Skip to main content
SpringerLink
Log in

Distributed adaptive formation control for underactuated quadrotors with guaranteed performances

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper investigates a distributed adaptive formation control problem for underactuated quadrotors with guaranteed performances. To ensure a robust and stable formation pattern with predefined behavior bounds, by transforming the original constrained formation synchronization error dynamics into an equivalent unconstrained one, a prescribed performance mechanism is introduced in the translational loop to render the formation regulation as a prior. An adaptive consensus strategy is developed according to undirected graph theory and Lyapunov stability rules for follower quadrotors to achieve a distributed cooperative formation with prescribed tracking abilities via exchanging local information with neighbors. The presented control scheme has the following salient merits: (1) the formation synchronization errors can be guaranteed within pre-assigned bounds with desired transient behaviors despite of uncertain disturbances; (2) by using a state estimation error to update neural network (NN) parameters, rather than the tracking error that widely applied in traditional NN approximators, and with the help of MLP technique, the proposed SE-MLP observer capable of decreasing the computational complexity can achieve a fast identification of lumped disturbances without causing high-frequency oscillations even using a large adaptive gain, and the transient solutions of L2 norm of the differential of neural weights are established to illustrate the mechanism of SE-MLP observer in reducing chattering behaviors. The merits of presented algorithm are confirmed by sufficient simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Xian, B., Wang, S.Z., Yang, S.: Nonlinear adaptive control for an unmanned aerial payload transportation system: theory and experimental validation. Nonlinear Dyn. 98(3), 1745–1760 (2019)

    MATH  Google Scholar 

  2. Shirani, B., Najafi, M., Izadi, I.: Cooperative load transportation using multiple UAVs. Aerosp. Sci. Technol. 84(1), 158–169 (2019)

    Google Scholar 

  3. Ai, X.L., Yu, J.Q.: Flatness-based finite-time leader-follower formation control of multiple quadrotors with external disturbances. Aerosp. Sci. Technol. 92, 20–33 (2019)

    Google Scholar 

  4. Zhang, D.-F., Duan, H.-B.: Switching topology approach for UAV formation based on binary-tree network. J. Frankl. Inst. 356(2), 835–859 (2019)

    MathSciNet  MATH  Google Scholar 

  5. Leahy, K., Zhou, D.J., Vasile, C.I., Oikonomopoulos, K.: Persistent surveillance for unmanned aerial vehicles subject to charging and temporal logic constraints. Auton. Robot. 40(8), 1363–1378 (2016)

    Google Scholar 

  6. Ghommam, J., Saad, M., Wright, S., Zhu, Q.M.: Relay manoeuver based fixed-time synchronized tracking control for UAV transport system. Aerosp. Sci. Technol. 103, 105877 (2020)

    Google Scholar 

  7. Dong, X.W., Hua, Y.Z., Zhou, Y., Ren, Z., Zhong, Y.S.: Theory and experiment on formation-containment control of multiple multirotor unmanned aerial vehicle systems. IEEE Trans. Autom. Sci. Eng. 16(1), 229–240 (2019)

    Google Scholar 

  8. Yue, X.H., Shao, X.L., Li, J.: Prescribed chattering reduction control for quadrotors using aperiodic signal updating. Appl. Math. Comput. (2021). https://doi.org/10.1016/j.amc.2021.126264

    Article  MathSciNet  Google Scholar 

  9. Rekabi, F., Shirazi, F.A., Sadigh, M.J.: Distributed nonlinear H-infinity control algorithm for multi-agent quadrotor formation flying. ISA Trans. 96, 81–94 (2020)

    Google Scholar 

  10. Shao, X.L., Yue, X.H., Li, J.: Event-triggered robust control for quadrotors with preassigned time performance constraints. Appl. Math. Comput. (2021). https://doi.org/10.1016/j.amc.2020.125667

    Article  MathSciNet  MATH  Google Scholar 

  11. Xu, Q.Z., Wang, Z.S., Zhen, Z.Y.: Adaptive neural network finite time control for quadrotor UAV with unknown input saturation. Nonlinear Dyn. 98(3), 1973–1998 (2019)

    MATH  Google Scholar 

  12. Zhou, D.J., Wang, Z.J., Schwager, M.: Agile coordination and assistive collision avoidance for quadrotor swarms using virtual structures. IEEE Trans. Robot. 34(4), 916–923 (2018)

    Google Scholar 

  13. Arul, S.H., Manocha, D.: DCAD: Decentralized collision avoidance with dynamics constraints for agile quadrotor swarms. IEEE Robot. Autom. Lett. 5(2), 1191–1198 (2020)

    Google Scholar 

  14. Wu, L.B., Park, J.H., Xie, X.P., Ren, Y.W., Yang, Z.H.: Distributed adaptive neural network consensus for a class of uncertain nonaffine nonlinear multi-agent systems. Nonlinear Dyn. 100(2), 1243–1255 (2020)

    MATH  Google Scholar 

  15. Wang, Y., Li, Q., Xiong, Q., Ma, S.: Distributed consensus of high-order continuous-time multi-agent systems with nonconvex input constraints, switching topologies, and delays. Neurocomputing 332(7), 10–14 (2019)

    Google Scholar 

  16. Zhao, L., Yu, J., Lin, C.: Distributed adaptive output consensus tracking of nonlinear multi-agent systems via state observer and command filtered backstepping. Inf. Sci. 478(4), 355–374 (2019)

    MathSciNet  MATH  Google Scholar 

  17. Zhang, Y.-B., Wang, D., Peng, Z.: Consensus maneuvering for a class of nonlinear multivehicle systems in strict-feedback form. IEEE Trans. Cybern. 49(5), 1759–1767 (2019)

    Google Scholar 

  18. Dong, T., Gong, Y.L.: Leader-following secure consensus for second-order multi-agent systems with nonlinear dynamics and event-triggered control strategy under DoS attack. Neurocomputing 416, 95–102 (2020)

    Google Scholar 

  19. Yao, D.Y., Li, H.Y., Lu, R.Q., Shi, Y.: Distributed sliding-mode tracking control of second-order nonlinear multiagent systems: an event-triggered approach. IEEE Trans. Cybern. 50(9), 3892–3902 (2020)

    Google Scholar 

  20. Zhang, Z., Chen, S.M., Su, H.S.: Scaled consensus of second-order nonlinear multiagent systems with time-varying delays via aperiodically intermittent control. IEEE Trans. Cybern. 50(8), 3503–3516 (2020)

    Google Scholar 

  21. Peng, Z.H., Wang, D., Li, T.S., Han, M.: Output-feedback cooperative formation maneuvering of autonomous surface vehicles with connectivity preservation and collision avoidance. IEEE Trans. Cybern. 50(6), 2527–2535 (2020)

    Google Scholar 

  22. Liu, H., Ma, T., Lewis, F.L., Wan, Y.: Robust formation trajectory tracking control for multiple quadrotors with communication delays. IEEE Trans. Control Syst. Technol. 28(6), 2633–2640 (2020)

    Google Scholar 

  23. Jasim, W., Gu, D.: Robust team formation control for quadrotors. IEEE Trans. Control Syst. Technol. 26(4), 1516–1523 (2018)

    Google Scholar 

  24. Liu, H., Ma, T., Lewis, F., Wan, Y.: Robust formation control for multiple quadrotors with nonlinearities and disturbances. IEEE Trans. Cybern. 50(4), 1362–1371 (2020)

    Google Scholar 

  25. Du, H.-B., Zhu, W., Wen, G., Duan, Z., Lu, J.: Distributed formation control of multiple quadrotor aircraft based on nonsmooth consensus algorithms. IEEE Trans. Cybern. 49(1), 342–353 (2019)

    Google Scholar 

  26. Wang, D.-D., Zong, Q., Tian, B., Wang, F., Dou, L.: Finite-time fully distributed formation reconfiguration control for UAV helicopters. Int. J. Robust Nonlinear Control 28(18), 5943–5961 (2018)

    MathSciNet  MATH  Google Scholar 

  27. Wei, C.-S., Luo, J., Dai, H., Duan, G.: Learning-based adaptive attitude control of spacecraft formation with guaranteed prescribed performance. IEEE Trans. Cybern. 49(11), 4004–4016 (2019)

    Google Scholar 

  28. Zhang, Q.-R., Liu, H.: UDE-based robust command filtered backstepping control for close formation flight. IEEE Trans. Ind. Electron. 65(11), 8818–8827 (2018)

    Google Scholar 

  29. Shao, X.L., Shi, Y.: Neural adaptive control for MEMS gyroscope with full-state constraints and quantized input. IEEE Trans. Ind. Inf. 16(10), 6444–6454 (2020)

    Google Scholar 

  30. Chen, Z., Huang, F.H., Sun, W.C., Gu, J., Yao, B.: RBF-neural-network-based adaptive robust control for nonlinear bilateral teleoperation manipulators with uncertainty and time delay. IEEE-ASME Trans. Mechatron. 25(2), 906–918 (2020)

    Google Scholar 

  31. Shahvali, M., Shojaei, K.: Distributed adaptive neural control of nonlinear multi-agent systems with unknown control directions. Nonlinear Dyn. 83(4), 2213–2228 (2016)

    MathSciNet  MATH  Google Scholar 

  32. Shao, X.L., Si, H.N., Zhang, W.D.: Fuzzy wavelet neural control with improved prescribed performance for MEMS gyroscope subject to input quantization. Fuzzy Sets Syst. 411, 136–154 (2021)

    MathSciNet  MATH  Google Scholar 

  33. Ni, J.K., Shi, P.: Adaptive neural network fixed-time leader-follower consensus for multiagent systems with constraints and disturbances. IEEE Trans. Cybern. 51(4), 1835–1848 (2021)

    Google Scholar 

  34. Mao, J., Karimi, H.R., Xiang, Z.: Observer-based adaptive consensus for a class of nonlinear multiagent systems. IEEE Trans. Syst. Man Cybern. Syst. 49(9), 1893–1900 (2019)

    Google Scholar 

  35. Gou, Y.Y., Li, H.B., Dong, X.M., Liu, Z.C.: Constrained adaptive neural network control of an MIMO aeroelastic system with input nonlinearities. Chin. J. Aeronaut. 30(2), 796–806 (2017)

    Google Scholar 

  36. Afaghi, A., Ghaemi, S., Ghiasi, A.R., Badamchizadeh, M.A.: Adaptive fuzzy observer-based cooperative control of unknown fractional-order multi-agent systems with uncertain dynamics. Soft. Comput. 4(50), 3737–3752 (2020)

    MATH  Google Scholar 

  37. Wang, F., Liu, Z., Zhang, Y., Chen, B.: Distributed adaptive coordination control for uncertain nonlinear multi-agent systems with dead-zone input. J. Frankl. Inst. 353(10), 2270–2289 (2016)

    MathSciNet  MATH  Google Scholar 

  38. Li, Y.Q., Wang, R.X., Xu, M.Q.: Rescheduling of observing spacecraft using fuzzy neural network and ant colony algorithm. Chin. J. Aeronaut. 27(3), 678–687 (2014)

    Google Scholar 

  39. Chen, C.L.P., Wen, G.-X., Liu, Y.-J., Wang, F.-Y.: Adaptive consensus control for a class of nonlinear multiagent time-delay systems using neural networks. IEEE Trans. Neural Netw. Learn. Syst. 25(6), 1217–1226 (2014)

    Google Scholar 

  40. Liu, X.-M., Ge, S., Goh, C.: Neural-network-based switching formation tracking control of multiagents with uncertainties in constrained space. IEEE Trans. Neural Netw. Learn. Syst. 49(5), 1006–1015 (2019)

    Google Scholar 

  41. Bu, X.W., Wu, X.Y., Ma, Z., Zhang, R.: Novel adaptive neural control of flexible air-breathing hypersonic vehicles based on sliding mode differentiator. Chin. J. Aeronaut. 28(4), 1209–1216 (2015)

    Google Scholar 

  42. Dou, L.Y., Song, C., Wang, X.F., Liu, L., Feng, G.: Target localization and enclosing control for networked mobile agents with bearing measurements. Automatica 118, 109022 (2020)

    MathSciNet  MATH  Google Scholar 

  43. Wang, Q.L., Psillakis, H.E., Sun, C.Y.: Cooperative control of multiple high-order agents with nonidentical unknown control directions under fixed and time-varying topologies. IEEE Trans. Syst. Man Cybern. Syst. 51(4), 2582–2591 (2021)

    Google Scholar 

  44. Shahvali, M., Askari, J.: Cooperative adaptive neural partial tracking errors constrained control for nonlinear multi-agent systems. Int. J. Adapt. Control Signal Process. 30(7), 1019–1042 (2016)

    MathSciNet  MATH  Google Scholar 

  45. Shahvali, M., Naghibi-Sistani, M.-B., Modares, H.: Distributed consensus control for a network of incommensurate fractional-order systems. IEEE Control Syst. Lett. 3(2), 481–486 (2019)

    MathSciNet  Google Scholar 

  46. Shahvali, M., Azarbahram, A., Naghibi-Sistani, M.-B., Askari, J.: Bipartite consensus control for fractional-order nonlinear multi-agent systems: an output constraint approach. Neurocomputing 397, 212–223 (2020)

    Google Scholar 

  47. Peng, Z.H., Liu, L., Wang, J.: Output-feedback flocking control of multiple autonomous surface vehicles based on data-driven adaptive extended state observers. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3009992

    Article  Google Scholar 

  48. Gu, N., Peng, Z.H., Wang, D., Zhang, F.M.: Path-guided containment maneuvering of mobile robots: theory and experiments. IEEE Trans. Ind. Electron. (2020). https://doi.org/10.1109/TIE.2020.3000120

    Article  Google Scholar 

  49. Yu, Q.X., Hou, Z.S., Bu, X.H., Yu, Q.F.: RBFNN-based data-driven predictive iterative learning control for nonaffine nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 31(4), 1170–1182 (2020)

    MathSciNet  Google Scholar 

  50. Gao, F., Chen, W., Li, Z., Li, J., Xu, B.: Neural network-based distributed cooperative learning control for multiagent systems via event-triggered communication. IEEE Trans. Neural Netw. Learn. Syst. 31(2), 407–419 (2020)

    MathSciNet  Google Scholar 

  51. Shao, X.L., Wang, L.W., Li, J., Liu, J.: High-order ESO based output feedback dynamic surface control for quadrotors under position constraints and uncertainties. Aerosp. Sci. Technol. 89, 288–298 (2019)

    Google Scholar 

  52. Shao, X.L., Yue, X.H., Li, J.: Event-triggered robust control for quadrotors with preassigned time performance constraints. Appl. Math. Comput. 392, 125667 (2021)

    MathSciNet  MATH  Google Scholar 

  53. Peng, Z.H., Wang, D., Wang, W., Liu, L.: Containment control of networked autonomous underwater vehicles: a predictor-based neural DSC design. ISA Trans. 59, 160–171 (2015)

    Google Scholar 

  54. Kocer, B.B., Tjahjowidodo, T., Seet, G.G.L.: Centralized predictive ceiling interaction control of quadrotor VTOL UAV. Aerosp. Sci. Technol. 76, 455–465 (2018)

    Google Scholar 

  55. Bechlioulis, C.-P., Rovithakis, G.A.: Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE Trans. Autom. Control 53(9), 2090–2099 (2008)

    MathSciNet  MATH  Google Scholar 

  56. Dimanidis, I.S., Bechlioulis, C.P., Rovithakis, G.A.: Output feedback approximation-free prescribed performance tracking control for uncertain MIMO nonlinear systems. IEEE Trans. Autom. Control 65(12), 5058–5069 (2020)

    MathSciNet  MATH  Google Scholar 

  57. Dai, S.L., He, S.D., Chen, X., Jin, X.: Adaptive leader-follower formation control of nonholonomic mobile robots with prescribed transient and steady-state performance. IEEE Trans. Ind. Inf. 16(6), 3662–3671 (2020)

    Google Scholar 

  58. Liang, H.-J., Zhang, Y., Huang, T., Ma, H.: Prescribed performance cooperative control for multiagent systems with input quantization. IEEE Trans. Cybern. 50(5), 1810–1819 (2020)

    Google Scholar 

  59. Wang, Y., Hu, J., Li, J., Liu, B.: Improved prescribed performance control for nonaffine pure-feedback systems with input saturation. Int. J. Robust Nonlinear Control 29(6), 1769–1788 (2019)

    MathSciNet  MATH  Google Scholar 

  60. Bu, X.W.: Guaranteeing prescribed output tracking performance for air-breathing hypersonic vehicles via non-affine back-stepping control design. Nonlinear Dyn. 91(1), 525–538 (2018)

    MATH  Google Scholar 

Download references

Acknowledgements

This research has been supported in part by National Natural Science Foundation of China under Grant 61803348, National Nature Science Foundation of China as National Major Scientific Instruments Development Project under Grant 61927807 , State Key Laboratory of Deep Buried Target Damage under Grant DXMBJJ2019-02, Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi under Grant 2020L0266, Shanxi Province Science Foundation for Youths under Grant 201701D221123 , Youth Academic North University of China under Grant QX201803, Program for the Innovative Talents of Higher Education Institutions of Shanxi, and Shanxi “1331 Project” Key Subjects Construction (1331KSC).

Author information

Authors and Affiliations

  1. Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Taiyuan, 030051, China

    Xingling Shao, Xiaohui Yue & Jun Liu

  2. National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan, 030051, China

    Xingling Shao, Xiaohui Yue & Jun Liu

Authors
  1. Xingling Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaohui Yue
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xingling Shao.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shao, X., Yue, X. & Liu, J. Distributed adaptive formation control for underactuated quadrotors with guaranteed performances. Nonlinear Dyn 105, 3167–3189 (2021). https://doi.org/10.1007/s11071-021-06757-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06757-w

Keywords

Search

Navigation