A symplectic optimisation method for rapid endo-atmospheric ascent trajectory planning
by Panxing Huang; Changzhu Wei; Yuanbei Gu; Naigang Cui
International Journal of Modelling, Identification and Control (IJMIC), Vol. 24, No. 3, 2015

Abstract: A symplectic optimisation approach is proposed for the rapid optimal endo-atmospheric ascent trajectory planning of launch vehicles. According to the optimal necessary conditions, the optimal fixed-time ascent problem with path constraints and final condition constraints is transformed into a system of Hamiltonian canonical equations. Based on the variational principle of least action, and meanwhile taking the state variables at two ends as independent variables on every discrete interval, the Hamiltonian system is converted into a system of nonlinear algebraic equations. A modified Newtonian iteration algorithm and an analytical initial guess method are applied to solve the algebraic equations. Also, a simple secant method is used to adjust the fixed time to satisfy the final velocity constraint. The proposed numerical solution method keeps the symplectic geometric structure of the Hamiltonian system. A series of tests using the data of a suborbital reusable launch vehicle have been designed to demonstrate the working and performance of the algorithm. The results show that the proposed symplectic algorithm has better solution accuracy and efficiency than those of classical indirect methods and Gaussian pseudo-spectral method.

Online publication date: Thu, 22-Oct-2015

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