Numerical method for solving the optimization problem of trajectory control and formation maintenance by a group of autonomous UAVs with predictive models

K.Yu. Ganshin, D.L. Vinokursky, O.S. Mezentseva, Ph.V. Samoilov

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Abstract: The article is devoted to the development of a numerical method for solving the optimization problem of trajectory control of a single UAV based on the penalty functions method with computational acceleration. The article described a numerical method for finding a solution to the trajectory control problem, presented as a quadratic programming problem, using the penalty function method with Aitken’s
computational acceleration.

Keywords: trajectory generation algorithms, UAV mathematical model, numerical method, Aitken’s acceleration, penalty function, Lagrange

For citation. Ganshin K.Yu., Vinokursky D.L., Mezentseva O.S., Samoilov F.V. Numerical method for solving the optimization problem of trajectory control and formation maintenance by a group of autonomous UAVs with predictive models. News of the Kabardino-Balkarian Scientific Center of RAS. 2023. No. 4(114). Pp. 55–60. DOI: 10.35330/1991-6639-2023-4-114-55-60

References

1. Jezierski A. A comparison of LQR and MPC control algorithms of an inverted pendulum / A. Jezierski, J. Mozaryn, D. Suski. Advances in Intelligent Systems and Computing. Cham: Springer International Publishing. 2017. Pp. 65–76.
2. Ławryńczuk M. Introduction to model predictive control // in book «Nonlinear Predictive Control Using Wiener Models». Cham: Springer International Publishing. 2022. Pp. 3–40.
3. Richalet J., Rault A., Testud J. et al. Model predictive heuristic control. Automatica (Oxf.). No. 14 (5). Pp. 413–428.
4. Vinogradov A.M., Krasil’shchik I.S. What is the Hamiltonian formalism? Russian mathematical surveys. 1975. Vol. 30. No. 1. Pp. 177–202.
5. Garcia G.A., Kim A.R., Jackson E. et al. Modeling and flight control of a commercial nano quadrotor // International Conference on Unmanned Aircraft Systems (ICUAS). IEEE. 2017. DOI: 10.1109/icuas.2017.7991439-2017.
6. Chinedu Amata Amadi W.S. Design and implementation of Model Predictive Control on Pixhawk Flight Controller. Stellenbosch University. 2018.
7. Giernacki W., Skwierczynski M., Witwicki W. et al. Crazyflie 2.0 quadrotor as a platform for research and education in robotics and control engineering. 22nd International Conference on Methods and Models in Automation and Robotics (MMAR). IEEE. 2017. DOI: 10.1109/mmar.2017.8046794-2017.
8. Arnold V.I., Kozlov V.V., Nejshtadt A.I. Mathematical aspects of classical and celestial mechanics. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya. 1985. No. 3. Pp. 5–290. (in Russian)
9. Wills A.G., Heath W.P. Barrier function based model predictive control. Automatica: the journal of IFAC, the International Federation of Automatic Control. 2004. No. 8(40). Pp. 1415–1422.
10. Gopal V., Biegler L.T. Large scale inequality constrained optimization and control. IEEE Control Systems Magazine. 1998. No. 18(6). Pp. 59–68.
11. Faddeev D.K., Faddeeva V.N. Vychislitel’nyye metody lineynoy algebry [Computational methods of linear algebra]. Leningrad: Nauka, 1975 (in Russian)
12. Aitken A.C. XXV. – On Bernoulli’s numerical solution of algebraic equations. Proceedings of the Royal Society of Edinburgh. 1927. (46). Pp. 289–305.

Information about the authors

Ganshin Konstantin Yuryevich, graduate student, Institute of Information Technologies and Telecommunications, North-Caucasus Federal University;
355017, Russia, Stavropol, 1, Pushkin street;
ORCID: https://orcid.org/0000-0001-7495-0736
Vinokursky Dmitry Leonidovich, Ph.D. (Phys. & Math.), Associate Professor, Institute of Information Technologies and Telecommunications, North-Caucasus Federal University;
355017, Russia, Stavropol, 1, Pushkin street;
dlvinokursky@gmail.com, ORCID: https://orcid.org/0000-0002-5225-8076
Mezentseva Oksana Stanislavovna, Ph.D. (Phys. & Math.) Associate Professor, Institute of Information Technologies and Telecommunications, North-Caucasus Federal University;
355017, Russia, Stavropol, 1, Pushkin street;
ORCID: https://orcid.org/0000-0001-5503-1056
Samoilov Philipp Vladimirovich, Ph.D. (Phys. & Math.), Associate Professor, Institute of Information Technologies and Telecommunications, North-Caucasus Federal University;
355017, Russia, Stavropol, 1, Pushkin street;
ORCID: https://orcid.org/0000-0003-3555-4479