Abstract
Flight trajectory optimization is a crucial aspect of aircraft design, and the numerical algorithms for trajectory optimization have always been a hot and challenging topic in domestic and international research. Starting from the classical classification of trajectory optimization methods and combining with recent advancements in the field of trajectory optimization, this paper provides an overview of various numerical algorithms for flight trajectory optimization, including their principles and applications. Furthermore, the characteristics of different methods and their suitability for solving specific problems are analyzed, offering valuable insights for the practical application of optimization methods. Finally, a brief analysis of the development of trajectory optimization is presented, along with a prospective outlook on the future direction of flight trajectory optimization algorithms.
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References
Bao, W.: Present situation and development tendency of aerospace control techniques. Acta Automatica Sinica 39(6), 697–702 (2013)
Dong, W., Wang, C., Wang, J., Xin, M.: Varying-gain proportional navigation guidance for precise impact time control. J. Guid. Control. Dyn. 46(3), 535–552 (2023)
Gontumukkala, S.S.T., Godavarthi, Y.S.V., Gonugunta, B.R.R.T., Subramani, R.: Kalman Filter and Proportional Navigation Based Missile Guidance System, pp. 1731–1736. IEEE (2022)
Park, B., Kim, T., Tahk, M.: Optimal impact angle control guidance law considering the seeker’s field-of-view limits. Proc. Inst. Mech. Eng. Part G: J. Aerospace Eng. 227(8), 1347–1364 (2013)
Kim, T., Park, B., Tahk, M.: Bias-shaping method for biased proportional navigation with terminal-angle constraint. J. Guid. Control. Dyn. 36(6), 1810–1816 (2013)
Tekin, R., Erer, K.S.: Switched-gain guidance for impact angle control under physical constraints. J. Guid. Control. Dyn. 38(2), 205–216 (2015)
Mall, K., Taheri, E.: Three-degree-of-freedom hypersonic reentry trajectory optimization using an advanced indirect method. J. Spacecr. Rocket. 59(5), 1463–1474 (2022)
Mall, K., Taheri, E.: Entry trajectory optimization for Mars science laboratory class missions using indirect uniform trigonometrization method, 2020, pp. 4182–4187. IEEE (2020)
Lu, P., Pan, B.: Highly constrained optimal launch ascent guidance. J. Guid. Control. Dyn. 33(2), 404–414 (2010)
Cui, N.G., Huang, P.X., Lu, F., Huang, R., Wei, C.: A hybrid optimization approach for rapid endo-atmospheric ascent trajectory planning of launch vehicles. Acta Aeronautica Et Astronautica Sinica 36(6), 1915–1923 (2015)
Hull, D.G., Speyer, J.L.: Optimal reentry and plane-change trajectories. In: AIAA, Astrodynamics Specialist Conference (1981)
Whitley, R., Ocampo, C.: Direct multiple shooting optimization with variable problem parameters. In: 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, p. 803 (2009)
Greco, C., Di Carlo, M., Vasile, M., Epenoy, R.: Direct multiple shooting transcription with polynomial algebra for optimal control problems under uncertainty. Acta Astronaut. 170, 224–234 (2020)
Guo, W., Zhao, Y.J., Capozzi, B.: Optimal unmanned aerial vehicle flights for seeability and endurance in winds. J. Aircr. 48(1), 305–314 (2011)
Silva, W., Frew, E.W.: Experimental assessment of online dynamic soaring optimization for small unmanned aircraft. AIAA Infotech@ Aerospace (2016)
Khan, N., Zollars, M., MacDermott, R.: Direct Collocation Methods for Hypersonic Trajectory Optimization by the Process of Continuation, 2023, pp. 1–9. IEEE (2023)
Darby, C.L.: hp-Pseudospectral method for solving continuous-time nonlinear optimal control problems. University of Florida (2011)
Darby, C.L., Hager, W.W., Rao, A.V.: An hp-adaptive pseudospectral method for solving optimal control problems. Optimal Control Appl. Methods 32(4), 476–502 (2011)
Gui, W., Babuska, I.: The hp and hp Versions of the Finite Element Method in 1 Dimension. Part 3. The Adaptive hp Version. Numerische Mathematik 49(6), 659–683 (1986)
Liu, G., Li, B., Ji, Y.: A modified HP-adaptive pseudospectral method for multi-UAV formation reconfiguration. ISA Trans. 129, 217–229 (2022)
Liu, X., Shen, Z., Lu, P.: Solving the maximum-crossrange problem via successive second-order cone programming with a line search. Aerosp. Sci. Technol. 47, 10–20 (2015)
Liu, X., Lu, P.: Solving nonconvex optimal control problems by convex optimization. J. Guid. Control. Dyn. 37(3), 750–765 (2014)
Liu, X., Shen, Z., Lu, P.: Entry trajectory optimization by second-order cone programming. J. Guid. Control. Dyn. 39(2), 227–241 (2016)
Szmuk, M., Acikmese, B.: Successive convexification for 6-dof mars rocket powered landing with free-final-time. In: 2018 AIAA Guidance, Navigation, and Control Conference, p. 0617 (2018)
Mao, Y., Dueri, D., Szmuk, M., Acikmese, B.: Successive convexification of non-convex optimal control problems with state constraints. IFAC-PapersOnLine 50(1), 4063–4069 (2017)
Harris, M.W., Acikmese, B.: Lossless convexification for a class of optimal control problems with quadratic state constraints. In: 2013 American Control Conference. IEEE, pp. 3415–3420 (2013)
Scheffe, P., Henneken, T.M., Kloock, M., Alrifaee, B.: Sequential convex programming methods for real-time optimal trajectory planning in autonomous vehicle racing. IEEE Trans. Intell. Vehicles 8(1), 661–672 (2022)
Pinson, R.M., Lu, P.: Trajectory design employing convex optimization for landing on irregularly shaped asteroids. J. Guid. Control. Dyn. 41(6), 1243–1256 (2018)
Szmuk, M., Reynolds, T.P., Acikmese, B.: Successive convexification for real-time six-degree-of-freedom powered descent guidance with state-triggered constraints. J. Guid. Control. Dyn. 43(8), 1399–1413 (2020)
Wang, Z., Lu, Y.: Improved sequential convex programming algorithms for entry trajectory optimization. J. Spacecr. Rocket.57(6), 1373–1386 (2020)
Hartl, R.F., Sethi, S.P., Vickson, R.G.: A survey of the maximum principles for optimal control problems with state constraints. SIAM Rev. 37(2), 181–218 (1995)
Harris, M.W., Acikmese, B.: Maximum divert for planetary landing using convex optimization. J. Optim. Theory Appl. 162(3), 975–995 (2014)
Kunhippurayil, S., Harris, M.W., Jansson, O.: Lossless convexification of optimal control problems with annular control constraints. Automatica 133, 109848 (2021)
Malyuta, D., Acikmese, B.: Lossless convexification of optimal control problems with semi-continuous inputs. IFAC-PapersOnLine 53(2), 6843–6850 (2020)
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Jiang, Y., Liu, J., Li, F., Hao, M. (2024). Review of Numerical Algorithms for Aircraft Trajectory Optimization. In: Qu, Y., Gu, M., Niu, Y., Fu, W. (eds) Proceedings of 3rd 2023 International Conference on Autonomous Unmanned Systems (3rd ICAUS 2023). ICAUS 2023. Lecture Notes in Electrical Engineering, vol 1170. Springer, Singapore. https://doi.org/10.1007/978-981-97-1107-9_50
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DOI: https://doi.org/10.1007/978-981-97-1107-9_50
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