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Formation of multi-agent systems with desired orientation: a distance-based control approach

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Abstract

This paper proposes a nonlinear distance-based rigid formation shape control strategy with desired orientation, where the mutual perceptual relationships among agents are represented by a persistent directed graph. Only the orientation of the local coordinates of an agent is required to be consistent with the orientation of the global coordinate frame. The domain of attraction is characterized for the multi-agent system to achieve the desired formation control. For the first-order model, some precise initial conditions for the multi-agent systems to achieve the formation shape with desired orientation are derived. Some simulation examples are provided to verify the effectiveness of the control laws.

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References

  1. Amani, A.M., Chen, G., Jalili, M., Yu, X., Stone, L.: Distributed rigidity recovery in distance-based formations using configuration lattice. IEEE Trans. Control Netw. Syst. 7(3), 1547–1558 (2020)

    Article  MathSciNet  Google Scholar 

  2. Anderson, B.D., Yu, C., Fidan, B., Hendrickx, J.M.: Rigid graph control architectures for autonomous formations. IEEE Control Syst. Mag. 28(6), 48–63 (2008)

    Article  MathSciNet  Google Scholar 

  3. Asimow, L., Roth, B.: The rigidity of graphs, ii. J. Math. Anal. Appl. 68(1), 171–190 (1979)

    Article  MathSciNet  Google Scholar 

  4. Bereg, S.: Certifying and constructing minimally rigid graphs in the plane. In: Proceedings of the twenty-first annual symposium on Computational geometry, pp. 73–80 (2005)

  5. Chen, L., Garcia de Marina, H., Cao, M.: Maneuvering formations of mobile agents using designed mismatched angles. IEEE Trans. Autom. Control pp. 1 (2021). 10.1109/TAC.2021.3066388

  6. De Marina, H.G., Cao, M., Jayawardhana, B.: Controlling rigid formations of mobile agents under inconsistent measurements. IEEE Trans. Robot. 31(1), 31–39 (2014)

    Article  Google Scholar 

  7. De Marina, H.G., Siemonsma, J., Jayawardhana, B., Cao, M.: Multi-robot motion-formation distributed control with sensor self-calibration: experimental validation. In: 2018 15th International Conference on Control, Automation, Robotics and Vision (ICARCV), pp. 235–240. IEEE (2018)

  8. Dong, W., Farrell, J.A.: Consensus of multiple nonholonomic systems. In: 2008 47th IEEE Conference on Decision and Control, pp. 2270–2275. IEEE (2008)

  9. Hendrickx, J.M., Anderson, B.D., Delvenne, J., Blondel, V.D.: Directed graphs for the analysis of rigidity and persistence in autonomous agent systems. Int. J. Robust Nonlinear Control IFAC-Affiliated J. 17(10–11), 960–981 (2007)

  10. Hu, J., Xu, J., Xie, L.: Cooperative search and exploration in robotic networks. Unmanned Syst. 1(01), 121–142 (2013)

    Article  Google Scholar 

  11. Izmestiev, I.: Infinitesimal rigidity of frameworks and surfaces. Lectures on Infinitesimal Rigidity (2009)

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

    Article  Google Scholar 

  13. Khalil, H.K., Grizzle, J.W.: Nonlinear Systems, vol. 3. Prentice hall Upper Saddle River, NJ (2002)

    Google Scholar 

  14. Krick, L., Broucke, M.E., Francis, B.A.: Stabilisation of infinitesimally rigid formations of multi-robot networks. Int. J. Control 82(3), 423–439 (2009)

    Article  MathSciNet  Google Scholar 

  15. Li, W., Chen, Z., Liu, Z.: Leader-following formation control for second-order multiagent systems with time-varying delay and nonlinear dynamics. Nonlinear Dyn. 72(4), 803–812 (2013)

    Article  MathSciNet  Google Scholar 

  16. Liu, H., Wang, Y., Xi, J.: Completely distributed formation control for networked quadrotors under switching communication topologies. Syst. Control Lett. 147, 104841 (2021)

    Article  MathSciNet  Google Scholar 

  17. Liu, T., Fernández-Kim, V., de Queiroz, M.: Switching formation shape control with distance+ area/angle feedback. Syst. Control Lett. 135, 104598 (2020)

    Article  MathSciNet  Google Scholar 

  18. Liu, T., de Queiroz, M., Zhang, P., Khaledyan, M.: Further results on the distance and area control of planar formations. Int. J. Control 94, 767–783 (2019)

    Article  MathSciNet  Google Scholar 

  19. Marquez, H.J.: Nonlinear Control Systems: Analysis and Design, vol. 161. John Wiley, Hoboken (2003)

    MATH  Google Scholar 

  20. Oh, K.K., Ahn, H.S.: Distance-based undirected formations of single-integrator and double-integrator modeled agents in n-dimensional space. Int. J. Robust Nonlinear Control 24(12), 1809–1820 (2014)

    Article  MathSciNet  Google Scholar 

  21. Park, M.C., Ahn, H.S.: Distance-based control of formations with orientation control. In: 2015 54th IEEE Conference on Decision and Control (CDC), pp. 2199–2204. IEEE (2015)

  22. 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)

    Article  MathSciNet  Google Scholar 

  23. Recker, T., Heinrich, M., Raatz, A.: A comparison of different approaches for formation control of nonholonomic mobile robots regarding object transport. Procedia CIRP 96, 248–253 (2021)

    Article  Google Scholar 

  24. Su, W., Hu, Y., Li, K., Chen, L.: Rigidity of similarity-based formation and formation shape stabilization. Automatica 121, 109183 (2020)

    Article  MathSciNet  Google Scholar 

  25. Sugie, T., Anderson, B.D., Sun, Z., Dong, H.: On a hierarchical control strategy for multi-agent formation without reflection. In: 2018 IEEE Conference on Decision and Control (CDC), pp. 2023–2028. IEEE (2018)

  26. Sun, Z., Anderson, B.D.: Rigid formation control with prescribed orientation. In: 2015 IEEE International Symposium on Intelligent Control (ISIC), pp. 639–645. IEEE (2015)

  27. Sun, Z., Mou, S., Anderson, B.D., Morse, A.S.: Formation movements in minimally rigid formation control with mismatched mutual distances. In: 53rd IEEE Conference on Decision and Control, pp. 6161–6166. IEEE (2014)

  28. Sun, Z., Park, M.C., Anderson, B.D., Ahn, H.S.: Distributed stabilization control of rigid formations with prescribed orientation. Automatica 78, 250–257 (2017)

    Article  MathSciNet  Google Scholar 

  29. Yan, L., Ma, B.: Adaptive practical leader-following formation control of multiple nonholonomic wheeled mobile robots. Int. J. Robust Nonlinear Control 30(17), 7216–7237 (2020)

    Article  MathSciNet  Google Scholar 

  30. Yu, X., Liu, L.: Distributed formation control of nonholonomic vehicles subject to velocity constraints. IEEE Trans. Ind. Electron. 63(2), 1289–1298 (2016). https://doi.org/10.1109/TIE.2015.2504042

    Article  Google Scholar 

  31. Zhao, S., Dimarogonas, D.V., Sun, Z., Bauso, D.: A general approach to coordination control of mobile agents with motion constraints. IEEE Trans. Autom. Control 63(5), 1509–1516 (2017)

    Article  MathSciNet  Google Scholar 

  32. Zou, A.M., Kumar, K.D.: Neural network-based adaptive output feedback formation control for multi-agent systems. Nonlinear Dyn. 70(2), 1283–1296 (2012)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation (NNSF) of China under Grant 11802006 Grant 12172020, Grant 62003013, and Grant 11932003, the Fundamental Research Funds for the Central Universities under Grant YWF-21-BJ-J-804, and the Hong Kong Research Grants Council under the GRF Grant CityU 11206320.

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Authors and Affiliations

  1. Department of Dynamics and Control, Beihang University, Beijing, 100191, China

    Yinxiang Zhao, Yuqing Hao, Qishao Wang & Qingyun Wang

  2. Department of Electrical Engineering, City University of Hong Kong, Hong Kong SAR, 999077, China

    Guanrong Chen

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  1. Yinxiang Zhao
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  2. Yuqing Hao
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  3. Qishao Wang
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  4. Qingyun Wang
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  5. Guanrong Chen
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Correspondence to Yuqing Hao.

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Zhao, Y., Hao, Y., Wang, Q. et al. Formation of multi-agent systems with desired orientation: a distance-based control approach. Nonlinear Dyn 106, 3351–3361 (2021). https://doi.org/10.1007/s11071-021-06948-5

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  • DOI: https://doi.org/10.1007/s11071-021-06948-5

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