APPROXIMATE OPTIMAL PLANAR GUIDANCE OF AN AEROASSISTED SPACE-VEHICLE

The objective is to develop a guidance law for the lift force during a planar aeroassisted maneuver such that the vehicle is guided from ini tial entry conditions to specified terminal conditions while minimizin g the velocity loss. An approximate solution is proposed to this two-p oint boundary-value problem, based on the assumption that along the at mospheric portion of typical aeroassisted maneuvers the aerodynamic fo rces are dominant. The suboptimal control law is thus derived for an a pproximate model of the vehicle's dynamics and is expressed as a serie s expansion with respect to a small parameter that reflects the ratio between the gravity and the aerodynamic forces. Zero- and first-order terms of the series are developed for two types of planar maneuvers. T he control law is formulated in a feedback form that includes analytic functions and quadrature integrals and thus is suitable for onboard i mplementation. Numerical examples compare the performance of the exact , zero-order, and first-order solutions. It is shown that the approxim ate solutions are quite close to the exact one. The first-order contro l law improves slightly the velocity loss, but generally the zero-orde r controller is adequate.