Routes optimization of continuous-discrete movement of controlled objects in the presence of obstacles


DOI: 10.34759/trd-2020-113-17

Аuthors

Bortakovsky A. S.*, Uryupin I. P.**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: asbortakov@mail.ru
**e-mail: uryupin93@yandex.ru

Abstract

The objective of the research consists in developing techniques for optimal routes forming of the aircraft flat motion in the presence of obstacles. The problems of aircraft control routes planning and optimizing are being studied currently with increasing intensity. The relevance of these studies is determined by the need for effective automated control of unmanned aerial vehicles (UAV) for various purposes.

The article regards the models of the flat motion of control objects along the specified map with obstacles with various quality functionals. The map represents a connected graph, which arcs correspond to the continuous movements of the object, its vertices correspond to the discrete changes of its state (switches), and the path connecting several vertices of the graph describes the continuous-discrete nature of the motion trajectory.

The first section considers the control object movement along the rectangular grid. The movement between two grid nodes is either uniform of uniformly accelerated. The movement direction changing in the grid nodes (turn) is considered to be switching. A number of the grid nodes is inadmissible for the movement due to the obstacles contained in them. The problem on minimizing the number of switches, response time or response time with account for the number of switches is being set.

The second section solves the problem on the flat movement optimization of the unmanned aerial vehicle (UAV). The Markov-Dubins model was selected as the model of motion. The feature of the response time problem consists in the presence of intermediate conditions, i.e. the points on the map, through which the UAV trajectory should pass. This problem is being reduced to solving an aggregate of Markov-Dubins problems with additional finite-dimensional minimization.

The third section combines the two problems discussed previously in the first two sections. The UAV rational trajectory is being formed in two stages. Initially, the optimal polyline, i.e. the trajectory of movement on the rectangular grid with obstacles, is being synthesized. Then, the optimal Markov-Dubins trajectory is being built «atop» this polyline, and the vertices of the polyline serve as intermediate points for the UAV trajectory.

The result of this work is algorithms, allowing build rational routes of the UAV’s flat movement with many obstacles, such as in the city. It is difficult to solve the optimal control problem under such phase restrictions. Thus, application of the proposed rational control patterns seems righteous.

Keywords:

continuous-discrete motion, switches minimizing, optimal control, response time

References

  1. Evdokimenkov V.N., Krasil'shchikov M.N., Orkin S.D. Upravlenie smeshannymi gruppami pilotiruemykh i bespilotnykh letatel'nykh apparatov v usloviyakh edinogo informatsionno-upravlyayushchego polya (Managing mixed groups of manned and unmanned aerial vehicles under the conditions of unified information-control field), Moscow, Izd-vo MAI, 2015, 272 p.

  2. Lebedev G.N., Rumakina A.V. Trudy MAI, 2015, no. 83. URL: http://trudymai.ru/eng/published.php?ID=61905

  3. Matyushin M.M., Lutsenko Yu.S., Gershman K.E. Trudy MAI, 2016, no. 89. URL: http://trudymai.ru/eng/published.php?ID=72869

  4. Richards A., How J.P. Aircraft trajectory planning with collision avoidance using mixed integer linear programming, Proceedings of the American Control Conference, ACC’ - 2002, 2002, vol. 3, IEEE Publ., pp. 1936 - 1941. DOI: 10.1109/ACC.2002.1023918

  5. Jia Zeng, Xiaoke Yang, Lingyu Yang, and Gongzhang Shen. Modeling for UAV resource scheduling under mission synchronization, Journal of Systems Engineering and Electronics, October 2010, vol. 21, no. 5, pp. 821 - 826. DOI: 10.3969/j.issn.1004-4132.2010.05.016

  6. Schouwenaars T., Valenti M., Feron E., How J. Linear Programming and Language Processing for Human/Unmanned-Aerial-Vehicle Team Missions, Journal of Guidance, Control, and Dynamics, March–April 2006, vol. 29, no. 2, pp. 303 - 313. DOI: 10.2514/1.13162

  7. Winstrand M. Mission Planning and Control of Multiple UAV's. Scientific Report № FOI-R-1382-SE Swedesh Defence Research Agency, 2004. p. 52.

  8. Rong Zhu, Dong Sun, Zhaoying Zhou. Cooperation Strategy of Unmanned Air Vehicles for Multitarget Interception, Journal Guidance, 2005, vol. 28, no. 5, pp.1068 - 1072. DOI: 10.2514/1.14412

  9. Kamal W.A. and Samar R. A Mission Planning Approach for UAV Applications, Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, Dec. 9-11, 2008, pp. 3101 - 3106. DOI: 10.1109/CDC.2008.4739187

  10. Schumacher C.J. and Kumar R. Adaptive sontrol of UAVs in slose-coupled formation flight, Proceedings of the American Control Conference, 2000, vol. 2, pp. 849 – 853.

  11. Dušan M. Stipanovic, Gökhan Inalhan, Rodney Teo, Claire J. Tomlin. Decentralized overlapping control of a formation of unmanned aerial vehicles, Automatica, 2004, vol. 40, no. 8, pp. 1285 - 1296.

  12. Jongki Moon. Mission-Based Guidance System Design for Autonomous UAVs. A Thesis Presented to The Academic Faculty, Georgia Institute of Technology, December 2009, 145 p.

  13. Ha J., Sattigeri R. Vision-based obstacle avoidance based on monocular slam and image segmentation for UAVs, Infotech@Aerospace, 2012, pp. 1 - 9.

  14. Tewari A. Optimal nonlinear spacecraft attitude control throung Hamilton – Jacobi formulation, Journal Astronautical Science, 2002, vol. 50, pp. 99 - 112.

  15. Bellman R. Dynamic Programming, Princeton: Princeton University Press, 1957, 365 p.

  16. Diveev A.I., Konyrbaev N.B. Trudy MAI, 2017, no. 96. URL: http://trudymai.ru/eng/published.php?ID=85774

  17. Bortakovskii A.S., Shchelchkov K.A. Trudy MAI, 2018, no. 99. URL: http://trudymai.ru/eng/published.php?ID=91644

  18. Bortakovskii A.S., Uryupin I.V. Izvestiya RAN. Teoriya i sistemy upravleniya, 2019, no. 4, pp. 29 - 46.

  19. Markov A.A. Soobshcheniya Khar'kovskogo matematicheskogo obshchestva, 1889, o. 5,6, pp. 250 – 276. URL: http://sector3.imm.uran.ru/stat_oth/markov1889/markov_1889.pdf

  20. Dubins L.E. On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents, American Journal Mathematics, 1957, vol. 79, no. 3, pp. 497 – 516. URL: http://dx.doi.org/10.2307/2372560

  21. Tsourdos A., White B., Shanmugavel M. Cooperative Path Planning of Unmanned Aerial Vehicles, New York, Wiley&Sons, 2011, 190 p.

  22. Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mishchenko E.F. Matematicheskaya teoriya optimal'nykh protsessov (Mathematical theory of optimal processes), Moscow, Fizmatgiz, 1961, 392 p.

  23. Agrachev A.A., Sachkov Yu.L. Geometricheskaya teoriya upravleniya (Geometric control theory), Moscow, Fizmatlit, 2005, 392 p.

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