Resolução do Problema de Estacionamento Paralelo em Tempo Mínimo Utilizando um Novo Pacote de Otimização: COPILOTS

Fran Sérgio Lobato; Arthur Henrique  Iasbeck; Pedro Augusto Queiroz de  Assis

doi:10.14295/vetor.v30i1.12869

Authors

Fran Sérgio Lobato Universidade Federal de Uberlândia https://orcid.org/0000-0002-7401-4718
Arthur Henrique Iasbeck Universidade Federal de Uberlândia https://orcid.org/0000-0003-2461-6769
Pedro Augusto Queiroz de Assis Universidade Federal de Uberlândia https://orcid.org/0000-0002-7145-7847

DOI:

https://doi.org/10.14295/vetor.v30i1.12869

Keywords:

COPILOTS, Parallel Parking, Optimal Control Problem, Direct Collocation, Optimization

Abstract

This work aims to present (BasiC OPtImaL COnTrol Solver), a proposed package for solving Optimal Control Problems (OCPs) based on Direct Methods, easy to use and ideal for users with little or no experience in solving PCOs. In general, the proposed tool performs the discretization of controls via trapezoidal colocation or Hermite-Simpson colocation, while cubic polynomials are used in the interpolation of the states. In effect, the original problem (algebraic-differential) is transformed into a purely algebraic problem, which is solved considering the SQP (Sequential Quadratic Programming). For validation purposes, was used to determine the minimum time path to be traveled by a vehicle when executing a parallel parking maneuver and a new algorithm for initializing states and controls was proposed in order to minimize the computational effort spent. The results demonstrate that the proposed package is configured as an alternative for the resolution of OCPs.

Downloads

Download data is not yet available.

References

V. M. Becerra, PSOPT Optimal Control Solver User Manual, 1a ed., 2019. Disponível em: https://github.com/PSOPT/psopt/releases/tag/V4.0.0

H. J. Sussmann e J. C. Willems, “300 years of optimal control: From the brachystochrone to the maximum principle,” IEEE Control Systems Magazine, vol. 3, no. 17, pp. 32–44, 1997. Disponível em: https://doi.org/10.1109/37.588098

A. E. Bryson, “Optimal control-1950 to 1985,” IEEE Control Systems, vol. 3, no. 16, pp. 26–33, 1996. Disponível em: https://doi.org/10.1109/37.506395

J. T. Betts, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, 2a ed. Advances in Design and Control: Society for Industrial and Applied Mathematics, 2010. Disponível em: https://doi.org/10.1137/1.9780898718577

F. Biral, E. Bertolazzi, e P. Bosetti, “Notes on numerical methods for solving optimal control problems,” IEEJ Journal of Industry Applications, vol. 5, no. 1, pp. 154–166, 2016. Disponível em: https://doi.org/10.1541/ieejjia.5.154

A. Wächter e L. T. Biegler, “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Mathematical Programming, vol. 1, no. 106, pp. 25–57, 2006. Disponível em: https://doi.org/10.1007/s10107-004-0559-y

I. Saclay, “Bocop: an open source toolbox for optimal control,” 2017. Disponível em: http://bocop.org

M. Rieck, M. Bittner, B. Grüter, J. Diepolder, e P. Piprek, “FALCON.m User Guide,” 2020. Disponível em: https://www.fsd.lrg.tum.de/software/wp-content/uploads/UserGuideMain.pdf

L. Beal, D. Hill, R. Martin, e J. Hedengren, “GEKKO Optimization Suite,” Processes, vol. 6, no. 8, p. 106, Jul. 2018. Disponível em: https://doi.org/10.3390/pr6080106

J.-B. Caillau, O. Cots, e J. Gergaud, “Differential continuation for regular optimal control problems,” Optimization Methods and Software, vol. 27, no. 2, pp. 177–196, 2012, publisher: Taylor & Francis. Disponível em: https://doi.org/10.1080/10556788.2011.593625

J. Koenemann, G. Licitra, M. Alp, e M. Diehl, “OpenOCLOpen Optimal Control Library,” 2017. Disponível em: https://openocl.github.io/

M. Kelly, “OptimTraj Users Guide,” 2018. Disponível em: https://github.com/MatthewPeterKelly/OptimTraj/blob/master/docs/UsersGuide/OptimTraj_UsersGuide.pdf

“OpenGoddard,” Dec. 2017. Disponível em: https://github.com/istellartech/OpenGoddard

“Beluga,” Jan. 2018. Disponível em: https://github.com/Rapid-Design-of-Systems-Laboratory/beluga

P. Falugi, E. Kerrigan, e E. van Wyk, “ICLOCS2: A MATLAB Toolbox for Optimization Based Control - Downloads,” 2018. Disponível em: http://www.ee.ic.ac.uk/ICLOCS/Downloads.html

V. M. Becerra, “PSOPT Optimal Control Solver User Manual,” p. 437, 2019.

H. Febbo, P. Jayakumar, J. L. Stein, e T. Ersal. (2020) NLOptControl: A modeling language for solving optimal control problems. arXiv:2003.00142. Disponível em: https://arxiv.org/abs/2003.00142

M. Rieck, M. Bittner, B. Grüter, J. Diepolder, e P. Piprek., FALCON.m: User Guide, 1a ed., Institute of Flight System Dynamics, Technical University of Munich, 2020. Disponível em: https://www.fsd.lrg.tum.de/ software/wp-content/uploads/UserGuideMain.pdf

Y. Nie, O. Faqir, e E. Kerrigan, ICLOCS2 - Imperial College London Optimal Control Software, 1a ed., 2018. Disponível em: http://www.ee.ic.ac.uk/ICLOCS/

M. A. Patterson e A. V. Rao, “GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive gaussian quadrature collocation methods and sparse nonlinear programming,” ACM Transactions on Mathematical Software, vol. 41, no. 1, pp. 1–12, 2014. Disponível em: https://doi.org/10.1145/2558904

P. E. Rutquist e M. M. Edvall, PROPT - Matlab Optimal Control Software, 1a ed., 2010. Disponível em: https://tomopt.com/docs/TOMLAB_PROPT.pdf

I. E. Paromtchik e C. Laugier, “Autonomous parallel parking of a nonholonomic vehicle,” em Proceedings of Conference on Intelligent Vehicles, V. Piper, Ed., 1996, pp. 1–10. Disponível em: https://doi.org/10.1109/IVS.1996.566343

M. Kelly, “An introduction to trajectory optimization: How to do your own direct collocation,” SIAM Review, vol. 59, no. 4, pp. 849–904, 2017. Disponível em: https://doi.org/10.1137/16M1062569

MathWorks, “Change Folders on the Search Path - MATLAB & Simulink,” 2020. Disponível em: https://www.mathworks.com/help/matlab/matlab_env/add-remove-or-reorder-folders-on-the-search-path.html

J. A. Parejo, A. Ruiz-Cortés, S. Lozano, e P. Fernandez, “Metaheuristic optimization frameworks: A survey and benchmarking,” Soft Computing, vol. 1, no. 16, pp. 527–561, 2012. Disponível em: https://doi.org/10.1007/s00500-011-0754-8

B. Li, K. Wang, e Z. Shao, “Time-optimal maneuver planning in automatic parallel parking using a simultaneous dynamic optimization approach,” IEEE Transactions on Intelligent Transportation Systems, vol. 11, no. 17, pp. 3263–3274, 2016. Disponível em: https://doi.org/10.1109/TITS.2016.2546386

O. Qx, I. Bongartz, A. Conn, N. Gould, e M. Saunders, “A numerical comparison between the LANCELOT and MINOS packages for large-scale constrained optimization,” Council for the Central Laboratory of The Research Councils, vol. 1, no. 1, pp. 1–9, 1997. Disponível em: https://cds.cern.ch/record/338797/files/SCAN-9711063.pdf

C. L. Darby, W. W. Hager, e A. V. Rao, “An hp-adaptive pseudospectral method for solving optimal control problems,” Optimal Control Applications and Methods, vol. 32, no. 4, pp. 476–502, 2011. Disponível em: https://doi.org/10.1002/oca.957

E. D. Dolan, J. J. Moré, e T. S. Munson, Benchmarking Optimization Software With COPS 3.0, 1a ed., 2018.Disponível em: https://doi.org/10.2172/834714