Optimal trajectories for aeroassisted orbital transfer

Abstract

This paper considers both classical and minimax problems of optimal control arising in the study of aeroassisted orbital transfer. The maneuver considered involves the coplanar transfer from a high planetary orbit to a low planetary orbit. An example is the HEO-to-LEO transfer of a spacecraft, where HEO denotes high Earth orbit and LEO denotes low Earth orbit. Trajectory control is achieved by means of lift modulation. An appropriate performance index is minimized. Specifically, within the frame of classical optimal control, the performance index is the energy required for orbital transfer; within the frame of minimax optimal control, the performance index is the peak heating rate. The presence of upper and lower bounds on the lift coefficient is considered. Numerical solutions are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. Numerical examples are presented, and their engineering implications are discussed.