Designing the Nonlinear Guidance Law Adaptable to Initial Deviations for the Vertical Landing of the Booster

In this study, terminal phase guidance of a vertical-landing booster has been considered. At first, dynamical equations have been derived assuming variable mass, density and gravity model. Then by considering these parameters as constants, sensitivity variables have been extracted using the vectorized high order expansions method. By using these sensitivity variables, a guidance law for updating optimal path and commands has been given. By implementing this guidance law, and considering initial deviations, near optimal path and guidance command have been extracted online, and the performance has been studied by means of simulations. To this end, intrinsic errors of the theory has been considered and confirmed at first. Then, a set of simulations considering variable mass, density and gravity have been implemented and the performance of the method has been evaluated in the presence of a vast variety of initial deviations. By investigating the results, which have been presented as graphs and numerical errors it can be seen that the landing errors are small and for booster landing mission, the vectorized high order method shows remarkable performance.