Nonlinear Optimal Trajectory Design for Mass-variant Lunar Landing Mission
by
Hamed Hossein Afshari
Iran - Tehran - K.N.Toosi University of Technology - Aerospace department
Coauthors: Dr.Alireza Novinzadeh, Dr.Jafar Roshanian, Iman Shafiee Nejad

Nonlinear optimal trajectory design of a mass-variant lander (MVL) for soft landing on the moon by minimizing the time is obtained. This analytical design is utilized the results of an analytical open-loop optimal solution determined for mass-in variant lander (MIL) in the minimum time. Having the results of mentioned work, optimal state trajectories and optimal control vector of MVL is determined by using an analytical method named perturbation feedback control. In the presented strategy, at first, the deviation between the control vector of MVL and MIL is computed and added to the MIL control vector. Afterward, the new obtained control vector is applied to the nonlinear MVL in each instant of time. By solving the MVL state-space equations the optimal trajectory is computed which can satisfy the terminal constraints for soft landing mission. It should be noted that the perturbation feedback control is an instantaneous function of states perturbation and constraints perturbation. This control strategy is a nonlinear optimal guidance law for time-variant lunar landing mission based on the results of the time optimal guidance law for MIL landing mission. Furthermore, in this strategy, the several difficulties associated with the numerical determination of optimal control solution for nonlinear systems, such as slow convergence rate and high sensitivity to initial guesstimates are not appeared.

Date received: March 10, 2008