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https://er.chdtu.edu.ua/handle/ChSTU/8354| Title: | Дослідження пристрою маршрутизації польоту безпілотних літальних апаратів |
| Authors: | Гальченко, Володимир Якович Бедь, Едуард Дмитрович |
| Keywords: | легкий безпілотний літальний апарат;автоматична маршрутизація;передпольотне планування;оптимізація траєкторії польоту;вітрове навантаження;програмно-алгоритмічне забезпечення |
| Issue Date: | 15-Dec-2025 |
| Abstract: | У роботі розробляється методика оптимального передпольотного планування маршруту для легкого безпілотного літального апарата з урахуванням тактико-технічних обмежень носія та впливу вітрового навантаження. The work develops a method for optimal pre-flight route planning for a light unmanned aerial vehicle, taking into account the vehicle’s tactical and technical limitations as well as the influence of wind load. |
| URI: | https://er.chdtu.edu.ua/handle/ChSTU/8354 |
| Appears in Collections: | 174 Автоматизація, комп'ютерно-інтегровані технології та робототехніка (Робототехнічні системи та автоматизація) |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| Диплом-магистр_Бедь Е.pdf Restricted Access | КРМ Бедь Е. | 11.39 MB | Adobe PDF | View/Open Request a copy |
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1 1-9-7-5-6-3-10-1 1729
2 1-9-8-7-6-3-10-1 1735
3 1-2-9-7-6-3-10-1 1785
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1 1-41-23-25-24-36-5-30-15-19-39-34-46-22-40-27-49-33-2- 10212
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2 1-4-9-13-50-7-44-16-3-12-31-47-17-37-48-10-28-45-18-42- 10265
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41-14-1
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1-10-11-22-9-18-4- 23-15-29-8-27-25-12-3-26-19-24-14-5-17-21-
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1-10-11-22-9-18-4-23-15-29-8-27-25-12-3-26- 26 5928,4
1
19-24-14-5-17-21-20-16-13-30
1-10-11-22-9-18-23-15-29-8-28-7-6-27-25-12- 28 5833,7
2
3-26-19-24-14-5-17-21-20-16-13-30
1-10-4-18-22-9-15-29-8-28-7-6-27-25-12-3-26- 27 5866,3
3
19-24-14-5-17-21-20-16-13-30
1-10-11-22-9-18-23-15-29-8-28-7-6-27-25-12- 28 5838,0
4
3-26-19-24-14-5-17-20-21-16-13-30
1-10-11-18-22-9-23-15-29-8-28-7-6-27-25-12- 28 5815,7
5
3-26-19-24-14-5-17-21-20-16-13-30
1-10-4-18-22-9-15-29-8-28-7-6-27-25-12-3-26- 27 5870,6
6
19-24-14-5-17-20-21-16-13-30
1-10-11-18-22-9-23-15-29-8-28-7-6-27-25-12- 28 5820,0
7
3-26-19-24-14-5-17-20-21-16-13-30
1-10-11-18-4-23-9-15-29-8-28-7-27-25-12-3- 27 5926,5
8
26-19-24-14-5-17-21-20-16-13-30
1-10-11-18-23-15-29-8-28-7-6-27-25-12-3-26- 28 5927,6
9
9-22-14-5-24-19-17-21-20-16-13-30
1-10-11-18-22-9-23-15-29-8-28-7-6-27-25-12- 28 5926,4
10
3-26-24-14-5-19-17-20-21-16-13-30
1-10-11-22-9-18-23-15-29-8-28-6-7-27-25-12- 28 5927,3
11
3-26-19-24-14-5-17-21-20-16-13-30
77
3.6
1-10-11-18-22-9-23-15-29-8-28-7-6-27-25-12- 28 5922,1
12
3-26-24-14-5-19-17-21-20-16-13-30
1-10-4-18-9-22-14-5-24-19-26-3-15-29-8-28-7- 27 5928,1
13
6-27-25-12-20-17-21-16-13-30
1-10-11-18-23-9-22-26-3-15-29-8-28-7-6-27- 28 5924,0
14
25-12-19-24-14-5-17-21-20-16-13-30
1-10-4-18-22-9-26-3-15-29-8-28-7-6-27-25-12- 27 5910,3
15
19-24-14-5-17-21-20-16-13-30
1-10-11-18-22-9-23-15-29-8-28-6-7-27-25-12- 28 5909,3
16
3-26-19-24-14-5-17-21-20-16-13-30
1-10-11-18-23-9-22-26-3-15-29-8-28-7-6-27- 28 5928,3
17
25-12-19-24-14-5-17-20-21-16-13-30
1-10-11-18-23-9-22-14-5-24-19-26-3-15-29-8- 28 5917,2
18
28-7-6-27-25-12-20-17-21-16-13-30
1-10-11-18-22-9-23-15-29-8-28-6-7-27-25-12- 28 5913,6
19
3-26-19-24-14-5-17-20-21-16-13-30
1-10-4-18-22-9-26-3-15-29-8-28-7-6-27-25-12- 27 5914,7
20
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1. Anderson J. D. Fundamentals of Aerodynamics / J. D. Anderson. – 5th ed. –
New York : McGraw-Hill Education, 2011. – 1116 p.
2. Applegate D. L. The Traveling Salesman Problem: A Computational Study / D.
L. Applegate, R. E. Bixby, V. Chvátal, W. J. Cook. – Princeton : Princeton University
Press, 2006. – 593 p.
3. Austin R. Unmanned Aircraft Systems: UAVS Design, Development and
Deployment / R. Austin. – Chichester : John Wiley & Sons, 2010. – 590 p.
4. Beard R. W. Small Unmanned Aircraft: Theory and Practice / R. W. Beard, T.
W. McLain. – Princeton : Princeton University Press, 2012. – 317 p.
5. Bekhti M. Path Planning of Unmanned Aerial Vehicles With Terrestrial Wireless
Network Tracking / M. Bekhti, M. Abdennebi, N. Achir, K. Boussetta // Wireless Days
(WD). – 2016. – P. 1–3.
6. Bortoff S. A. Path planning for UAVs / S. A. Bortoff // Proceedings of the 2000
American Control Conference. – 2000. – Vol. 1. – P. 364–368.
7. Boyd S. Convex Optimization / S. Boyd, L. Vandenberghe. – Cambridge :
Cambridge University Press, 2004. – 716 p.
8. Ceccarelli N. Micro UAV Path Planning for Reconnaissance in Wind / N.
Ceccarelli, J. J. Enright, E. Frazzoli, S. J. Rasmussen, C. J. Schumacher // Proceedings of
the 2007 American Control Conference. – 2007. – P. 5310–5315.
9. Clothier R. A. Airworthiness certification framework for unmanned aircraft
systems / R. A. Clothier, B. P. Williams, N. L. Fulton // Handbook of Unmanned Aerial
Vehicles / ed. by K. P. Valavanis, G. J. Vachtsevanos. – Dordrecht : Springer, 2015. – P.
2969–2992.
10. Colomina I. Unmanned aerial systems for photogrammetry and remote sensing:
A review / I. Colomina, P. Molina // ISPRS Journal of Photogrammetry and Remote
Sensing. – 2014. – Vol. 92. – P. 79–97.
101
11. Dalamagkidis K. Handbook of Unmanned Aerial Vehicles: Applications in
Civilian and Commercial Domains / K. Dalamagkidis (Ed.). – Dordrecht : Springer, 2019.
– 2134 p.
12. Deb K. Multi-Objective Optimization using Evolutionary Algorithms / K. Deb.
– Chichester : John Wiley & Sons, 2001. – 518 p.
13. Durbana H. Employing Multiple Unmanned Aerial Vehicles for Co-Operative
Path Planning / H. Durbana, H. Jamal, S. A. Khan // International Journal of Advanced
Robotic Systems. – 2013. – Vol. 10. – Article 235.
14. Eiben A. E. Introduction to Evolutionary Computing / A. E. Eiben, J. E. Smith.
– 2nd ed. – Berlin : Springer, 2015. – 287 p.
15. Elston J. Overview of small fixed-wing unmanned aircraft for meteorological
measurement / J. Elston, B. Argrow, M. Stachura, D. Weibel, D. Lawrence, D. Pope //
Journal of Atmospheric and Oceanic Technology. – 2015. – Vol. 32, No. 1. – P. 97–115.
16. Ellsaesser H. W. Wind variability as a function of time / H. W. Ellsaesser //
Monthly Weather Review. – 1969. – Vol. 97. – P. 424–428.
17. European Union Aviation Safety Agency (EASA). Introduction of a Regulatory
Framework for the Operation of Unmanned Aircraft Systems. – Cologne : EASA, 2020.
– 45 p.
18. Federal Aviation Administration (FAA). Unmanned Aircraft Systems
[ ]. – : https://www.faa.gov/uas/. – .
19. Finn R. L. Unmanned aircraft systems: Surveillance, ethics and privacy in civil
applications / R. L. Finn, D. Wright // Computer Law & Security Review. – 2012. – Vol.
28, No. 2. – P. 184–194.
20. Garey M. R. Computers and Intractability: A Guide to the Theory of NP-
Completeness / M. R. Garey, D. S. Johnson. – San Francisco : W. H. Freeman, 1979. –
338 p.
21. Gettinger D. Drone Proliferation: Policy Challenges and Opportunities / D.
Gettinger, A. H. Michel. – Annandale-on-Hudson : Center for the Study of the Drone at
Bard College, 2020. – 67 p.
102
22. Goerzen C. A survey of motion planning algorithms from the perspective of
autonomous UAV guidance / C. Goerzen, Z. Kong, B. Mettler // Journal of Intelligent
and Robotic Systems. – 2010. – Vol. 57, No. 1-4. – P. 65–100.
23. Goldberg D. E. Genetic Algorithms in Search, Optimization and Machine
Learning / D. E. Goldberg. – Boston : Addison-Wesley Professional, 1989. – 412 p.
24. Gutin G. The Traveling Salesman Problem and Its Variations / G. Gutin, A. P.
Punnen (Eds.). – Boston : Springer, 2007. – 830 p.
25. Holland J. H. Adaptation in Natural and Artificial Systems / J. H. Holland. –
Cambridge : MIT Press, 1992. – 211 p.
26. Holton J. R. An Introduction to Dynamic Meteorology / J. R. Holton, G. J.
Hakim. – 5th ed. – Cambridge : Academic Press, 2012. – 552 p.
27. International Civil Aviation Organization (ICAO). Manual on Remotely
Piloted Aircraft Systems (RPAS). Doc 10019. – Montreal : ICAO, 2015. – 119 p.
28. Koh L. P. Dawn of drone ecology: low-cost autonomous aerial vehicles for
conservation / L. P. Koh, S. A. Wich // Tropical Conservation Science. – 2012. – Vol. 5,
No. 2. – P. 121–132.
29. Lawler E. L. Combinatorial Optimization: Networks and Matroids / E. L.
Lawler. – New York : Dover Publications, 2001. – 374 p.
30. Luke S. Essentials of Metaheuristics / S. Luke. – 2nd ed. – Morrisville : Lulu,
2013. – 235 p.
31. Manyika J. Disruptive technologies: Advances that will transform life,
business, and the global economy / J. Manyika, M. Chui, J. Bughin, R. Dobbs, P. Bisson,
A. Marrs // McKinsey Global Institute. – 2013. – 176 p.
32. Mason S. J. Multi-Objective UAV Mission Planning Using Evolutionary
Computation / S. J. Mason, R. R. Hill, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler
(eds.) // Proceedings of the 2008 Winter Simulation Conference. – 2008. – P. 1268–1279.
33. Matese A. Intercomparison of UAV, aircraft and satellite remote sensing
platforms for precision viticulture / A. Matese, P. Toscano, S. F. Di Gennaro, L. Genesio,
F. P. Vaccari, J. Primicerio, B. Gioli // Remote Sensing. – 2015. – Vol. 7, No. 3. – P.
2971–2990.
103
34. MathWorks. MATLAB Global Optimization Toolbox User's Guide
[ ]. – 2023. – :
https://www.mathworks.com/help/gads/. – .
35. MathWorks. MATLAB Optimization Toolbox User's Guide [
]. – 2023. – : https://www.mathworks.com/help/optim/. –
.
36. McCormick B. W. Aerodynamics, Aeronautics, and Flight Mechanics / B. W.
McCormick. – 2nd ed. – New York : John Wiley & Sons, 1995. – 586 p.
37. McGee T. G. Optimal path planning in a constant wind with a bounded turning
rate / T. G. McGee, S. Spry, J. K. Hedrick // Proceedings of the 2005 American Control
Conference. – 2005. – P. 1317–1322.
38. McGee T. G. Path Planning and Control for Multiple Point Surveillance by an
Unmanned Aircraft in Wind / T. G. McGee, J. K. Hedrick // Proceedings of the 2006
American Control Conference. – 2006. – P. 4261–4266.
39. Mersheeva V. Multi-UAV Monitoring with Priorities and Limited Energy
Resources / V. Mersheeva, G. Friedrich // Proceedings of the Twenty-Fifth International
Conference on Automated Planning and Scheduling. – 2015. – P. 347–355.
40. Miettinen K. Nonlinear Multiobjective Optimization / K. Miettinen. – Boston :
Springer, 1999. – 298 p.
41. Michalewicz Z. How to Solve It: Modern Heuristics / Z. Michalewicz, D. B.
Fogel. – 2nd ed. – Berlin : Springer, 2004. – 554 p.
42. Mitchell M. An Introduction to Genetic Algorithms / M. Mitchell. – Cambridge
: MIT Press, 1998. – 158 p.
43. Nemhauser G. L. Integer and Combinatorial Optimization / G. L. Nemhauser,
L. A. Wolsey. – New York : Wiley-Interscience, 1999. – 784 p.
44. Nex F. UAV for 3D mapping applications: a review / F. Nex, F. Remondino //
Applied Geomatics. – 2014. – Vol. 6, No. 1. – P. 1–15.
45. Nonami K. Autonomous Flying Robots: Unmanned Aerial Vehicles and Micro
Aerial Vehicles / K. Nonami, F. Kendoul, S. Suzuki, W. Wang, D. Nakazawa. – Tokyo :
Springer, 2010. – 329 p.
104
46. Pajares G. Overview and current status of remote sensing applications based on
unmanned aerial vehicles (UAVs) / G. Pajares // Photogrammetric Engineering & Remote
Sensing. – 2015. – Vol. 81, No. 4. – P. 281–330.
47. Papadimitriou C. H. Combinatorial Optimization: Algorithms and Complexity
/ C. H. Papadimitriou, K. Steiglitz. – New York : Dover Publications, 1998. – 528 p.
48. Python Software Foundation. SciPy Reference Guide: Optimization and Root
Finding [ ]. – 2023. – :
https://docs.scipy.org/doc/scipy/reference/optimize.html. – .
49. Roberge V. Comparison of parallel genetic algorithm and particle swarm
optimization for real-time UAV path planning / V. Roberge, M. Tarbouchi, G. Labonté //
IEEE Transactions on Industrial Informatics. – 2013. – Vol. 9, No. 1. – P. 132–141.
50. Shahbazi M. Recent applications of unmanned aerial imagery in natural
resource management / M. Shahbazi, J. Theau, P. Menard // GIScience & Remote
Sensing. – 2014. – Vol. 51, No. 4. – P. 339–365.
51. Shima T. UAV Cooperative Decision and Control: Challenges and Practical
Approaches / T. Shima, S. Rasmussen (Eds.). – Philadelphia : SIAM, 2009. – 237 p.
52. Singer P. W. Wired for War: The Robotics Revolution and Conflict in the 21st
Century / P. W. Singer. – New York : Penguin Books, 2009. – 512 p.
53. Sonmezocak E. Optimum Route Planning and Scheduling for Unmanned Aerial
Vehicles / E. Sonmezocak, S. Kurt. – Monterey : Naval Postgraduate School, 2016. – 89
p.
54. Stull R. B. An Introduction to Boundary Layer Meteorology / R. B. Stull. –
Dordrecht : Springer, 2012. – 670 p.
55. Talbi E. G. Metaheuristics: From Design to Implementation / E. G. Talbi. –
Hoboken : John Wiley & Sons, 2009. – 618 p.
56. Techy L. Minimum-time path planning for unmanned aerial vehicles in steady
uniform winds / L. Techy, C. A. Woolsey // Journal of Guidance, Control, and Dynamics.
– 2009. – Vol. 32, No. 6. – P. 1736–1746.
105
57. The MATLAB Team. MATLAB Documentation: Linear Programming
[ ]. – 2022. – :
https://www.mathworks.com/help/optim/linear-programming.html. – .
58. UVS International. Unmanned Vehicle Systems International [
]. – 2023. – : https://www.uvs-international.org/. –
.
59. Valavanis K. P. Handbook of Unmanned Aerial Vehicles / K. P. Valavanis, G.
J. Vachtsevanos (Eds.). – Dordrecht : Springer, 2015. – 3022 p.
60. Van Rossum G. Python 3 Reference Manual / G. Van Rossum, F. L. Drake. –
Scotts Valley : CreateSpace, 2009. – 142 p.
61. Vanderbei R. J. Linear Programming: Foundations and Extensions / R. J.
Vanderbei. – 4th ed. – New York : Springer, 2014. – 414 p.
62. Watts A. C. Unmanned aircraft systems in environmental monitoring / A. C.
Watts, V. G. Ambrosia, E. A. Hinkley // Geography Compass. – 2012. – Vol. 6, No. 1. –
P. 1–14.
63. Watts A. C. Unmanned aircraft systems in remote sensing and scientific
research: Classification and considerations of use / A. C. Watts, V. G. Ambrosia, E. A.
Hinkley // Remote Sensing. – 2012. – Vol. 4, No. 6. – P. 1671–1692.
64. Williams H. P. Model Building in Mathematical Programming / H. P. Williams.
– 5th ed. – Chichester : John Wiley & Sons, 2013. – 432 p.
65. Wolsey L. A. Integer Programming / L. A. Wolsey. – New York : John Wiley
& Sons, 1998. – 276 p.
66. Yang Q. Optimal UAV path planning: Sensing data acquisition over IoT sensor
networks using multi-objective bio-inspired algorithms / Q. Yang, S. J. Yoo // IEEE
Access. – 2018. – Vol. 6. – P. 13671–13684.
67. Zhang C. The application of small unmanned aerial systems for precision
agriculture: a review / C. Zhang, J. M. Kovacs // Precision Agriculture. – 2012. – Vol. 13,
No. 6. – P. 693–712.
106
68. Zhen Z. Cooperative search-attack mission planning for multi-UAV based on
intelligent self-organized algorithm / Z. Zhen, D. Xing, C. Gao // Aerospace Science and
Technology. – 2017. – Vol. 72. – P. 182–195.
69. . .
/ . . , . . // ,
’ . – 2020. – 4(60). – . 112–118.
70. . . /
. . , . . . – : " ", 2009. – 245 .
71. . - [
]. – : https://avia.gov.ua/. – .
72. .
. – : , 2023. – 56 .
73. . . : / . .
, . . . – : , 2018. – 324 .
74. .
. – : , 2022. – 48 .
75. . . / . . , . .
. – : , 2016. – 288 .
76. . . / . . . – :
, 2004. – 312 .
77. European Union Aviation Safety Agency (EASA). Unmanned Aircraft Systems
[ ]. – 2023. – :
https://www.easa.europa.eu/en/domains/civil-drones. – .