Efficient Optimal Control Problem Solution for Car-Like Mobile Robots With the Picard-Shooting Method
Abstract
This article investigates the optimal control problem of a Car-Like mobile robot, with our primary objective being the identification of the optimal control strategy that facilitates the transition from an initial point to an endpoint in the shortest possible time. To address this challenge, we employ Pontryagin’s Maximum Principle, coupling it with the shooting method to determine the initial condition of the adjoint state (p0), which is then integrated through the iterative Picard method. The validation of our approach is demonstrated through a numerical example utilizing real-world data, and we provide a comparative analysis of our results against those from previous studies for comprehensive assessment.
References
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A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics. 10.1007/b98885
A. Fortin, Analyse Num´erique pour Ing´enieurs. Springer, 2000. doi: Presses Internationales Polytechnique Montéreal, 2001.
F. Demim, A. Nemra, K. Louadj, and M. Hamerlain, “Simultaneous localization, mapping and path planning for unmanned vehicle using optimal control,” Advances in Mechanical Engineering Journal, vol. 10, no. 1, pp. 1–25, 2018. doi: 10.1177/1687814017736653
S. Titouche, P. Spiteri, F. Messine, and M. Aidene, “Optimal control of a large thermic process,” Journal of Process Control, vol. 25, pp. 50–58, 2015. doi: 10.1016/j.jprocont.2014.09.015
F. Demim, A. Nemra, K. Louadj, Z. Mehal, M. Hamerlain, and A. Bazoula, “Simultaneous localization and mapping algorithm for unmanned ground vehicle with svsf filter,” in 8th International Conference on Modelling, Identification and Control. IEEE, 2016, p. 155–162.
F. Demim, K. Louadj, M. Aidene, and A. Nemra, “Solution of an optimal control problem with vector control using relaxation method,” Journal of Automatic Control and System Engineering, vol. 16, no. 2, pp. 29–41, 2016.
K. Louadj, P. Spitéri, M. Aidene, and F. Messine, “An optimal control problem with free final time for aircraft flight with wind,” in Colloque sur l’Optimisation et les Systèmes d’Information, 2014, pp. 239–250.
K. Louadj, P. Spitéri, M. Aidene, and F. Messine, “Optimal command for the control of the air navigation of an aircraft,” in The Second International Conference on Electrical Engineering and Control Applications. IEEE, 2014, p. 19.
F. Kara, P. Spiteri, F. Messine, and M. Aidene, “A numerical optimal control method for solving a large thermic process,” RAIRO- Operations Research, vol. 50, no. 2, pp. 297–314, 2016. doi: 10.1051/ro/2015018
J. B. Thomas and F. Benjamin, Hybrid Systems, Optimal Control and Hybrid Vehicles. Springer, 2017. doi: 10.1007/978-3-319-51317-1
E. B. Lee and L. Markus, Foundations of Optimal Control Theory. John Wiley & sons, 1967.
E. Trélat, Contrôle Optimal: Théorie et Applications. Vuibert, 2005.
L. Pontryagin, V. Boltyanski, R. Gamkrelidze, and E. Mishchenko, The Mathematical Theory of Optimal Processes. John Wiley & sons, 1962.
E. Picard, Traité d’Analyse Tome II. Gauthier-Villars et Fils, 1893.
E. Picard,Traité d’Analyse Tome III. Gauthier-Villars et Fils, 1896.
E. Picard, “Mémoire sur la théorie des ´ equations aux dérivées partielles et la méthode des approximations successives,” Journal de Mathématiques Pures et Appliquées, vol. 4, no. 6, pp. 145–210, 1890.
J. Stoer and R. Bulirsch, Introduction to Numerical Analysis. 10.1007/978-1-4757-5592-3 Springer, 1980. doi:
H. Maurer, “On optimal control problems with bounded state variables and control appearing linearly,” SIAM Journal on Control and Optimization, vol. 15, no. 3, p. 345–362, 1977. doi: 10.1137/0315023
R. F. Hartl, S. P. Sethi, and R. G. Vickson, “A survey of the maximum principles for optimal control problems with state constraints,” SIAM Review, vol. 37, no. 2, p. 181–218, 1995. doi: 10.1137/1037043
Published
2025-08-18
How to Cite
LOUNIS, Abbes et al.
Efficient Optimal Control Problem Solution for Car-Like Mobile Robots With the Picard-Shooting Method.
Yugoslav Journal of Operations Research, [S.l.], aug. 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1363>. Date accessed: 21 aug. 2025.
doi: https://doi.org/10.2298/YJOR231215031L.
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Section
Research Articles
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
