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Robust IDA-PBC for under-actuated systems with inertia matrix dependent of the unactuated coordinates: application to a UAV carrying a load

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Abstract

This paper presents a methodology to solve the problem of robustification of Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) scheme for the case of under-actuated systems with inertia matrix dependent of the unactuated coordinates. Specifically, we analyze the robustness of the IDA-PBC strategy with respect to constant external disturbances. This algorithm requires adding an integral action with a particular change of coordinates in an outer-loop to the IDA-PBC strategy to reject constant external disturbances. The asymptotic stability of the proposed controller despite constant external disturbances is proved using the closed-loop Hamiltonian as a Lyapunov candidate function and LaSalle’s invariance principle. Finally, as a proof of concept, we have applied the proposed robust IDA-PBC strategy to an Unmanned Aerial vehicle that transports a payload suspended by a cable, which is a class of underactuated system with inertia matrix dependent of the unactuated coordinate. Satisfactory results in numerical experiments demonstrate the applicability of the method.

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Funding

This work has been supported by Tecnológico Nacional de México grant number 9992.21-P. Additional funding was provided by Conacyt under the program Cátedras Patrimoniales Projects 88 and 2759.

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Authors and Affiliations

  1. Cátedras Conacyt, Tecnológico Nacional de México/I.T. Hermosillo, Ave. Tecnológico y Per. Poniente S/N, 83170, Hermosillo, Mexico

    M. E. Guerrero-Sánchez & O. Hernández-González

  2. Tecnológico Nacional de México/I.T. Hermosillo, Ave. Tecnológico y Per. Poniente S/N, 83170, Hermosillo, Mexico

    G. Valencia-Palomo & J. A. Hoyo-Montaño

  3. Cátedras Conacyt, Center for Research in Mathematics CIMAT AC, campus Zacatecas, Ave. Lasec Andador Galileo Galilei, Manzana 3 Lote 7, Parque Quantum, 98160, Zacatecas, Mexico

    D. A. Mercado-Ravell

  4. TURIX-Dynamics Diagnosis and Control Group, Tecnológico Nacional de México/I.T. Tuxtla Gutiérrez, Carr. Panam. km 1080, 29050, Tuxtla Gutierrez, Mexico

    F. R. López-Estrada

Authors
  1. M. E. Guerrero-Sánchez
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  2. O. Hernández-González
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  3. G. Valencia-Palomo
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  4. D. A. Mercado-Ravell
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  5. F. R. López-Estrada
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  6. J. A. Hoyo-Montaño
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Correspondence to G. Valencia-Palomo.

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Guerrero-Sánchez, M.E., Hernández-González, O., Valencia-Palomo, G. et al. Robust IDA-PBC for under-actuated systems with inertia matrix dependent of the unactuated coordinates: application to a UAV carrying a load. Nonlinear Dyn 105, 3225–3238 (2021). https://doi.org/10.1007/s11071-021-06776-7

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  • DOI: https://doi.org/10.1007/s11071-021-06776-7

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