A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 9 Issue 8
Aug.  2022

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 7.847, Top 10% (SCI Q1)
    CiteScore: 13.0, Top 5% (Q1)
    Google Scholar h5-index: 64, TOP 7
Turn off MathJax
Article Contents
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
Citation: 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

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
More Information
  • 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.

     

  • loading
  • 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}} $.
  • [1]
    H. S. Ahn, Formation Control. Cham, Germany: Springer, 2020.
    [2]
    Y. G. Liu and G. Nejat, “Robotic urban search and rescue: A survey from the control perspective,” J. Intell. Robot. Syst., vol. 72, no. 2, pp. 147–165, Mar. 2013. doi: 10.1007/s10846-013-9822-x
    [3]
    J. Y. Hu, P. Bhowmick, I. Jang, F. Arvin, and A. Lanzon, “A decentralized cluster formation containment framework for multirobot systems,” IEEE Trans. Robot., vol. 37, no. 6, pp. 1936–1955, Dec. 2021. doi: 10.1109/TRO.2021.3071615
    [4]
    Q. Wang, Y. Z. Wang, and H. X. Zhang, “The formation control of multi-agent systems on a circle,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 148–154, Jan. 2016.
    [5]
    S. Y. Zhao, “Affine formation maneuver control of multiagent systems,” IEEE Trans. Automat. Contr., vol. 63, no. 12, pp. 4140–4155, Dec. 2018. doi: 10.1109/TAC.2018.2798805
    [6]
    Z. M. Han, L. L. Wang, Z. Y. Lin, and R. H. Zheng, “Formation control with size scaling via a complex Laplacian-based approach,” IEEE Trans. Cybern., vol. 46, no. 10, pp. 2348–2359, Oct. 2015.
    [7]
    L. M. Chen, H. G. De Marina, and M. Cao, “Maneuvering formations of mobile agents using designed mismatched angles,” IEEE Trans. Automat. Contr., vol. 67, no. 4, pp. 1655–1668, Apr. 2021.
    [8]
    X. Fang, X. L. Li, and L. H. Xie, “Distributed formation maneuver control of multiagent systems over directed graphs,” IEEE Trans. Cybern., 2021, DOI: 10.1109/TCYB.2020.3044581.
    [9]
    A. L. Yang, W. Naeem, and M. R. Fei, “Decentralised formation control and stability analysis for multi-vehicle cooperative manoeuvre,” IEEE/CAA J. Autom. Sinica, vol. 1, no. 1, pp. 92–100, Jan. 2014. doi: 10.1109/JAS.2014.7004625
    [10]
    X. W. Dong and G. Q. Hu, “Time-varying formation control for general linear multi-agent systems with switching directed topologies,” Automatica, vol. 73, pp. 47–55, Nov. 2016. doi: 10.1016/j.automatica.2016.06.024
    [11]
    A. Mondal, L. Behera, S. R. Sahoo, and A. Shukla, “A novel multi-agent formation control law with collision avoidance,” IEEE/CAA J. Autom. Sinica, vol. 4, no. 3, pp. 558–568, Jul. 2017. doi: 10.1109/JAS.2017.7510565
    [12]
    Y. J. Lin, Z. Y. Lin, Z. Y. Sun, and B. D. O. Anderson, “A unified approach for finite-time global stabilization of affine, rigid, and translational formation,” IEEE Trans. Automat. Contr., vol. 67, no. 4, pp. 1869–1881, Apr. 2022. doi: 10.1109/TAC.2021.3084247
    [13]
    S. Y. Zhao and D. Zelazo, “Translational and scaling formation maneuver control via a bearing-based approach,” IEEE Trans. Contr. Netw. Syst., vol. 4, no. 3, pp. 429–438, Sep. 2017. doi: 10.1109/TCNS.2015.2507547
    [14]
    Z. M. Han, K. X. Guo, L. H. Xie, and Z. Y. Lin, “Integrated relative localization and leader-follower formation control,” IEEE Trans. Automat. Contr, vol. 64, no. 1, pp. 20–34, Jan. 2018.
    [15]
    T. R. Han, Z. Y. Lin, R. H. Zheng, and M. Y. Fu, “A barycentric coordinate-based approach to formation control under directed and switching sensing graphs,” IEEE Trans. Cybern., vol. 48, no. 4, pp. 1202–1215, Apr. 2017.
    [16]
    Z. X. Liu, Y. B. Li, F. Y. Wang, and Z. Q. Chen, “Reduced-order observer-based leader-following formation control for discrete-time linear multi-agent systems,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 10, pp. 1715–1723, Oct. 2020.
    [17]
    Z. Y. Gao and G. Guo, “Fixed-time sliding mode formation control of AUVs based on a disturbance observer,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 539–545, Mar. 2020. doi: 10.1109/JAS.2020.1003057
    [18]
    H. G. De Marina, B. Jayawardhana, and M. Cao, “Distributed rotational and translational maneuvering of rigid formations and their applications,” IEEE Trans. Robot., vol. 32, no. 3, pp. 684–697, Jun. 2016. doi: 10.1109/TRO.2016.2559511
    [19]
    M. H. Trinh and H. S. Ahn, “Finite-time bearing-based maneuver of acyclic leader-follower formations,” IEEE Contr. Syst. Lett., vol. 6, pp. 1004–1009, Jun. 2021.
    [20]
    X. L. Li, M. J. Er, G. H. Yang, and N. Wang, “Bearing-based formation manoeuvre control of nonholonomic multi-agent systems,” Int. J. Syst. Sci., vol. 50, no. 16, pp. 2993–3002, Nov. 2019. doi: 10.1080/00207721.2019.1692094
    [21]
    M. H. Trinh, Q. Van Tran, D. Van Vu, P. D. Nguyen, and H. S. Ahn, “Robust tracking control of bearing-constrained leader-follower formation,” Automatica, vol. 131, p. 109733, Sep. 2021.
    [22]
    S. Y. Zhao, Z. H. Li, and Z. T. Ding, “Bearing-only formation tracking control of multiagent systems,” IEEE Trans. Automat. Contr., vol. 64, no. 11, pp. 4541–4554, Nov. 2019. doi: 10.1109/TAC.2019.2903290
    [23]
    L. M. Chen, M. Cao, and C. J. Li, “Angle rigidity and its usage to stabilize multiagent formations in 2-D,” IEEE Trans. Automat. Contr., vol. 66, no. 8, pp. 3667–3681, Aug. 2021. doi: 10.1109/TAC.2020.3025539
    [24]
    G. S. Jing, G. F. Zhang, H. W. J. Lee, and L. Wang, “Angle-based shape determination theory of planar graphs with application to formation stabilization,” Automatica, vol. 105, pp. 117–129, Jul. 2019. doi: 10.1016/j.automatica.2019.03.026
    [25]
    L. M. Chen, M. M. Shi, H. G. De Marina, and M. Cao, “Stabilizing and maneuvering angle rigid multi-agent formations with double-integrator agent dynamics,” IEEE Trans. Contr. Netw. Syst., 2022, DOI: 10.1109/TCNS.2022.3153885.
    [26]
    J. Yang, X. M. Wang, S. Baldi, S. Singh, and S. Farì, “A software-in-the-loop implementation of adaptive formation control for fixed-wing UAVs,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1230–1239, Sept. 2019. doi: 10.1109/JAS.2019.1911702
    [27]
    G. S. Jing and L. Wang, “Multiagent flocking with angle-based formation shape control,” IEEE Trans. Automat. Contr., vol. 65, no. 2, pp. 817–823, Feb. 2020. doi: 10.1109/TAC.2019.2917143
    [28]
    Z. Y. Lin, L. L. Wang, Z. Y. Chen, M. Y. Fu, and Z. M. Han, “Necessary and sufficient graphical conditions for affine formation control,” IEEE Trans. Automat. Contr., vol. 61, no. 10, pp. 2877–2891, Oct. 2016. doi: 10.1109/TAC.2015.2504265
    [29]
    L. M. Chen, J. Mei, C. J. Li, and G. F. Ma, “Distributed leader-follower affine formation maneuver control for high-order multiagent systems,” IEEE Trans. Automat. Control, vol. 65, no. 11, pp. 4941–4948, Nov. 2020. doi: 10.1109/TAC.2020.2986684
    [30]
    L. M. Chen and Z. Y. Sun, “Globally stabilizing triangularly angle rigid formations,” IEEE Trans. Autom. Contr., 2022, DOI: 10.1109/TAC.2022.3151567.
    [31]
    R. Connelly, “Generic global rigidity,” Discrete Comput. Geom., vol. 33, no. 4, pp. 549–563, Apr. 2005. doi: 10.1007/s00454-004-1124-4
    [32]
    X. Fang, X. L. Li, and L. H. Xie, “Angle-displacement rigidity theory with application to distributed network localization,” IEEE Trans. Automat. Contr., vol. 66, no. 6, pp. 2574–2587, Jun. 2021. doi: 10.1109/TAC.2020.3012630
    [33]
    D. P. Yang, W. Ren, and X. D. Liu, “Fully distributed adaptive sliding-mode controller design for containment control of multiple Lagrangian systems,” Syst. Control Lett., vol. 72, pp. 44–52, Oct. 2014. doi: 10.1016/j.sysconle.2014.07.006
    [34]
    L. G. Wu, J. X. Liu, S. Vazquez, and S. K. Mazumder, “Sliding mode control in power converters and drives: A review,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 3, pp. 392–406, Mar. 2022. doi: 10.1109/JAS.2021.1004380
    [35]
    M. C. Park, Z. Y. Sun, M. H. Trinh, B. D. O. Anderson, and H. S. Ahn, “Distance-based control of K4 formation with almost global convergence,” in Proc. IEEE 55th Conf. Decision and Control, Las Vegas, USA, 2016, pp. 904–909.
    [36]
    M. C. Park, Z. Y. Sun, B. D. O. Anderson, and H. S. Ahn, “Distance-based control of K n formations in general space with almost global convergence,” IEEE Trans. Automat. Contr., vol. 63, no. 8, pp. 2678–2685, Aug. 2018. doi: 10.1109/TAC.2017.2776524
    [37]
    R. Kennedy and C. J. Taylor, “Network localization from relative bearing measurements,” in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, Chicago, USA, 2014, pp. 149–156.
    [38]
    G. R. Duan, “High-order system approaches: I. Fully-actuated systems and parametric designs,” Acta Autom. Sinica, vol. 46, no. 7, pp. 1333–1345, Jul. 2020.

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(9)

    Article Metrics

    Article views (110) PDF downloads(29) Cited by()

    Highlights

    • 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

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return