Abstract
This work proposes single-layer nonlinear model predictive control schemes to solve the autonomous navigation problem while providing obstacle avoidance feature in cluttered environments with previously unknown obstacles. Considering model predictive control frameworks for set-point stabilization and set-point tracking, the penalty method of nonlinear programming is taken into account to enforce avoidance constraints without losing stability and feasibility guarantees. The set-point tracking schemes are shown to be more suitable for motion systems due to their enlarged domain of attraction with respect to the regulation formulations, making it feasible for any changing targets. Further, for the set-point tracking problem, the proposed schemes avoid the use of terminal regions, which, for nonlinear systems, might be cumbersome to compute. Thus, simple design schemes based on a relaxed terminal equality constraint and on a weighted terminal cost are considered. Finally, two case studies considering a differential mobile robot and a quadrotor unmanned aerial vehicle are provided to evaluate the set-point tracking formulations.
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All data necessary to reproduce the results are given in the manuscript.
Notes
See documentation at https://www.mathworks.com/help/control/ref/dlqr.html.
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Acknowledgements
This work extends the results of Santos et al. (2021) in terms of the proposed control strategies and the analyzed case studies. Also, the feasibility and stability analyses are now provided. Besides, here we generalize how obstacles are handled by considering a penalty approach. However, this work presents a similar motivation and one of the case studies considers the same quadrotor UAV system. Considering a similar case study with different controllers allows explaining how the proposed controllers solve the issues of the formulation presented in Santos et al. (2021).
Funding
This work was partially supported by the Brazilian agencies Conselho Nacional de Desenvolvimento Científico (CNPq), under grants 465755/2014-3 (INCT project) and 315695/2020-0; Fundação de Aparo à Pesquisa do Estado de São Paulo (FAPESP), under grant 2014/50851-0; Cordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), under the grants 001 and 88887.136349/2017-00; and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), under grant APQ-03090-17.
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All authors contributed to the study conception, control design, and analysis. Coding and numerical experiments were performed by Marcelo Alves dos Santos. The first draft of the manuscript was written by Marcelo Alves dos Santos, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Santos, M.A., Ferramosca, A. & Raffo, G.V. Nonlinear Model Predictive Control Schemes for Obstacle Avoidance. J Control Autom Electr Syst 34, 891–906 (2023). https://doi.org/10.1007/s40313-023-01024-2
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DOI: https://doi.org/10.1007/s40313-023-01024-2