Generation of an optimal low-altitude trajectory for a fixed-wing unmanned aerial vehicle in a mountainous area
Abstract
In this study, the three-dimensional optimal trajectory planning of an unmanned fixed-wing aerial vehicle was investigated for Terrain Following – Terrain Avoidance (TF-TA) purposes using the Direct Collocation method. For this purpose, firstly, the appropriate equations representing the translational movement of the aircraft were described. The three-dimensional optimal trajectory planning of the flying vehicle was formulated in the TF-TA manoeuvre as an optimal control problem. The terrain profile, as the main allowable height constraint was modelled using the Fractal Generation Method. The resulting optimal control problem was discretized by applying the Direct Collocation numerical technique and then, was transformed into a Nonlinear Programming Problem (NLP). The efficacy of the proposed method was demonstrated by extensive simulations, and it was particularly verified that the purposed approach can produce a solution satisfying almost all the performance and environmental constraints encountering in a low -altitude flight.
Keyword : trajectory planning, Terrain Following - Terrain Avoidance (TF-TA), unmanned fixed-wing aerial vehicle, Direct Collocation method
How to Cite
Maghsoudi, H., & Kosari, A. (2021). Generation of an optimal low-altitude trajectory for a fixed-wing unmanned aerial vehicle in a mountainous area. Aviation, 25(2), 115-122. https://doi.org/10.3846/aviation.2021.13291
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Lindfield, G., & Penny, J. (2018). Numerical methods: using MATLAB (4th ed.). Academic Press.
Malaek, S. M., & Kosari, A. R. (2007). Novel minimum time trajectory planning in terrain following flights. IEEE Transactions on Aerospace and Electronic Systems, 43(1), 2–12. https://doi.org/10.1109/TAES.2007.357150
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Pourtakdoust, S. H., Kiani, M., & Hassanpour, A. (2011). Optimal trajectory planning for flight through microburst wind shears. Aerospace Science and Technology, 15(7), 567–576. https://doi.org/10.1016/j.ast.2010.11.002
Rao, A. V. (2009). A survey of numerical methods for optimal control. Advances in the Astronautical Sciences, 135(1), 497–528.
Sharma, T. (2006). Optimum flight trajectories for terrain collision avoidance [Master thesis, RMIT University].
Sharma, T., Bil, C., & Eberhard, A. (2005). Control system for optimal flight trajectories for terrain collision avoidance. In International Conference on Knowledge-Based and Intelligent Information and Engineering Systems (pp. 622–627). Springer. https://doi.org/10.1007/11552451_85
Von Stryk, O., & Bulirsch, R. (1992). Direct and indirect methods for trajectory optimization. Annals of Operations Research, 37(1), 357–373. https://doi.org/10.1007/BF02071065
Babaei, A., & Karimi, A. (2018). Optimal trajectory-planning of UAVs via B-splines and disjunctive programming. In ArXiv preprint arXiv:1807.02931 (pp. 1–12).
Bagherian, M. (2018). Unmanned Aerial Vehicle Terrain Following/Terrain Avoidance/Threat Avoidance trajectory planning using fuzzy logic. Journal of Intelligent & Fuzzy Systems, 34(3), 1791–1799. https://doi.org/10.3233/JIFS-161977
Benson, D. (1978). A Gauss pseudo-spectral transcription for optimal control. Massachusetts Institute of Technology (pp. 1–224). Department of Aeronautics and Astronautics. http://hdl.handle.net/1721.1/28919
Betts, J. T. (1998). Survey of numerical methods for trajectory optimization. Journal of Guidance, Control, and Dynamics, 21(2), 193–207. https://doi.org/10.2514/2.4231
Betts, J. T. (2010). Advances in design and control. Practical methods for optimal control and estimation using nonlinear programming (2nd ed.). Siam. https://doi.org/10.1137/1.9780898718577
Conway, B. A. (2012). A survey of methods available for the numerical optimization of continuous dynamic systems. Journal of Optimization Theory and Applications, 152(2), 271–306. https://doi.org/10.1007/s10957-011-9918-z
Fahroo, F., & Ross, I. M. (2008). Advances in pseudospectral methods for optimal control. In AIAA Guidance, Navigation and Control Conference and Exhibit (pp. 1–23). Honolulu, Hawaii. https://doi.org/10.2514/6.2008-7309
Garg, D. (2011). Advances in global pseudospectral methods for optimal control [Doctoral dissertation, University of Florida].
Grimm, W., & Hiltmann, P. (1987). Direct and indirect approach for real-time optimization of flight paths. In Optimal control (pp. 190–206). Springer. https://doi.org/10.1007/BFb0040209
Hargraves, C. R., & Paris, S. W. (1987). Direct trajectory optimization using nonlinear programming and collocation. Journal of Guidance, Control, and Dynamics, 10(4), 338–342. https://doi.org/10.2514/3.20223
Huang, G., Lu, Y., & Nan, Y. (2012). A survey of numerical algorithms for trajectory optimization of flight vehicles. Science China Technological Sciences, 55(9), 2538–2560. https://doi.org/10.1007/s11431-012-4946-y
Jalali-Naini, S. H., & Ebrahimi, M. (2017, May). Second-order optimal line-of-sight guidance law for minimum and nonminimum phase control systems. In 2017 International Conference on Mechanical, System and Control Engineering (ICMSC) (pp. 225–229). IEEE. https://doi.org/10.1109/ICMSC.2017.7959476
Jalali-Naini, S. H., & Sajjadi, S. H. (2016). First-order optimal line-of-sight guidance for stationary targets. Scientia Iranica. Transaction B, Mechanical Engineering, 23(2), 588–599. https://doi.org/10.24200/sci.2016.3846
Kamyar, R., & Taheri, E. (2014). Aircraft optimal terrain/threatbased trajectory planning and control. Journal of Guidance, Control, and Dynamics, 37(2), 466–483. https://doi.org/10.2514/1.61339
Kassaei, S. I., & Kosari, A. (2018). Aircraft trajectory planning with an altitude-bound in terrain-following flight. Modares Mechanical Engineering, 17(12), 135–144.
Kazemifar, O., Babaei, A. R., & Mortazavi, M. (2017). Online aircraft velocity and normal acceleration planning for rough terrain following. The Aeronautical Journal, 121(1244), 1561–1577. https://doi.org/10.1017/aer.2017.27
Kosari, A., & Kassaei, S. I. (2019). TF/TA optimal flight trajectory planning using a novel regenerative flattener mapping method. Scientia Iranica. https://doi.org/10.24200/sci.2019.51314.2109
Kosari, A., Maghsoudi, H., & Lavaei, A. (2017). Path generation for flying robots in mountainous regions. International Journal of Micro Air Vehicles, 9(1), 44–60. https://doi.org/10.1177/1756829316678877
Kosari, A., Maghsoudi, H., Lavaei, A., & Ahmadi, R. (2015). Optimal online trajectory generation for a flying robot for terrain following purposes using neural network. In Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 229(6), 1124–1141. https://doi.org/10.1177/0954410014545797
Lindfield, G., & Penny, J. (2018). Numerical methods: using MATLAB (4th ed.). Academic Press.
Malaek, S. M., & Kosari, A. R. (2007). Novel minimum time trajectory planning in terrain following flights. IEEE Transactions on Aerospace and Electronic Systems, 43(1), 2–12. https://doi.org/10.1109/TAES.2007.357150
Malaek, S. M., & Kosari, A. R. (2012). Dynamic based cost functions for TF/TA flights. IEEE Transactions on Aerospace and Electronic Systems, 48(1), 44–63. https://doi.org/10.1109/TAES.2012.6129620
Pourtakdoust, S. H., Kiani, M., & Hassanpour, A. (2011). Optimal trajectory planning for flight through microburst wind shears. Aerospace Science and Technology, 15(7), 567–576. https://doi.org/10.1016/j.ast.2010.11.002
Rao, A. V. (2009). A survey of numerical methods for optimal control. Advances in the Astronautical Sciences, 135(1), 497–528.
Sharma, T. (2006). Optimum flight trajectories for terrain collision avoidance [Master thesis, RMIT University].
Sharma, T., Bil, C., & Eberhard, A. (2005). Control system for optimal flight trajectories for terrain collision avoidance. In International Conference on Knowledge-Based and Intelligent Information and Engineering Systems (pp. 622–627). Springer. https://doi.org/10.1007/11552451_85
Von Stryk, O., & Bulirsch, R. (1992). Direct and indirect methods for trajectory optimization. Annals of Operations Research, 37(1), 357–373. https://doi.org/10.1007/BF02071065