graduate student
Russian Federation
employee
St. Petersburg, Russian Federation
UDC 51-74
With the expansion of the scope of unmanned aerial vehicles, reliable forecasting of their behavior at the design stage is becoming an increasingly urgent task. This problem can be solved using appropriate modeling methods. Purpose: to identify and compare the methods used in simulating the flight characteristics of unmanned aerial vehicles. Results: a model of spatial motion with six degrees of freedom (6DoF, Six Degrees of Freedom) was considered, a comparison was made of the main methods used to simulate flight characteristics (Euler’s method, the classic Runge — Kutta fourth-order method and the adaptive Runge — Kutta — Felberg scheme), route planning algorithms (A*, RRT*, genetic particle swarm algorithm and method. It has been established that for most research problems, the Runge — Kutta method of the fourth order turns out to be a reasonable compromise in accuracy and computational cost, while adaptive schemes are preferred in modes with different-scale dynamics. Recommendations are formulated on the selection of the method depending on the class of the problem and the permissible error. Practical significance: the results of the work are applicable to the creation of flight simulation software and the selection of a computing core for a specific class of unmanned aerial vehicles.
unmanned aerial vehicle, mathematical modeling, flight dynamics, numerical methods, Runge — Kutta method, trajectory optimization, A* algorithm, particle swarm optimization, flight simulation
1. Lebedev A. A., Chernobrovkin L. S. Dinamika poleta bespilotnykh letatelnykh apparatov: uchebnoe posobie dlya vuzov [Flight Dynamics of Unmanned Aerial Vehicles: A Textbook for Universities]. Moscow, Mashinostroenie Publishing House, 1973, 616 p. (In Russian)
2. Krasilshchikov M. N., Sebryakov G. G. (eds). Upravlenie i navedenie bespilotnykh manevrennykh letatelnykh apparatov na osnove sovremennykh informatsionnykh tekhnologiy [Control and Guidance of Unmanned Maneuverable Aircraft Based on Modern Information Technologies]. Moscow, Fizmatlit Publishing House, 2003, 280 p. (In Russian)
3. Byushgens G. S., Studnev R. V. Aerodinamika samoleta. Dinamika prodolnogo i bokovogo dvizheniya [Aerodynamics of an Aircraft. Dynamics of Longitudinal and Lateral Motion]. Moscow, Mashinostroenie Publishing House, 1979, 352 p. (In Russian)
4. Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M. Chislennye metody: uchebnik [Numerical Methods: A Textbook]. Moscow, Laboratoriya Znaniy Publishing House, 2024, 639 p. (In Russian)
5. Stevens B. L., Lewis F. L., Johnson E. N. Aircraft Control and Simulation: Dynamics, Controls Design, and Autonomous Systems. Third Edition. Hoboken (NJ), Wiley-Blackwell, 2015, 768 p. DOI: https://doi.org/10.1002/9781119174882
6. Etkin B., Reid L. D. Dynamics of Flight: Stability and Control. Third Edition. Hoboken (NJ), Wiley, 1996, 400 p.
7. Mkhitaryan A. M. Aerodinamika: uchebnik dlya vuzov [Aerodynamics: A Textbook for Universities]. Moscow, KnoRus Publishing House, 2012, 448 p. (In Russian)
8. Kim D. P. Teoriya avtomaticheskogo upravleniya: uchebnik dlya vuzov. T. 1. Lineynye sistemy [Automatic Control Theory: A Textbook for Universities. Vol. 1. Linear Systems]. Moscow, Fizmatlit Publishing House, 2016, 312 p. (In Russian)
9. Hairer E., Nørsett S., Wanner G. Reshenie obyknovennykh differentsialnykh uravneniy. Nezhestkie zadachi [Solution of ordinary differential equations. Non-rigid problems]. Moscow, Mir Publishers, 1990, 512 p. (In Russian)
10. Bodner V. A. Sistemy upravleniya letatelnymi apparatami: uchebnik dlya vuzov [Aircraft Control Systems: A Textbook for Universities]. Moscow, Mashinostroenie Publishing House, 1973, 504 p. (In Russian)
11. Karpenko A. P. Sovremennye algoritmy poiskovoy optimizatsii. Algoritmy, vdokhnovlennye prirodoy: uchebnoe posobie [Modern Search Engine Optimization Algorithms. Nature-Inspired Algorithms: A Textbook]. Moscow, Bauman Moscow State Technical University Press, 2017, 446 p. (In Russian)
12. Cormen T. H., et al. Algoritmy: postroenie i analiz. Tretye izdanie [Introduction to algorithms. Third Edition]. Moscow, Williams Publishing House, 2013, 1328 p. (In Russian)
13. Karaman S., Frazzoli E. Sampling-Based Algorithms for Optimal Motion Planning, International Journal of Robotics Research, 2011, vol. 30, no. 7, pp. 846–894. DOI:https://doi.org/10.1177/0278364911406761
14. LaValle S. M. Planning Algorithms. Cambridge, Cambridge University Press, 2006, 844 p. DOI: https://doi.org/10.1017/CBO9780511546877
15. Gladkov L. A., Kureychik V. V., Kureychik V. M. Geneticheskie algoritmy: uchebnik [Genetic Algorithms: A Textbook]. Moscow, Fizmatlit Publishing House, 2010, 368 p. (In Russian)
16. Kennedy J., Eberhart R. Particle Swarm Optimization, Proceedings of ICNN ‘95 — International Conference on Neural Networks, Perth, Australia, November 27 – December 01, 1995, vol. 4. Institute of Electrical and Electronics Engineers, 1995, pp. 1942–1948. DOI:https://doi.org/10.1109/ICNN.1995.488968
17. Beard R. W., McLain T. W. Small Unmanned Aircraft: Theory and Practice. Second Edition. Princeton (NJ), Princeton University Press, 2012, 320 p. DOI: https://doi.org/10.1515/9781400840601



