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Fixed-time formation tracking for multiple nonholonomic wheeled mobile robots based on distributed observer

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Abstract

This paper studies the distributed fixed-time formation tracking problem of multiple nonholonomic wheeled mobile robots system over directed fixed and switching topologies. Through a classical nonlinear transformation, the formation control problem is transformed into a consensus problem. New control protocols based on a distributed observer are proposed. The directed communication topology between multiple nonholonomic wheeled mobile robots is considered. Some sufficient conditions of multiple robots achieving the desired formation shape are given. All follower robots can form the desired formation shape within a fixed settling time and make the leader in the geometric center of the formation. By adopting graph theory and fixed-time stability theory, an upper bound of settling time that is independent of the system’s initial states is obtained. Finally, two examples are presented to illustrate the correctness of the main results.

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No data were used to support this study.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grants Nos. 61503053, 61673080 and 61773082), the Natural Science Funds of Chongqing CSTC (Grant No. cstc2019jcyj-msxmX0102), the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJZD-K202000601), the Venture and Innovation Support Program for Chongqing Overseas Returnees (Grant No. cx2017099), and JK was supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers “Digital biodesign and personalized healthcare” (Grant No. 075-15-2020-926).

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Authors and Affiliations

  1. Key Laboratory of Intelligent Analysis and Decision on Complex Systems, School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 400065, People’s Republic of China

    Fenglan Sun & Wei Zhu

  2. Key Laboratory of Intelligent Air-Ground Cooperative Control for Universities in Chongqing, College of Automation, Chongqing University of Posts and Telecommunications, Chongqing, 400065, People’s Republic of China

    Fenglan Sun & Hao Li

  3. Department of Complexity Science, Potsdam Institute for Climate Impact Research, Potsdam, 14473, Germany

    Fenglan Sun & Juergen Kurths

  4. Institute of Physics, Humboldt University of Berlin, Berlin, 12489, Germany

    Juergen Kurths

  5. Centre for Analysis of Complex Systems, World-Class Research Center “Digital biodesign and personalized healthcare”, Sechenov First Moscow State Medical University, Moscow, Russia, 119991

    Juergen Kurths

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  1. Fenglan Sun
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Correspondence to Fenglan Sun.

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Sun, F., Li, H., Zhu, W. et al. Fixed-time formation tracking for multiple nonholonomic wheeled mobile robots based on distributed observer. Nonlinear Dyn 106, 3331–3349 (2021). https://doi.org/10.1007/s11071-021-06946-7

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