№1, 2024
DETERMINATION OF THE OPTIMAL TRAJECTORY OF THE MOVEMENT OF AIRCRAFT IN AREAS WITH COMPLEX TERRAIN UNDER THE CONTROL OF THE ENEMY
One of the main issues in the controlling of aircraft in difficult terrain during wartime is to ensure normal movement, but also to fulfill the requirements of evading enemy control. This paper proposes an improved ant swarm algorithm that makes it possible to pre-determine and optimize the trajectory of aircraft in such areas. When applying this method, a special parameter is included in the probability of choosing a movement trajectory – the height of the terrain above sea level, so that each ant does not enter territory controlled by the enemy. Using a 2D-H digital elevation map, the rectangular area under study is divided into 90 m × 90 m squares. To take into account the variability of the terrain, the heuristic function of the ant swarm algorithm takes into account the parameters of distance, height and smooth surface. Additionally, to reduce the number of iterations and computations, the ants are divided in half by number and released from the start and end points simultaneously. As a result, it allows you to choose the shortest and minimum trajectory among various calculated trajectories. To verify the effectiveness of the proposed scheme, a number of computational experiments were conducted. Experimental results on various simulated and real terrain maps show that this algorithm can be used to select an initial reference trajectory in difficult terrain (pp.26-36).
Keywords: Flight trajectory, Complex terrain, Digital terrain map, Evading enemy control, Ant swarm algorithm, Determining the optimal trajectory, Distance parameter, Height parameter, Smooth surface parameter
References
- Agayev, N. B., Orudzhov, G. G., & Kalbiyev, N. N. (2023). Planirovaniye optimal'noy obespechivayushchey trayektorii poleta samoleta s ispol'zovaniyem karty mestnosti. //Mekhatronika, avtomatizatsiya, upravleniye, 24(9), 496-502.
https://doi.org/10.17587/mau.24.496-502 (in Russian) - Aghazada, S. & Ciylan, B. (2018). Determining the Optimal Route of Drones in Restricted Areas. Materials İnternational Scientific Conference for the Information Systems and Technologies Achievements and Perspectives (pp. 258-260). (in Azerbaijani)
- Aghazada, S. & Ciylan, B. (2019). Engel Olarak Belirlenen Araziler Olduğunda İnsansız Hava Araçlarının Karınca Kolonisi Algoritması ile Optimal Rotanın Bulunması. İCEST’19 I Uluslararası Bilimsel-Uygulamalı Konferansı (pp. 220-225). (in Turkish)
- Arantes, J. D., Arantes, M. D., Toledo, C. F., Júnior, O. T., & Williams, B. C. (2017). Heuristic and genetic algorithm approaches for UAV path planning under critical situation. International Journal on Artificial Intelligence Tools, 26, 1–30.
https://doi.org/10.1142/S0218213017600089 - Bakdi, A., Hentout, A., Boutami, H., Maoudj, A., Hachour, O., & Bouzouia, B. (2017). Optimal path planning and execution for mobile robots using genetic algorithm and adaptive fuzzy-logic control. Robotics and Autonomous Systems, 89, 95-109.
https://doi.org/10.1016/j.robot.2016.12.008 - Carloni, R., Lippiello, V., D'auria, M., Fumagalli, M., Mersha, A. Y., Stramigioli, S., & Siciliano, B. (2013). Robot vision: Obstacle-avoidance techniques for unmanned aerial vehicles. IEEE Robotics & Automation Magazine, 20(4), 22-31.
https://doi.org/10.1109/MRA.2013.2283632 - Cetin, O. & Yilmaz, G. (2014). Sigmoid limiting functions and potential field based autonomous air refueling path planning for UAVs. Journal of Intelligent & Robotic Systems, 73, 797–810.
https://doi.org/10.1007/s10846-013-9902-y - Cheng, C. T., Fallahi, K., Leung, H., & Tse, C. K. (2010). An AUVs path planner using genetic algorithms with a deterministic crossover operator. 2010 IEEE International Conference on Robotics and Automation, Anchorage, USA, May 2010 (pp. 2995-3000).
https://doi.org/10.1109/ROBOT.2010.5509335 - Dai, X., Long, S., Zhang, Z., & Gong, D. (2019). Mobile Robot Path Planning Based on Ant Colony Algorithm With A* Heuristic Method. Frontiers in Neurorobotics, 13, 444376. https://doi.org/10.3389/fnbot.2019.00015
- Das, P., Behera, H., & Panigrahi, B. (2016). A hybridization of an improved particle swarm optimization and gravitational search algorithm for multi-robot path planning. Swarm and Evolutionary Computation, 28, 14-28.
https://doi.org/10.1016/j.swevo.2015.10.011 - Deepak, B. B. V. L., Parhi, D. R., & Kundu, S. (2012). Innate immune based path planner of an autonomous mobile robot. Procedia Engineering, 38, 2663-2671.
https://doi.org/10.1016/j.proeng.2012.06.313 - Dorigo, M. & Gambardella, L.M. (1997). Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 1(1), 53-66.
https://doi.org/10.1109/4235.585892 - Dorigo, M. (1992). Optimization, Learning and Natural Algorithms, PhD thesis, Politecnico di Milano, Italie.
- Earl, M. G. & D’Andrea, R. (2005). Iterative MILP methods for vehicle-control problems. IEEE Transactions on Robotics, 21(6), 1158-1167. https://doi.org/10.1109/TRO.2005.853499
- Fahmi, H., Zarlis, M. Nababan, E., & Sihombing, P. (2019). Ant Colony Optimization (ACO) algorithm for determining the nearest route search in distribution of light food production. 4th International Conference on Computing and Applied Informatics 2019 (ICCAI 2019), Medan, Indonesia, November 2019 (pp. 1-7).
- https://doi.org/10.1088/1742-6596/1566/1/012045
- He, W. & Zhang, S. (2017c). Control design for nonlinear flexible wings of a robotic aircraft. IEEE Transactions on Control Systems Technology, 25(1), 351–357. https://doi.org/10.1109/TCST.2016.2536708
- He, W., Chen, Y., & Yin, Z. (2016). Adaptive neural network control of an uncertain robot with full-state constraints. EEE Transactions on Cybernetics, 46(3), 620–629. https://doi.org/10.1109/TCYB.2015.2411285
- He, W., Dong, Y., & Sun, C. (2016a). Adaptive neural impedance control of a robotic manipulator with input saturation. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 46(3), 334–344. https://doi.org/10.1109/TSMC.2015.2429555
- He, W., Yan, Z., Sun, C., & Chen, Y. (2017a). Adaptive neural network control of a flapping wing micro aerial vehicle with disturbance observer. IEEE Transactions on Cybernetics, 47(10), 3452–3465.
https://doi.org/10.1109/TCYB.2017.2720801 - He, W., Yin, Z., & Sun, C. (2017b). Adaptive neural network control of a marine vessel with constraints using the asymmetric barrier lyapunov function. IEEE Transactions on Cybernetics, 47, 1641–1651.
https://doi.org/10.1109/TCYB.2016.2554621 - Jiang, K., & Li, C. G. (2014). Path Planning Based on Fuzzy Logic Algorithm for Robots in Hierarchical Control. Applied Mechanics and Materials, 644–650, 701–704.
https://doi.org/10.4028/www.scientific.net/amm.644-650.701 - Jovanovic, R., Tuba, M., & Voß, S. (2016). An ant colony optimization algorithm for partitioning graphs with supply and demand. Applied Soft Computing, 41, 317-330.
https://doi.org/10.1016/j.asoc.2016.01.013 - Kochegurova, Ye. A., Martynov, YU. A., Martynova, YU. A., & Tsapko, S. G. (2014). Algoritm murav'inykh koloniy dlya zadachi proyektirovaniya ratsional'nykh marshrutnykh setey gorodskogo passazhirskogo transporta. Vestnik SibGUTI, 3, 89–100. (in Russian)
- Kureychik, V. M. & Kazharov, A. A. (2008). O nekotorykh modifikatsiyakh murav'inogo algoritma. Izvestiya YUFU. Tekhnicheskiye nauki, 4(81), 7–12. (in Russian)
- Kureychik, V. M. & Kazharov, A. A. (2010). Murav'inyye algoritmy resheniya transportnyye zadachi. Izvestiya RAN. Teoriya i sistemy upravleniya, 1, 32–45. (in Russian)
- Levanov, T. V. & Usko, O. V. (2010). Algoritm raboty murav'inoy kolonii dlya odnoy zadachi razmeshcheniya s ogranicheniyami po proizvodstvennoy moshchnosti. Vestnik UGATU, 2(37), 202–208. (in Russian)
- Li, Q., Zhang, C., Han, C., Xu, Y., Yin, Y., & Zhang, W. (2013). Path planning based on fuzzy logic algorithm for mobile robots in static environment, 2013 25th Chinese Control and Decision Conference (CCDC), Guiyang, China, May 2013 (pp. 2866-2871). https://doi.org/10.1109/CCDC.2013.6561434
- Li, X., Li, Q., & Zhang, J. (2022). Research on global path planning of unmanned vehicles based on improved ant colony algorithm in the complex road environment. Measurement and Control, 55, 9-10.
https://doi.org/10.1177/00202940221118132 - Lin, D., Shen, B., Liu, Y., Alsaadi, F. E., Alsaedi, A., & Cheng, H. (2017). Genetic algorithm-based compliant robot path planning: an improved Bi-RRT-based initialization method. Assembly Automation, 37(3), 261–270.
https://doi.org/10.1108/AA-12-2016-173 - Liu, J., Yang, J., Liu, H., Tian, X., & Gao, M. (2016). An improved ant colony algorithm for robot path planning. Soft Computing, 1, 1–11.
https://doi.org/10.1007/s00500-016-2161-7 - Lučić, P. & Teodorović, D. (2003). Computing with bees: attacking complex transportation engineering problems. International Journal on Artificial Intelligence Tools, 12(3), 375–394. https://doi.org/10.1142/S0218213003001289
- Merz, T. & Kendoul, F. (2013). Dependable low-altitude obstacle avoidance for robotic helicopters operating in rural areas. Journal of Field Robotics, 30(3), 439-471.
https://doi.org/10.1002/rob.21455 - Miao, H. & Tian, Y. (2013). Dynamic robot path planning using an enhanced simulated annealing approach. Applied Mathematics and Computation, 222, 420-437.
https://doi.org/10.1016/j.amc.2013.07.022 - Nair, R. R., Behera, L., Kumar, V., & Jamshidi, M. M. (2015). Multisatellite formation control for remote sensing applications using artificial potential field and adaptive fuzzy sliding mode control. IEEE Systems Journal, 9(2), 508–518.
https://doi.org/10.1109/JSYST.2014.2335442 - Pham, D. T., & Castellani, M. (2009). The Bees Algorithm: Modelling foraging behaviour to solve continuous optimization problems. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 223(12), 2919-2938. https://doi.org/10.1243/09544062JMES1494
- Schouwenaars, T., De Moor, B., Feron, E., & How, J. (2001). Mixed integer programming for multivehicle path planning. 2001 European control conference (ECC), Porto, Portugal, September 2001 (pp. 2603–2608). https://doi.org/10.23919/ECC.2001.7076321
- Song, B., Wang, Z., & Zou, L. (2016). On global smooth path planning for mobile robots using a novel multimodal delayed PSO algorithm. Cognitive Computation, 9, 5–17. https://doi.org/10.1007/s12559-016-9442-4
- Stützle, T. & Hoos, H. H. (2000). MAX MIN Ant System. Future Generation Computer Systems, 16(8), 889-914.
https://doi.org/10.1016/S0167-739X(00)00043-1 - Wang, P., Lin, H., & Wang, T. (2015). An improved ant colony system algorithm for solving the IP traceback problem. Information Sciences, 326, 172-187.
https://doi.org/10.1016/j.ins.2015.07.006 - Yen, C. T. & Cheng, M. F. (2018). A study of fuzzy control with ant colony algorithm used in mobile robot for shortest path planning and obstacle avoidance. Microsystem Technologies, 24, 125-135.
https://doi.org/10.1007/s00542-016-3192-9 - Zeng, M., Xi, L., & Xiao, A. (2016). The free step length ant colony algorithm in mobile robot path planning. Advanced Robotics, 30(23), 1509–1514.
https://doi.org/10.1080/01691864.2016.1240627 - Zhang, W., Gong, X., Han, G., & Zhao, Y. (2017). An improved ant colony algorithm for path planning in one scenic area with many spots. IEEE Access, 5, 13260–13269. https://doi.org/10.1109/ACCESS.2017.2723892
- Zhao, J., Cheng, D., & Hao, C. (2016). An improved ant colony algorithm for solving the path planning problem of the omnidirectional mobile vehicle. Mathematical Problems in Engineering, 2016, 7672839, 1–10.
https://doi.org/10.1155/2016/7672839 - Zhou, Z., Nie, Y., & Min, G. (2013). Enhanced ant colony optimization algorithm for global path planning of mobile robots. 2013 International Conference on Computational and Information Sciences, Shiyang, China, June 2013 (pp. 698–701).
https://doi.org/10.1109/ICCIS.2013.189
