Approximate Optimal Planar Guidance of an Aeroassisted Space Vehicle

Abstract

The objective is to develop a guidance law for the lift force during a planar aeroassisted maneuver such that the vehicle is guided from initial entry conditions to specie ed terminal conditions while minimizing the velocity loss. An approximate solution is proposed to this two-point boundary-value problem, based on the assumption that along the atmospheric portion of typical aeroassisted maneuvers the aerodynamic forces are dominant. The suboptimal control law is thus derived for an approximate model of the vehicle’ s dynamics and is expressed as a series expansion with respect to a small parameter that ree ects the ratio between the gravity and the aerodynamic forces. Zero- and e rst-order terms of the series are developed for two types of planar maneuvers. The control law is formulated in a feedback form that includes analytic functions and quadrature integrals and thus is suitable for onboard implementation. Numerical examples compare the performance of the exact, zero-order, and e rst-order solutions. It is shown that the approximate solutions are quite close to the exact one. The e rst-order control law improves slightly the velocity loss, but generally the zero-order controller is adequate.