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A geometric extension design for spherical formation tracking control of second-order agents in unknown spatiotemporal flowfields

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Abstract

This article proposes a solution to the problem of directing multiple second-order agents sphere landing, orbit tracking and formation moving around a family of given concentric spheres in unknown spatiotemporal flowfields. The flowfields put stress on each agent’s velocity and acceleration at once, and the specification of each one is composed of three known base vectors and unknown responding coefficients. First, our pervious two-dimensional geometric extension design is extended to deal with the extension of surface in three-dimensional space. Then, two new adaptive estimators and the cooperative control law are constructed to accomplish the robust spherical formation tracking motion by using the tools of adaptive backstepping, geometric extension and consensus. The asymptotic stability of system is proved when the bidirectional communication topology is connected. The effectiveness of the analytical result is verified by numerical simulations.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China Under Grants 61673106, 61473081, 61473138, 61503329, Natural Science Foundation of Jiangsu Province Under Grant BK20141341 and in part by a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. School of Automation, Southeast University, Nanjing, 210096, People’s Republic of China

    Yang-Yang Chen, Zan-Zan Wang & Ya Zhang

  2. Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, Nanjing, 210096, China

    Yang-Yang Chen, Zan-Zan Wang & Ya Zhang

  3. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University, Wuxi, 214122, China

    Cheng-Lin Liu

  4. College of Information Engineering, Yangzhou University, Yangzhou, 225127, China

    Qin Wang

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  1. Yang-Yang Chen
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  2. Zan-Zan Wang
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Correspondence to Yang-Yang Chen.

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Chen, YY., Wang, ZZ., Zhang, Y. et al. A geometric extension design for spherical formation tracking control of second-order agents in unknown spatiotemporal flowfields. Nonlinear Dyn 88, 1173–1186 (2017). https://doi.org/10.1007/s11071-016-3303-2

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  • DOI: https://doi.org/10.1007/s11071-016-3303-2

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