Optimal trajectories for LEO-to-LEO aeroassisted orbital transfer

Abstract

This paper considers both classical and minimax problems of optimal control arising in the study of noncoplanar, aeroassisted orbital transfer. The maneuver considered involves the transfer from one planetary orbit to another having different orbital inclination, but the same radius. An example is the LEO-to-LEO transfer of a spacecraft with a prescribed plane change, where LEO denotes low Earth orbit. The basic idea is to employ the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. Hence, this type of flight is also called synergetic space flight. With reference to the atmospheric part of the maneuver, trajectory control is achieved by modulating the lift coefficient (hence, the angle of attack) and the angle of bank. The presence of upper and lower bounds on the lift coefficient is considered. Three different transfer maneuvers are studied. Type 1 involves four impulses and four space plane changes; Type 2 involves three impulses and three space plane changes; and Type 3 involves three impulses and no space plane change. In Type 1, the initial impulse directs the spacecraft away from Earth, and then is followed by an apogee impulse propelling the spacecraft toward Earth; in Types 2 and 3, the initial impulse directs the spacecraft toward Earth. A common element of these maneuvers is that they all include an atmospheric pass, with velocity depletion coupled with plane change. Within the framework of classical optimal control, the following problems are studied: (P1) minimize the energy required for orbital transfer; (P4) maximize the time of flight during the atmospheric portion of the trajectory; (P5) minimize the time integral of the square of the path inclination. Within the framework of minimax optimal control, the following problem is studied: (Q1) minimize the peak heating rate. Numerical solutions for Problems (P1), (P4), (P5), (Q1) are obtained by means of the sequential gradient-restoration algorithm for optimal control problems under following conditions: for Problem (P1), the plane change components and the apogee radius are optimized; for Problems (P4), (P5), (Q1), the plane change components and the apogee radius are kept at the same levels determined for Problem (P1). This is done in order to impart good energy characteristics to the solutions of Problems (P4), (P5), (Q1). The engineering implications of the solutions are discussed, in order to determine the most useful solutions in the light of energy requirements and heat transfer requirements. In particular, the merits of the nearly-grazing solution (P5) are discussed. For all maneuver types, it appears that the nearly-grazing solution (P5) is an excellent compromise between energy requirements and heating requirements.