Generation of an optimal low-altitude trajectory for a fixed-wing unmanned aerial vehicle in a mountainous area

    Hossein Maghsoudi Affiliation
    ; Amirreza Kosari Affiliation


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.
Published in Issue
Aug 20, 2021
Abstract Views
PDF Downloads
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.


Babaei, A. R., & Mortazavi, M. (2010). Three-dimensional curvature-constrained trajectory planning based on in-flight waypoints. Journal of Aircraft, 47(4), 1391–1398.

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.

Benson, D. (1978). A Gauss pseudo-spectral transcription for optimal control. Massachusetts Institute of Technology (pp. 1–224). Department of Aeronautics and Astronautics.

Betts, J. T. (1998). Survey of numerical methods for trajectory optimization. Journal of Guidance, Control, and Dynamics, 21(2), 193–207.

Betts, J. T. (2010). Advances in design and control. Practical methods for optimal control and estimation using nonlinear programming (2nd ed.). Siam.

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.

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.

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.

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.

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.

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.

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.

Kamyar, R., & Taheri, E. (2014). Aircraft optimal terrain/threatbased trajectory planning and control. Journal of Guidance, Control, and Dynamics, 37(2), 466–483.

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.

Kosari, A., & Kassaei, S. I. (2019). TF/TA optimal flight trajectory planning using a novel regenerative flattener mapping method. Scientia Iranica.

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.

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.

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.

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.

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.

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.

Von Stryk, O., & Bulirsch, R. (1992). Direct and indirect methods for trajectory optimization. Annals of Operations Research, 37(1), 357–373.