004.021.8

unmanned aerial vehicle, mountainous terrain, algorithm, planning, flight, route.

The principles of planning of unmanned aerial vehicle movement in mountainous terrain are described in this paper. It is emphasized that the movement of the aerial vehicle takes place along the trajectory on a certain trajectory movement model, where unmanned aerial vehicle is represented as material point, the mass of which is concentrated in the center of mass. A discrete model in the linear state space that approximates the dynamics of an unmanned aerial vehicle is proposed. The general spatial movement of unmanned aerial vehicle is divided into longitudinal and lateral movement, and the longitudinal movement is considered independently of the lateral movement, taking into account the characteristics of the flight of unmanned aerial vehicle in mountainous terrain. The selection of the polygon from a certain set of irregularities in relation to the speed limit, acceleration limit and change in acceleration of unmanned aerial vehicle in the conditions of movement in mountainous terrain is graphically presented. It is emphasized that since the corresponding heights for any point on the curved surface of the relief are unknown, in order to obtain them, it is necessary to use the interpolation of the vertices of the corresponding triangle. It is noted that while choosing certain values of the coefficients, it is possible to describe the surface of the terrain using triangles, taking into account the combinations of coordinates of each known peak, and using the combinations of undefined coefficients as variable solutions, it is possible to describe the restrictions on the bending of the mountainous terrain. It is emphasized that during trajectory movement, the unmanned aerial vehicle is presented as material point, and in a real flight over mountainous terrain, its characteristic dimensions must be taken into account in order to avoid the obstacle successfully. It is proposed to increase the dimensions by a certain amount in each direction for effective obstacle avoidance of the unmanned aerial vehicle in mountainous terrain.

1. Mykyichuk M. M., Zihanshyn N. S. Analiz metodiv keruvannia bezpilotnymy litalnymy aparatam. Vymiriuvalna tekhnika ta metrolohiia. 2019. No. 4 (80). P. 37–41. [In Ukrainian].
2. Kulyk Ya. A., Knysh B. P., Baraban M. V. Modeliuvannia peremishchennia vantazhiv na osnovi murashynoho alhorytmu za dopomohoiu hrupy bezpilotnykh litalnykh aparativ. Visnyk Vinnytskoho politekhnichnoho instytutu. 2022. No. 5 (2). P. 73–79. [In Ukrainian].
3. Romaniuk L., Chykhira I. Aerodynamichna model hrupy bezpilotnykh litalnykh aparativ u prostori z pereshkodamy. Kompiuterno-intehrovani tekhnolohii: osvita, nauka, vyrobnytstvo. 2020. Vol. 38. P. 59–66. [In Ukrainian].
4. Romaniuk L., Chykhira I.  Avtomatyzovana systema upravlinnia povitrianym rukhom bezpilotnoho litalnoho aparatu. Vchena zapysky Tavriiskoho natsionalnoho universytetu imeni V. I. Vernadskoho. Seriia: Tekhnichni nauky. 2020. Т. 31. Vol. 70. P. 131–135. [In Ukrainian].
5. Romaniuk L., Chykhira I. Mekhanizm formuvannia bezpechnoho rukhu BPLA v umovakh radioatak. Komunalne hospodarstvo mist. 2020. T. 4. No. 157. Seriia: Tekhnichni nauky ta arkhitektura. P. 178–183. [In Ukrainian].
6. Berezhnyi A. O. Metody ta informatsiina tekhnolohia avtomatyzovanoho planuvannia marshrutiv polotiv bezpilotnykh litalnykh aparativ dlia pidvyshchennia efektyvnosti poshuku obiektiv. Kvalifikatsiina naukova pratsiia na pravakh rukopysu. Dysertatsiia na zdobuttia naukovoho stupenia kandydata tekhnichnykh nauk za spetsialnistiu 05.13.06 – Informatsiini tekhnolohii  universytet Povitrianykh Syl imeni Ivana Kozheduba, Kharkiv, 2020, Cherkaskyi derzhavnyi tekhnolohichnyi universytet, Cherkasy, 2020, 192 p. [In Ukrainian].
7. Molchanov K. D., Boiko D. I., Khatsko N. E. Razrabotka geometrycheskoho metoda postroenia marshruta BPLA dlia obkhoda prepiatstvi. XIII Mizhnarodna naukovo-praktychna konferentsia mahistrantiv ta aspirantiv: materialy konf., 19–22 lystopada 2019 r.; red. Ye. I. Sokol; Nats. tekh. un-t “Kharkiv. politekhn. in-t” [ta in.]. Kharkiv: NTU “KHPI”, 2019. P. 95–96. [In Russian].
8. Berezhnyi A. O. & Kalachova V. V. & Rozhkov M. I. (2019). Modeliuvannia rukhu dynamichnykh obiektiv v systemi pidtrymky pryiniattia rishen planuvannia marshrutiv bezpilotnykh litalnykh aparativ. Systemy obrobky informatsii. 4 (159). Р. 44–49. Doi: 10.30748/soi.2019.159.05. [In Ukrainian].
9. Husak O. M. “Informatiina tekhnolohiia rannoho vyiavlennia lisovykh pozhezh za dopomohoiu bezpilotnykh litalnykh aparativ” – kvalifikatsiina naukova pratsiia na pravakh rukopysu. Dysertatsiia na zdobuttia naukovoho stupenia kandydata tekhnichnykh nauk za spetsialnistiu 05.13.06 – “Informatsiini tekhnolohii” (126 – informatsiini systemy ta tekhnolohii) – Lvivskyi derzhavnyi universytet bezpeky zhyttiedialnosti Derzhavnoi sluzhby Ukrainy z nadzvychainykh sytuatsii, Lviv, 2019, 187 p. [In Ukrainian].
10. Beishenalieva Aliia, Yoo Sang-jo. Multi-Objective Three-Dimensional UAV Movement Planning in Wireless Sensor Networks Using Bio-inspired Swarm Intelligence. IEEE Internet of Things Journal. 2022. P. 1–1. Doi: http://doi.10.1109/JIOT.2022.3231302.
11. Airlangga Gregorius, Liu Alan. Online Path Planning Framework for UAV in Rural Areas. IEEE Access. 2022. No. 10. Р. 1–1. Doi: http://doi.10.1109/ACCESS.2022.3164505.
12. Kim M., Pevzner L., Temkin I. Development of automatic system for Unmanned Aerial Vehicle (UAV) motion control for mine conditions. Mining Science and Technology. 2021. No. 6. Р. 203–210. Doi: http:// doi.10.17073/2500-0632-2021-3-203-210.
13. Xing Peizhen, Zhang Hui, Ghoneim Mohamed, Shutaywi Meshal. UAV flight path design using multi-objective grasshopper with harmony search for cluster head selection in wireless sensor networks. Wireless Networks. 2022. No. 29. Р. 1–13. Doi: http://doi.10.1007/s11276-022-03160-0.
14. Wang Na, Dai Fei, Liu Fangxin, Zhang Guomin. Dynamic Obstacle Avoidance Planning Algorithm for UAV Based on Dubins Path: 18th International Conference, ICA3PP 2018, Guangzhou, China, November 15–17, 2018, Proceedings, Part II. Doi: http://doi.10.1007/978-3-030-05054-2_29.
15. Izhboldina Valeriia, Igor Lebedev. Group movement of UAVs in environment with dynamic obstacles: a survey. International Journal of Intelligent Unmanned Systems. ahead-of-print. 2022. Doi: http://doi.10. 1108/IJIUS-06-2021-0038.
16. Li Menglei, Chunhui Zhao, Hu Jinwen, Xu Zhao, Guo Chubing, Dou Zengfa. Efficient Path Planning for UAV Swarm Under Dense Obstacle Environment. 2022. Doi: http://doi.10.1007/978-981-16-9492-9_11.
17. Peng Yingsheng, Liu Yong, Dong Li, Zhang Han. Deep Reinforcement Learning Based Freshness-Aware Path Planning for UAV-Assisted Edge Computing Networks with Device Mobility. Remote Sensing. 2022. No. 14. Р. 4016. Doi: http://doi.10.3390/rs14164016.
18. Gao Yang, Li Yuankai, Guo Ziqi, Tan Xiaosu. Adaptive risk-free coordinated trajectory planning for UAV cluster in dynamic obstacle environment. Aerospace Systems. 2022. Doi: http://doi.5. 10.1007/s42401-022-00144-y.

1. Mykyichuk M. M., Zihanshyn N. S. Analiz metodiv keruvannia bezpilotnymy litalnymy aparatam. Vymiriuvalna tekhnika ta metrolohiia. 2019. No. 4 (80). P. 37–41. [In Ukrainian].
2. Kulyk Ya. A., Knysh B. P., Baraban M. V. Modeliuvannia peremishchennia vantazhiv na osnovi murashynoho alhorytmu za dopomohoiu hrupy bezpilotnykh litalnykh aparativ. Visnyk Vinnytskoho politekhnichnoho instytutu. 2022. No. 5 (2). P. 73–79. [In Ukrainian].
3. Romaniuk L., Chykhira I. Aerodynamichna model hrupy bezpilotnykh litalnykh aparativ u prostori z pereshkodamy. Kompiuterno-intehrovani tekhnolohii: osvita, nauka, vyrobnytstvo. 2020. Vol. 38. P. 59–66. [In Ukrainian].
4. Romaniuk L., Chykhira I.  Avtomatyzovana systema upravlinnia povitrianym rukhom bezpilotnoho litalnoho aparatu. Vchena zapysky Tavriiskoho natsionalnoho universytetu imeni V. I. Vernadskoho. Seriia: Tekhnichni nauky. 2020. Т. 31. Vol. 70. P. 131–135. [In Ukrainian].
5. Romaniuk L., Chykhira I. Mekhanizm formuvannia bezpechnoho rukhu BPLA v umovakh radioatak. Komunalne hospodarstvo mist. 2020. T. 4. No. 157. Seriia: Tekhnichni nauky ta arkhitektura. P. 178–183. [In Ukrainian].
6. Berezhnyi A. O. Metody ta informatsiina tekhnolohia avtomatyzovanoho planuvannia marshrutiv polotiv bezpilotnykh litalnykh aparativ dlia pidvyshchennia efektyvnosti poshuku obiektiv. Kvalifikatsiina naukova pratsiia na pravakh rukopysu. Dysertatsiia na zdobuttia naukovoho stupenia kandydata tekhnichnykh nauk za spetsialnistiu 05.13.06 – Informatsiini tekhnolohii  universytet Povitrianykh Syl imeni Ivana Kozheduba, Kharkiv, 2020, Cherkaskyi derzhavnyi tekhnolohichnyi universytet, Cherkasy, 2020, 192 p. [In Ukrainian].
7. Molchanov K. D., Boiko D. I., Khatsko N. E. Razrabotka geometrycheskoho metoda postroenia marshruta BPLA dlia obkhoda prepiatstvi. XIII Mizhnarodna naukovo-praktychna konferentsia mahistrantiv ta aspirantiv: materialy konf., 19–22 lystopada 2019 r.; red. Ye. I. Sokol; Nats. tekh. un-t “Kharkiv. politekhn. in-t” [ta in.]. Kharkiv: NTU “KHPI”, 2019. P. 95–96. [In Russian].
8. Berezhnyi A. O. & Kalachova V. V. & Rozhkov M. I. (2019). Modeliuvannia rukhu dynamichnykh obiektiv v systemi pidtrymky pryiniattia rishen planuvannia marshrutiv bezpilotnykh litalnykh aparativ. Systemy obrobky informatsii. 4 (159). Р. 44–49. Doi: 10.30748/soi.2019.159.05. [In Ukrainian].
9. Husak O. M. “Informatiina tekhnolohiia rannoho vyiavlennia lisovykh pozhezh za dopomohoiu bezpilotnykh litalnykh aparativ” – kvalifikatsiina naukova pratsiia na pravakh rukopysu. Dysertatsiia na zdobuttia naukovoho stupenia kandydata tekhnichnykh nauk za spetsialnistiu 05.13.06 – “Informatsiini tekhnolohii” (126 – informatsiini systemy ta tekhnolohii) – Lvivskyi derzhavnyi universytet bezpeky zhyttiedialnosti Derzhavnoi sluzhby Ukrainy z nadzvychainykh sytuatsii, Lviv, 2019, 187 p. [In Ukrainian].
10. Beishenalieva Aliia, Yoo Sang-jo. Multi-Objective Three-Dimensional UAV Movement Planning in Wireless Sensor Networks Using Bio-inspired Swarm Intelligence. IEEE Internet of Things Journal. 2022. P. 1–1. Doi: http://doi.10.1109/JIOT.2022.3231302.
11. Airlangga Gregorius, Liu Alan. Online Path Planning Framework for UAV in Rural Areas. IEEE Access. 2022. No. 10. Р. 1–1. Doi: http://doi.10.1109/ACCESS.2022.3164505.
12. Kim M., Pevzner L., Temkin I. Development of automatic system for Unmanned Aerial Vehicle (UAV) motion control for mine conditions. Mining Science and Technology. 2021. No. 6. Р. 203–210. Doi: http:// doi.10.17073/2500-0632-2021-3-203-210.
13. Xing Peizhen, Zhang Hui, Ghoneim Mohamed, Shutaywi Meshal. UAV flight path design using multi-objective grasshopper with harmony search for cluster head selection in wireless sensor networks. Wireless Networks. 2022. No. 29. Р. 1–13. Doi: http://doi.10.1007/s11276-022-03160-0.
14. Wang Na, Dai Fei, Liu Fangxin, Zhang Guomin. Dynamic Obstacle Avoidance Planning Algorithm for UAV Based on Dubins Path: 18th International Conference, ICA3PP 2018, Guangzhou, China, November 15–17, 2018, Proceedings, Part II. Doi: http://doi.10.1007/978-3-030-05054-2_29.
15. Izhboldina Valeriia, Igor Lebedev. Group movement of UAVs in environment with dynamic obstacles: a survey. International Journal of Intelligent Unmanned Systems. ahead-of-print. 2022. Doi: http://doi.10. 1108/IJIUS-06-2021-0038.
16. Li Menglei, Chunhui Zhao, Hu Jinwen, Xu Zhao, Guo Chubing, Dou Zengfa. Efficient Path Planning for UAV Swarm Under Dense Obstacle Environment. 2022. Doi: http://doi.10.1007/978-981-16-9492-9_11.
17. Peng Yingsheng, Liu Yong, Dong Li, Zhang Han. Deep Reinforcement Learning Based Freshness-Aware Path Planning for UAV-Assisted Edge Computing Networks with Device Mobility. Remote Sensing. 2022. No. 14. Р. 4016. Doi: http://doi.10.3390/rs14164016.
18. Gao Yang, Li Yuankai, Guo Ziqi, Tan Xiaosu. Adaptive risk-free coordinated trajectory planning for UAV cluster in dynamic obstacle environment. Aerospace Systems. 2022. Doi: http://doi.5. 10.1007/s42401-022-00144-y.