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Finite-time encirclement rotating tracking for surface formation targets with bearing-only measurements

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Abstract

This paper investigates the problem of encirclement rotating tracking for surface formation targets by multiple agents. Unlike most existing studies in which the agent trajectory is considered as a circle with a prescribed radius, the ellipse trajectories of agents changing with formation targets are addressed in this paper. The agents can only measure the bearing information of targets with unknown bounded velocity and acceleration. A least-square (LS) estimator is presented to localize each target and estimate the geometric center of the formation. Then, the target formation is approximated by an ellipse and the corresponding extended ellipse target model is established. To control agent behavior more conveniently, the motion of agent is decomposed into rotation and translation. On this basis, a finite-time control protocol is proposed for agents to travel along the desired trajectory around the extended target within finite time. Finally, a numerical experiment is performed to demonstrate the effectiveness of the proposed method.

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Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. Koohifar, F., Kumbhar, A., Guvenc, I.: Receding horizon multi-UAV cooperative tracking of moving RF source. IEEE Commun. Lett. 21(6), 1433–1436 (2016)

    Google Scholar 

  2. Zhang, C., Li, Y., Qi, G., Sheng, A.: Distributed finite-time control for coordinated circumnavigation with multiple non-holonomic robots. Nonlinear Dyn. 98(1), 573–588 (2019)

    Google Scholar 

  3. Ji, M., Egerstedt, M.: Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans. Robot. 23(4), 693–703 (2007)

    Google Scholar 

  4. Liu, H., Chen, F., Xiang, L., Lan, W.: Distributed average tracking with input saturation. Nonlinear Dyn. 90(4), 2827–2839 (2017)

    MathSciNet  MATH  Google Scholar 

  5. Qin, W., Liu, Z., Chen, Z.: A novel observer-based formation for nonlinear multi-agent systems with time delay and intermittent communication. Nonlinear Dyn. 79(3), 1651–1664 (2015)

    MathSciNet  MATH  Google Scholar 

  6. Zhang, Z., Chen, S.M., Zheng, Y.: Fully distributed scaled consensus tracking of high-order multi-agent systems with time delays and disturbances. IEEE Trans. Ind. Inf. (2021). https://doi.org/10.1109/TII.2021.3069207

    Article  Google Scholar 

  7. Zheng, Y., Zhao, Q., Ma, J., Wang, L.: Second-order consensus of hybrid multi-agent systems. Syst. Control Lett. 125, 51–58 (2019). https://doi.org/10.1016/j.sysconle.2019.01.009

    Article  MathSciNet  MATH  Google Scholar 

  8. Deghat, M., Shames, I., Anderson, B.D.O., Yu, C.: Target localization and circumnavigation using bearing measurements in 2D. In: 49th IEEE Conference on Decision and Control (CDC), pp. 334–339 (2010). https://doi.org/10.1109/CDC.2010.5717795

  9. Deghat, M., Shames, I., Anderson, B.D.O., Yu, C.: Localization and circumnavigation of a slowly moving target using bearing measurements. IEEE Trans. Autom. Control 59(8), 2182–2188 (2014)

    MathSciNet  MATH  Google Scholar 

  10. Li, R., Shi, Y., Song, Y.: Localization and circumnavigation of multiple agents along an unknown target based on bearing-only measurement: a three dimensional solution. Automatica 94, 18–25 (2018)

    MathSciNet  MATH  Google Scholar 

  11. Garcia de Marina, H., Jayawardhana, B., Cao, M.: Distributed rotational and translational maneuvering of rigid formations and their applications. IEEE Trans. Robot. 32(3), 684–697 (2016)

    Google Scholar 

  12. Zhao, S.: Affine formation maneuver control of multiagent systems. IEEE Trans. Autom. Control 63(12), 4140–4155 (2018)

    MathSciNet  MATH  Google Scholar 

  13. Lin, Z., Wang, L., Han, Z., Fu, M.: Distributed formation control of multi-agent systems using complex Laplacian. IEEE Trans. Autom. Control 59(7), 1765–1777 (2014)

    MathSciNet  MATH  Google Scholar 

  14. Mo, L., Yu, Y.: Finite-time rotating encirclement control of multi-agent systems. Acta Autom. Sin. 43(9), 1665–1672 (2017)

    MATH  Google Scholar 

  15. Chun, S., Tian, Y.P.: Multi-targets localization and elliptical circumnavigation by multi-agents using bearing-only measurements in two-dimensional space. Int. J. Robust Nonlinear Control 30(8), 3250–3268 (2020)

    MathSciNet  MATH  Google Scholar 

  16. Zhao, Y., Duan, Z.: Finite-time containment control without velocity and acceleration measurements. Nonlinear Dyn. 82(1–2), 259–268 (2015)

    MathSciNet  MATH  Google Scholar 

  17. Zhao, L.W., Hua, C.C.: Finite-time consensus tracking of second-order multi-agent systems via nonsingular TSM. Nonlinear Dyn. 75(1–2), 311–318 (2014)

    MathSciNet  MATH  Google Scholar 

  18. Cheng, Y., Du, H., He, Y., Jia, R.: Finite-time tracking control for a class of high-order nonlinear systems and its applications. Nonlinear Dyn. 76(2), 1133–1140 (2014)

    MathSciNet  MATH  Google Scholar 

  19. Xiao, Q., Wu, Z., Peng, L.: Fast finite-time consensus tracking of second-order multi-agent systems with a virtual leader. J. Netw. 9(12), 3268–3274 (2014)

    Google Scholar 

  20. Kim, T.H., Hara, S., Hori, Y.: Cooperative control of multi-agent dynamical systems in target-enclosing operations using cyclic pursuit strategy. Int. J. Control 83(10), 2040–2052 (2010)

    MathSciNet  MATH  Google Scholar 

  21. Ceccarelli, N., Di Marco, M., Garulli, A., Giannitrapani, A.: Collective circular motion of multi-vehicle systems. Automatica 44(12), 3025–3035 (2008)

    MathSciNet  MATH  Google Scholar 

  22. Shi, Y.J., Li, R., Teo, K.L.: Rotary enclosing control of second-order multi-agent systems for a group of targets. Int. J. Syst. Sci. 48(1), 13–21 (2017)

    MathSciNet  MATH  Google Scholar 

  23. Zhao, S., Li, Z., Ding, Z.: Bearing-only formation tracking control of multi-agent systems. IEEE Trans. Autom. Control 64(11), 4541–4554 (2019)

    MATH  Google Scholar 

  24. Shao, J., Tian, Y.P.: Multi-target localisation and circumnavigation by a multi-agent system with bearing measurements in 2D space. Int. J. Syst. Sci. 49(1), 15–26 (2018)

    MathSciNet  MATH  Google Scholar 

  25. 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)

    Google Scholar 

  26. Zhao, S., Zelazo, D.: Bearing rigidity and almost global bearing-only formation stabilization. IEEE Trans. Autom. Control 61(5), 1255–1268 (2016)

    MathSciNet  MATH  Google Scholar 

  27. Van Tran, Q., Trinh, M.H., Zelazo, D., Mukherjee, D., Ahn, H.S.: Finite-time bearing-only formation control via distributed global orientation estimation. IEEE Trans. Control Network Syst. 6(2), 702–712 (2019)

    MathSciNet  MATH  Google Scholar 

  28. Ma, L.: Cooperative target tracking in elliptical formation. In: 2019 24th International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 58–63 (2019). https://doi.org/10.1109/MMAR.2019.8864715

  29. Zhao, Y., Duan, Z., Wen, G., Chen, G.: Distributed finite-time tracking of multiple non-identical second-order nonlinear systems with settling time estimation. Automatica 64, 86–93 (2016)

    MathSciNet  MATH  Google Scholar 

  30. Mo, L., Yuan, X., Yu, Y.: Target-encirclement control of fractional-order multi-agent systems with a leader. Phys. A 509, 479–491 (2018)

    MathSciNet  Google Scholar 

  31. Zhang, C., Li, Y., Qi, G., Sheng, A.: Distributed finite-time control for coordinated circumnavigation with multiple agents under directed topology. J. Frankl. Inst. 357(16), 11710–11729 (2020)

    MathSciNet  MATH  Google Scholar 

  32. Chen, W., Jiao, L.C.: Finite-time stability theorem of stochastic nonlinear systems. Automatica 46(12), 2105–2108 (2010)

    MathSciNet  MATH  Google Scholar 

  33. Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)

    MathSciNet  MATH  Google Scholar 

  34. Liu, X., Lam, J., Yu, W., Chen, G.: Finite-time consensus of multiagent systems with a switching protocol. IEEE Trans. Neural Netw. Learn. Syst. 27(4), 853–862 (2015)

    MathSciNet  Google Scholar 

  35. Qian, C., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Autom. Control 46(7), 1061–1079 (2001)

    MathSciNet  MATH  Google Scholar 

  36. Hardy, G.H., Littlewood, J.E., Pólya, G., Pólya, G., Littlewood, D., et al.: Inequalities. Cambridge University Press, Cambridge (1952)

    MATH  Google Scholar 

  37. Du, H., Wen, G., Chen, G., Cao, J., Alsaadi, F.E.: A distributed finite-time consensus algorithm for higher-order leaderless and leader-following multiagent systems. IEEE Trans. Syst., Man, Cybern., Syst. 47(7), 1625–1634 (2017)

    Google Scholar 

  38. Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)

    MathSciNet  MATH  Google Scholar 

  39. Liu, J., Wang, Q., Yu, Y.: Fixed-time consensus algorithm for second-order multi-agent systems with bounded disturbances. In: 2016 31st Youth Academic Annual Conference of Chinese Association of Automation (YAC), pp. 165–170 (2016). https://doi.org/10.1109/YAC.2016.7804883

  40. Shi, Y., Li, R., Teo, K.L.: Cooperative enclosing control for multiple moving targets by a group of agents. Int. J. Control 88(1), 80–89 (2015)

    MathSciNet  MATH  Google Scholar 

  41. Li, Y., Qi, G., Sheng, A.: Optimal deployment of vehicles with circular formation for bearings-only multi-target localization. Automatica 105, 347–355 (2019)

    MathSciNet  MATH  Google Scholar 

  42. Zhong, Y., Wu, X., Huang, S., Li, C., Wu, J.: Optimality analysis of sensor-target geometries for bearing-only passive localization in three dimensional space. Chin. J. Electron. 25(2), 391–396 (2016)

    Google Scholar 

  43. Bar-Shalom, Y., Li, X.R., Kirubarajan, T.: Estimation with applications to tracking and navigation: theory algorithms and software. Wiley, New York (2004)

    Google Scholar 

  44. Doğançay, K.: On the bias of linear least squares algorithms for passive target localization. Signal Process. 84(3), 475–486 (2004)

    Google Scholar 

  45. Franchi, A., Stegagno, P., Oriolo, G.: Decentralized multi-robot encirclement of a 3D target with guaranteed collision avoidance. Auton. Robots 40(2), 245–265 (2016)

    Google Scholar 

  46. Li, Z., Liu, X., Ren, W., Xie, L.: Distributed tracking control for linear multiagent systems with a leader of bounded unknown input. IEEE Trans. Autom. Control 58(2), 518–523 (2012)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work has been supported in part by the National Natural Science Foundation of China (Grant Numbers 61871221, 61773210, and 62171223) and in part by the National Defense Basic Scientific Research Program of China (JCKY2018209B010).

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Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Zhoujian Ma & Yinya Li

  2. Electrical and Computer Engineering Department (ITB-A112), McMaster University, Hamilton, L8S 4K1, ON, Canada

    Thiagalingam Kirubarajan

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  1. Zhoujian Ma
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Correspondence to Yinya Li.

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Ma, Z., Kirubarajan, T. & Li, Y. Finite-time encirclement rotating tracking for surface formation targets with bearing-only measurements. Nonlinear Dyn 105, 3323–3339 (2021). https://doi.org/10.1007/s11071-021-06818-0

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