Explicit Guidance of Aeroassisted Orbital Transfer Using Matched Asymptotic Expansions

Abstract

An explicit guidance of aeroassisted orbital transfer by using the method of matched asymptotic expansions is presented. The aeroassisted orbit transfer comprises three consecutive phases: a descending phase entering atmospherewithanegativee ightpathangle,atransatmospherice ighttodepleteitsexcessenergy,andanascending e ight targeting the desired apogee. Feedback control via lift modulation is used to guide the vehicle during the atmospheric e y-through, whereas a matched asymptotic solution for the exit trajectory is available to aim the apogee of the target orbit, thus determining the pull-up condition. The feedback control ensures the stability of a trajectory around the nominal trajectory by compensating for the nonlinear terms in the motion of the vehicle. When the method of matched asymptotic expansions is used, the control algorithms for the explicit guidance are derived and tested against the 1976 U.S. Standard Atmosphere. Simulation results indicate that the control algorithms can effectively control the trajectories in both the lower atmosphere and in the exit phase under the targeting dispersions of atmospheric variations.