A group time-optimal tasks of aerial vehicles

System analysis, control and data processing


Аuthors

Bortakovsky A. S.1*, Shchelchkov K. A.2**

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Udmurt State University, UdSU, Universitetskaya str., Izhevsk, 426034, Russia

*e-mail: asbortakov@mail.ru
**e-mail: incognitobox@mail.ru

Abstract

The goal of the study consists in developing methods for forming the time optimal control laws for groups of objects. The problems of group performance find practical application in the field of controlling the groups of manned and unmanned aerial vehicles. There are also applications in biology and robotics. In the theory of optimal control such problems are new and insufficiently explored. The article considers four group performance problems. They are the task of simultaneous achieving one goal by a group of objects, the task of managing a group with its leader selection, the task of achieving several goals with a single or multiple sequential separation of active control objects from the carrier. The solution of these rather simple academic tasks allows developing and testing methods for optimal position control synthesis, which can be implemented in complex applied problems.

Optimal positional control developing is based on the method of dynamic programming, consisting in finding the price function (the Hamilton-Jacobi-Bellman function). In the problems under consideration, the centralized management of a group is based on the optimal decentralized positional control of individual mobile objects. The price function is formed from auxiliary functions, i.e. partial price functions for individual objects of the group.

The result of this work is the solution of the assigned group time-optimal problems, as well as the methods of constructing the price function and optimal positional control. The developed methods can be employed in the aerospace field while planning the aircraft groups’ application.

For theoretical studies in the field of optimal control of the groups of mobile objects, the solved problems can be employed as testing ones. The developed methods of the price function constructing can be employed for solving other more complex problems. Given that even in academic examples the solution is being found numerically, the application of the proposed methods of synthesis indissolubly related to the development of the appropriate approximate algorithms, as well as programs for the numerical implementation of these algorithms.

Keywords:

optimal control, time-optimal problem, centralized group management, decentralized group management

References

  1. Evdokimenkov V.N., Krasilshchikov M.N., Orkin S.D. Upravlenie smeshannymi gruppami pilotiruemykh i bespilotnykh letatelnykh apparatov v usloviyakh edinogo informacionno-upravlyayushchego polya (Managing mixed groups of manned and unmanned aerial vehicles in conditions of unified information and control field), Moscow, MAI, 2015, 272 p.

  2. 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.

  3. 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.

  4. 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.

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

  6. 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.

  7. 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.

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

  9. Dušan M. Stipanovic, Gökhan Inalhan, Rodney Teo, Claire J. Tomlin. Decentralized overlapping control of a formation of unmanned aerial vehicles, Automatica, 2004, vol. 40, pp. 1285 – 1296.

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

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

  12. Petrov N.N., Shchelchkov K.A. On the interrelationship of two problems on evasion with many evaders, Journal of Applied Mathematics and Mechanics, 2016, vol. 80, no. 4, pp. 333 – 338.

  13. Petrov N.N., Shchelchkov K.A. On the Interrelation of Two Linear NonStationary Problems with Multiple Evaders, International Game Theory Review, 2015, vol. 17, no. 4, pp. 1550013-9 – 1550013-11.

  14. Ermin Wei, Eric W. Justh and P.S. Krishnaprasad. Pursuit and an evolutionary game, Proceedings of the Royal Society, 2009, vol. 465, pp. 1539 – 1559.

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

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

  17. Bellman R. Dinamicheskoe programmirovanie (Dynamic Programming), Princeton, Moscow, IL, 1960, 400 p.

  18. Bortakovskii A.S. Optimal and Suboptimal Control over Bunches of Trajectories of Automaton-Type Deterministic Systems, Journal of Computer and Systems Sciences International, 2016, vol. 55, no. 1, pp. 1 – 20.

  19. Bortakovskii A.S. Sufficient Optimality Conditions for Controlling Switched Systems, Journal of Computer and Systems Sciences International, 2017, vol. 56, no. 4, pp. 636 – 651.

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


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