Rapid Indirect Trajectory Optimization for Conceptual Design of Hypersonic Missions
Abstract
During conceptual design, trajectory optimization is often performed using direct methods. This investigation illustrates that trajectory optimization and vehicle performance characterization can be rapidly performed by coupling indirect optimization, continuation, and symbolic manipulation. Examples illustrate that the historical challenges associated with indirect optimization methods can be overcome, enabling the rapid construction of high-quality solutions. In this design methodology, highly constrained optimal trajectories are rapidly constructed by traversing optimal manifolds of varying design problems throughout the continuation process.
References
[1] , “Trajectory Optimization for a Fixed-Trim Reentry Vehicle Using Direct Collocation and Nonlinear Programming,” AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA Paper 2000-4262, Aug. 2000.
[2] , “Direct Optimization Using Collocation Based on High-Order Gauss-Lobatto Quadrature Rules,” Journal of Guidance, Control, and Dynamics, Vol. 19, No. 3, 1996, pp. 592–593. doi:https://doi.org/10.2514/3.21662 JGCDDT 0162-3192
[3] , “Rapid Verification Method for the Trajectory Optimization of Reentry Vehicles,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 3, 2003, pp. 505–508. doi:https://doi.org/10.2514/2.5074 JGCDDT 0162-3192
[4] , “Mars Science Laboratory Entry Optimization Using Particle Swarm Methodology,” AIAA Atmospheric Flight Mechanics Conference and Exhibit, AIAA Paper 2007-6393, Aug. 2007.
[5] , “Connections Between the Covector Mapping Theorem and Convergence of Pseudospectral Methods for Optimal Control,” Journal of Computational Optimization and Applications, Vol. 41, No. 3, 2008, pp. 307–335. doi:https://doi.org/10.1007/s10589-007-9102-4
[6] , “On the Pseudospectral Covector Mapping Theorem for Nonlinear Optimal Control,” 45th IEEE Conference on Decision and Control, IEEE, Piscataway, NJ, Dec. 2006, pp. 2679–2686.
[7] , Practical Methods for Optimal Control and Estimation Using Nonlinear Programming,
Soc. for Industrial and Applied Mathematics , Philadelphia, 2010.[8] , “Survey of Numerical Methods for Trajectory Optimization,” Journal of Guidance, Control, and Dynamics, Vol. 21, No. 2, 1998, pp. 193–207. doi:https://doi.org/10.2514/2.4231 JGCDDT 0162-3192
[9] , Applied Optimal Control, Taylor and Francis, Washington, D.C., 1975.
[10] , Calculus of Variations, Dover, New York, 2007.
[11] , Variational Methods in Optimum Control Theory, Academic Press, New York, 1968.
[12] , Optimal Control Theory: An Introduction, Prentice–Hall, Upper Saddle River, NJ, 1970.
[13] , Introduction to Optimal Control Theory, Wiley, New York, 1969.
[14] , “Rapid, Simultaneous Hypersonic Aerodynamic and Trajectory Optimization for Conceptual Design,” Ph.D. Thesis, School of Aerospace Engineering, Georgia Inst. of Technology, Atlanta, May 2012.
[15] , “Guidance and Control Analysis of the Entry of a Lifting Body Personnel Launch Vehicle,” 29th Aerospace Sciences Meeting, AIAA Paper 1991-0055, Jan. 1991.
[16] , “Thermal Protection System Technology and Facility Needs for Demanding Future Planetary Missions,” International Workshop on Planetary Probe Atmospheric Entry and Descent Trajectory Analysis and Science Proceedings, Oct. 2003.
[17] , “Analytic Hypersonic Aerodynamics for Conceptual Design of Entry Vehicles,” 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA Paper 2010-1212, Jan. 2010.
