Maneuvering Angle Rigid Formations With Global Convergence Guarantees

Liangming Chen; Zhiyun Lin; Hector Garcia de Marina; Zhiyong Sun; Mir Feroskhan

doi:10.1109/JAS.2022.105749

Volume 9 Issue 8

Aug. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(8): 1464-1475

L. Chen, Z. Lin, H. Garcia de Marina, Z. Sun, and M. Feroskhan, “Maneuvering angle rigid formations with global convergence guarantees,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 8, pp. 1464–1475, Aug. 2022. doi: 10.1109/JAS.2022.105749

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L. Chen, Z. Lin, H. Garcia de Marina, Z. Sun, and M. Feroskhan, “Maneuvering angle rigid formations with global convergence guarantees,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 8, pp. 1464–1475, Aug. 2022. doi: 10.1109/JAS.2022.105749

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Maneuvering Angle Rigid Formations With Global Convergence Guarantees

doi: 10.1109/JAS.2022.105749

Funds: The work of Z. Lin was supported by National Natural Science Foundation of China (62173118). The work of H. Garcia de Marina was supported by the Ramon y Cajal (RYC2020-030090-I) from the Spanish Ministry of Science

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Author Bio:
Liangming Chen received the B. E. degree in automation from Southwest Jiaotong University, in 2015. From 2015 to 2021, he has enrolled jointly in the Ph.D. program of systems and control in Harbin Institute of Technology, China and University of Groningen, the Netherlands. From 2021 to 2022, he has been a Research Fellow in the School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore. His current research interests include formation control and distributed localization

Zhiyun Lin (Senior Member, IEEE) received the Ph.D. degree in electrical and computer engineering from the University of Toronto, Canada, in 2005. He is currently a Full Professor in the Department of Electronic and Electrical Engineering, Southern University of Science and Technology. Preceding to this position, he was a Postdoctoral Research Associate (2005–2007) in the Department of Electrical and Computer Engineering, University of Toronto, then worked as a Research Professor (2007–2011) and Full Professor (2012–2017) at the College of Electrical Engineering, Zhejiang University, and served as the Director of the Artificial Intelligence Institute (2017–2021), Hangzhou Dianzi University. He has held many visiting professor appointments, including at Yale University (USA), The Australian National University (Australia), University of Groningen (The Netherlands), University of Cagliari (Italy), University of Newcastle (Australia), University of Technology Sydney (Australia), etc. His research interests focus on multi-agent systems, distributed artificial intelligence, autonomous systems and swarm robots, and cyber-physical systems. He was an Associate Editor for IEEE Control Systems Letters, Hybrid Systems: Nonlinear Analysis, etc. He is a Foreign Member of the Russian Academy of Engineering and a Fellow of IET

Hector Garcia de Marina (Member, IEEE) received the M.Sc. degree in electronics engineering from the Complutense University of Madrid, Spain, in 2008, the M.Sc. degree in control engineering from the University of Alcala, Spain, in 2011, and the Ph.D. degree in systems and control from the University of Groningen, the Netherlands, in 2016. He held a postdoctoral position in the Ecole Nationale de l’Aviation Civile’ in Toulouse from 2016 to 2018. From 2018 to 2020, he was an Assistant Professor at the Unmanned Aerial Systems Center, University of Southern Denmark. In 2020, he was a Research Fellow in the Complutense University of Madrid. Currently, he is a Research Fellow in the University of Granada under the Ramon y Cajal program. He is an Associate Editor for IEEE Transactions on Robotics. His research interests include the guidance navigation and control for autonomous robots, and multi-agent systems

Zhiyong Sun received the Ph.D. degree from The Australian National University (ANU), Canberra ACT, Australia, in February 2017. He was a Research Fellow/Lecturer with the Research School of Engineering, ANU, from 2017 to 2018. From June 2018 to January 2020, he worked as a Postdoctoral Researcher at Department of Automatic Control, Lund University, Sweden. Since January 2020 he has been at Eindhoven University of Technology (TU/e), the Netherlands, as an Assistant Professor. His research interests include multi-agent systems, control of autonomous formations and distributed optimization

Mir Feroskhan received first-class honors in aerospace engineering from Nanyang Technological University, Singapore, in 2011, and the Ph.D. degree in aerospace engineering from the Florida Institute of Technology, USA, in 2016. He is currently an Assistant Professor with the School of Mechanical and Aerospace Engineering at NTU. His research interests include nonlinear control systems, VTOL systems, drone design and development, flight dynamics and control, and aerial robotics
Corresponding author: Z. Lin is with the Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China (e-mail: linzy@sustech.edu.cn);
¹ This follows the definition in [31, Section 1.2].
² Although \begin{document}$ {\cal{S}}_{{\includegraphics[width=0.01\paperwidth]{1.png}} i_1j_1k_1m_1}\cap{\cal{S}}_{{\includegraphics[width=0.01\paperwidth]{1.png}} i_2j_2k_2m_2} $\end{document} may be nonempty, this will not affect the total effective number of angle constraints in \begin{document}$ {\cal{A}} $\end{document}.
Received Date: 2022-04-25
Accepted Date: 2022-05-18

Available Online: 2022-06-24

Abstract

Abstract

Angle rigid multi-agent formations can simultaneously undergo translational, rotational, and scaling maneuvering, therefore combining the maneuvering capabilities of both distance and bearing rigid formations. However, maneuvering angle rigid formations in 2D or 3D with global convergence guarantees is shown to be a challenging problem in the existing literature even when relative position measurements are available. Motivated by angle-induced linear equations in 2D triangles and 3D tetrahedra, this paper aims to solve this challenging problem in both 2D and 3D under a leader-follower framework. For the 2D case where the leaders have constant velocities, by using local relative position and velocity measurements, a formation maneuvering law is designed for the followers governed by double-integrator dynamics. When the leaders have time-varying velocities, a sliding mode formation maneuvering law is proposed by using the same measurements. For the 3D case, to establish an angle-induced linear equation for each tetrahedron, we assume that all the followers’ coordinate frames share a common Z direction. Then, a formation maneuvering law is proposed for the followers to globally maneuver Z-weakly angle rigid formations in 3D. The extension to Lagrangian agent dynamics and the construction of the desired rigid formations by using the minimum number of angle constraints are also discussed. Simulation examples are provided to validate the effectiveness of the proposed algorithms.
- Angle rigid formations,
- formation control,
- formation maneuvering,
- global convergence,
- multi-agent systems

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¹ This follows the definition in [31, Section 1.2].
² Although $ {\cal{S}}_{{\includegraphics[width=0.01\paperwidth]{1.png}} i_1j_1k_1m_1}\cap{\cal{S}}_{{\includegraphics[width=0.01\paperwidth]{1.png}} i_2j_2k_2m_2} $ may be nonempty, this will not affect the total effective number of angle constraints in $ {\cal{A}} $.

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Angle rigid formations can undergo simultaneously translational, rotational and scaling maneuvering. However, maneuvering angle rigid formations in 2D or 3D with global convergence guarantee is shown to be a challenging problem in the existing literature even when relative position measurements are available. Motivated by angle-induced linear equations in 2D triangles and 3D tetrahedra, this paper aims to solve this challenging problem in both 2D and 3D under a leader-follower framework
Compared with relative position-constrained, distance-constrained and bearing-constrained formation maneuvering approaches, the proposed angle-constrained formation maneuvering laws enable the maneuvering motions of simultaneous translation, rotation and scaling. Compared with relative position-constrained and bearing-constrained formations which require agents to have aligned coordinate frames, angle rigid formations allow agents to have non-aligned local coordinate frames
Compared with the existing 2D angle-constrained formation maneuvering laws guaranteeing local convergence and angle-constrained flocking law guaranteeing almost global convergence, both of our proposed 2D and 3D angle-constrained formation maneuvering laws have global convergence guarantee
Although both the angle-displacement and affine formation maneuvering approaches enable the maneuvering motions of simultaneous translation, rotation and scaling, the number of leaders required for maneuvering motion control in these works is higher than that of our work which only requires 2 leaders in both 2D and 3D cases. For example, the number of leaders should be at least 3 for the 2D affine formation algorithms in 2D, while at least 4 for the 3D affine formation algorithms in 3D

Maneuvering Angle Rigid Formations With Global Convergence Guarantees

doi: 10.1109/JAS.2022.105749

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