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Volume 9 Issue 2
Feb.  2022

IEEE/CAA Journal of Automatica Sinica

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Xiaodong He, Zhiyong Sun, Zhiyong Geng and Anders Robertsson, "Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space," IEEE/CAA J. Autom. Sinica, vol. 9, no. 2, pp. 270-282, Feb. 2022. doi: 10.1109/JAS.2021.1004323
Citation: Xiaodong He, Zhiyong Sun, Zhiyong Geng and Anders Robertsson, "Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space," IEEE/CAA J. Autom. Sinica, vol. 9, no. 2, pp. 270-282, Feb. 2022. doi: 10.1109/JAS.2021.1004323

Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space

doi: 10.1109/JAS.2021.1004323
Funds:  This work was supported by the National Natural Science Foundation of China (61773024, 62073002), the Eindhoven Artificial Intelligence Systems Institute (EAISI), and the ELLIIT Excellence Center and the Swedish Foundation for Strategic Research, Sweden (RIT15-0038)
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  • This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space. The vehicle’s model is established on the matrix Lie group SE(3), which describes the configuration of rigid bodies globally and uniquely. We focus on the kinematic model of the underactuated vehicle, which features an underactuation form that has no sway and heave velocity. To compensate for the lack of these two velocities, we construct additional rotation matrices to generate a motion of rotation coupled with translation. Then, the state feedback is designed with the help of the logarithmic map, and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction. Later, the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance. Finally, simulation examples are provided to verify the effectiveness of the stabilization controller.

     

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  • [1]
    N. E. Leonard, “Control synthesis and adaptation for an underactuated autonomous underwater vehicle,” IEEE J. Ocean. Eng., vol. 20, no. 3, pp. 211–220, Jul. 1995. doi: 10.1109/48.393076
    [2]
    O. Egeland, M. Dalsmo, and O. J. Sørdalen, “Feedback control of a nonholonomic underwater vehicle with a constant desired configuration,” Int. J. Robot. Res., vol. 15, no. 1, pp. 24–35, Feb. 1996. doi: 10.1177/027836499601500102
    [3]
    H. P. Li, P. Xie, and W. S. Yan, “Receding horizon formation tracking control of constrained underactuated autonomous underwater vehicles,” IEEE Trans. Ind. Electron., vol. 64, no. 6, pp. 5004–5013, Jun. 2017. doi: 10.1109/TIE.2016.2589921
    [4]
    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
    [5]
    S. Fari, X. M. Wang, S. Roy, and S. Baldi, “Addressing unmodeled pathfollowing dynamics via adaptive vector field: A UAV test case,” IEEE Trans. Aerosp. Electron. Syst., vol. 56, no. 2, pp. 1613–1622, Apr. 2020. doi: 10.1109/TAES.2019.2925487
    [6]
    J. L. D. Olavo, G. D. Thums, T. A. Jesus, L. C. D. Pimenta, L. A. B. Torres, and R. M. Palhares, “Robust guidance strategy for target circulation by controlled UAV,” IEEE Trans. Aerosp. Electron. Syst., vol. 54, no. 3, pp. 1415–1431, Jun. 2018. doi: 10.1109/TAES.2018.2793058
    [7]
    J. Liu, W. Han, X. W. Wang, and J. Li, “Research on cooperative trajectory planning and tracking problem for multiple carrier aircraft on the deck,” IEEE Syst. J., vol. 14, no. 2, pp. 3027–3038, Jun. 2020. doi: 10.1109/JSYST.2019.2932783
    [8]
    Y. Y. Chen, R. Yu, Y. Zhang, and C. L. Liu, “Circular formation flight control for unmanned aerial vehicles with directed network and external disturbance,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 505–516, Mar. 2020. doi: 10.1109/JAS.2019.1911669
    [9]
    R. W. Brockett, “Asymptotic stability and feedback stabilization,” in R. W. Brockett, R. S. Millman, H. J. Sussmann (eds.) Differential Geometric Control Theory, Birkhäuser, Boston, 1983, pp. 181–191.
    [10]
    R. K. Gupta and S. D. Senturia, “Robust attitude stabilization of an underactuated AUV,” in Proc. European Control Conf., Brussels, Belgium, Jul. 1997, pp. 1398–1402.
    [11]
    Y. M. Li, Y. Li, and Q. Wu, “Design for three-dimensional stabilization control of underactuated autonomous underwater vehicles,” Ocean Eng., vol. 150, pp. 327–336, Feb. 2018. doi: 10.1016/j.oceaneng.2017.12.071
    [12]
    M. Reyhanoglu, “Exponential stabilization of an underactuated autonomous surface vessel,” Automatica, vol. 33, no. 12, pp. 2249–2254, Dec. 1997. doi: 10.1016/S0005-1098(97)00141-6
    [13]
    J. Cheng, J. Q. Yi, and D. B. Zhao, “Stabilization of an underactuated surface vessel via discontinuous control,” in Proc. American Control Conf., New York, NY, USA, Jul. 2007, pp. 206–211.
    [14]
    A. P. Aguiar and A. M. Pascoal, “Global stabilization of an underactuated autonomous underwater vehicle via logic-based switching,” in Proc. IEEE Conf. Decision and Control, Las Vegas, NV, USA, Dec. 2002, pp. 3267–3272.
    [15]
    D. Panagou and K. J. Kyriakopoulos, “Dynamic positioning for an underactuated marine vehicle using hybrid control,” Int. J. Control, vol. 87, no. 2, pp. 264–280, Feb. 2014. doi: 10.1080/00207179.2013.828853
    [16]
    K. Y. Pettersen and O. Egeland, “Time-varying exponential stabilization of the position and attitude of an underactuated autonomous underwater vehicle,” IEEE Trans. Autom. Control, vol. 41, no. 1, pp. 112–115, Jan. 1999.
    [17]
    A. P. Aguiar, J. P. Hespanha, and A. M. Pascoal, “Switched seesaw control for the stabilization of underactuated vehicles,” Automatica, vol. 43, no. 12, pp. 1997–2008, Dec. 2007. doi: 10.1016/j.automatica.2007.03.023
    [18]
    D. Panagou, S. Maniatopoulos, and K. Kyriakopoulos, “Control of an underactuated underwater vehicle in 3D space under field-of-view constraints,” IFAC Proceedings Volumes, vol. 45, no. 5, pp. 25–30, 2012. doi: 10.3182/20120410-3-PT-4028.00006
    [19]
    M. Mirzaei, F. Abdollahi, and N. Meskin, “Global stabilization of autonomous underactuated underwater vehicles in 3D space,” in Proc. IEEE Int. Conf. Advanced Intelligent Mechatronics, Banff, Canada, Jul. 2016, pp. 148–153.
    [20]
    H. P. Li and W. S. Yan, “Model predictive stabilization of constrained underactuated autonomous underwater vehicles with guaranteed feasibility and stability,” IEEE/ASME Trans. Mechatronics, vol. 22, no. 3, pp. 1185–1194, Jun. 2017. doi: 10.1109/TMECH.2016.2587288
    [21]
    Z. Y. Zuo, L. Cheng, X. X. Wang, and K. W. Sun, “Three-dimensional pathfollowing backstepping control for an underactuated stratospheric airship,” IEEE Trans. Aerosp. Electron. Syst., vol. 55, no. 3, pp. 1483–1497, Jun. 2019. doi: 10.1109/TAES.2018.2873054
    [22]
    K. Rsetam, Z. W. Cao, and Z. H. Man, “Cascaded extended state observer based sliding mode control for underactuated flexible joint robot,” IEEE Trans. Ind. Electron., vol. 67, no. 12, pp. 10822–10832, Dec. 2020. doi: 10.1109/TIE.2019.2958283
    [23]
    M. Ramírez-Neria, H. Sira-Ramírez, R. Garrido-Moctezuma, and A. Luviano-Juárez, “Linear active disturbance rejection control of underactuated systems: The case of the furuta pendulum,” ISA Trans., vol. 53, no. 4, pp. 920–928, Jul. 2014. doi: 10.1016/j.isatra.2013.09.023
    [24]
    F. Bullo and A. D. Lewis, Geometric Control of Mechanical Systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems. New York, NY, USA: Springer, 2005.
    [25]
    S. P. Bhat and D. S. Bernstein, “A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon,” Syst. Control Lett., vol. 39, no. 1, pp. 63–70, Jan. 2000. doi: 10.1016/S0167-6911(99)00090-0
    [26]
    D. E. Koditschek, “Application of a new Lyapunov function to global adaptive tracking,” in Proc. IEEE Conf. Decision and Control, Austin, TX, USA, Dec. 1988, pp. 63–68.
    [27]
    E. W. Justh and P. S. Krishnaprasad, “Equilibria and steering laws for planar formations,” Syst. Control Lett., vol. 52, no. 1, pp. 25–38, May 2004. doi: 10.1016/j.sysconle.2003.10.004
    [28]
    R. Sepulchre, D. A. Paley, and N. E. Leonard, “Stabilization of planar collective motion: All-to-all communication,” IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 811–824, May 2007. doi: 10.1109/TAC.2007.898077
    [29]
    M. Tayefi, Z. Y. Geng, and X. H. Peng, “Coordinated tracking formultiple nonholonomic vehicles on SE(2),” Nonlinear Dyn., vol. 87, no. 1, pp. 665–675, Jan. 2017. doi: 10.1007/s11071-016-3067-8
    [30]
    X. D. He and Z. Y. Geng, “Arbitrary point-to-point stabilization control in specified finite time for wheeled mobile robots based on dynamic model,” Nonlinear Dyn., vol. 97, no. 2, pp. 937–954, Jul. 2019. doi: 10.1007/s11071-019-05019-0
    [31]
    F. Bullo and R. Murray, “Proportional derivative (PD) control on the Euclidean group,” in Proc. European Control Conf., Rome, Italy, Sep. 1995, pp. 1091–1097.
    [32]
    H. K. Khalil, Nonlinear Systems, 3rd edition. NJ, USA: Prentice-Hall, 2002.
    [33]
    M. Tayefi and Z. Y. Geng, “Logarithmic control, trajectory tracking, and formation for nonholonomic vehicles on Lie group SE(2),” Int. J. Control, vol. 92, no. 2, pp. 204–224, Feb. 2019. doi: 10.1080/00207179.2017.1349341

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    Highlights

    • The vehicle investigated in this paper is an underactuated system, which has six degrees of freedom but only four independent control inputs
    • The model of the underactuated vehicle is established on the matrix Lie group SE(3), which describes the rigid body’s configuration globally and uniquely
    • Two additional rotation matrices are constructed to generate a motion of rotation coupled with translation, so that the underactuated states can be driven by the control inputs
    • The control law can exponentially stabilize the underactuated vehicle with almost global domain of convergence, that is, any point on SE(3) except for several ones with measure zero

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