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Design and experimental validation of a nonlinear controller for underactuated surface vessels

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A Correction to this article was published on 03 March 2021

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Abstract

This paper addresses the problem of trajectory tracking control of an underactuated surface vessel moving in a two-dimensional space in the presence of unknown disturbances. In a preliminary stage, a couple of nonlinear observers is derived to obtain an estimate of the perturbations, which are assumed to originate from unmodeled time-varying dynamics and/or exogenous disturbances. Secondly, we resort to the Lyapunov-based backstepping technique to design two stabilizing control laws, governing the thrust force and torque actuations, that are proved to render the overall control system error globally uniformly bounded. Each control law yields an actuator signal which is implicitly bounded with respect to the position error, and the resulting estimation and tracking errors can be made arbitrarily small by tweaking the control parameters. A set of realistic simulations results is presented to validate our strategy. Experimental trials using an autonomous surface vehicle are also showcased to further demonstrate the efficacy and robustness of the proposed controller.

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Notes

  1. At some point in the calculations, the term \(r(t)\mathbf {z}_{2}^{\mathsf {T}}(t)\mathbf {M}\mathbf {S}\mathbf {M}\mathbf {z}_{2}(t)\) arises; it equals zero due to the general property of the vector cross-product.

  2. Note that this is not a necessary condition, but one which is sufficient to guarantee that errors are bounded and converge, i.e., are dynamically stable.

  3. This particular lake, located on the northeast side of the University of Macau campus, has a river flowing into and out of it.

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Funding

This work was partly funded by the Macau Science and Technology Development Fund under Grant FDCT/0146/2019/A3, by the Project MYRG2018-00198-FST of the University of Macau and by LARSyS FCT Project UIDB/50009/2020. The work of David Cabecinhas was supported by FCT Scientific Employment Stimulus Grant CEECIND/04199/2017.

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Authors and Affiliations

  1. Faculty of Science and Technology, University of Macau, Taipa, Macau, China

    Wei Xie, Joel Reis & Carlos Silvestre

  2. Institute for Systems and Robotics, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisbon, Portugal

    David Cabecinhas

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  1. Wei Xie
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  2. Joel Reis
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  3. David Cabecinhas
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  4. Carlos Silvestre
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Correspondence to Carlos Silvestre.

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The original online version of this article was revised: The correct figures 2, 3, 4, 5, and 6 are shown in the correction article.

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Xie, W., Reis, J., Cabecinhas, D. et al. Design and experimental validation of a nonlinear controller for underactuated surface vessels. Nonlinear Dyn 102, 2563–2581 (2020). https://doi.org/10.1007/s11071-020-06058-8

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  • DOI: https://doi.org/10.1007/s11071-020-06058-8

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