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Volume 9 Issue 2
Feb.  2022

IEEE/CAA Journal of Automatica Sinica

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X. D. He, Z. Y. Sun, Z. Y. Geng, and A. 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: X. D. He, Z. Y. Sun, Z. Y. Geng, and A. 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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    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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