 41, pp 622–628.CrossRefGoogle Scholar
Gao, Z., et al. Scaling and bandwidth-parameterization based controller tuning, ACC, 2003, pp 4989–4996.Google Scholar
Wang, J., Liu, L., Wang, P. and Tang, G. Guidance and control system design for hypersonic vehicles in dive phase, Aerospace Sci. Technol., 2016, 53, pp 47–60.CrossRefGoogle Scholar
Tao, H., Lin, D., Song, T. and Li, H. Optimal spatial-temporal cooperative guidance against a maneuvering target, J. Franklin Inst., 2023, 360, pp 9886–9903.CrossRefGoogle Scholar