Optimal aeroassisted symmetric transfer between coplanar elliptical orbits

The problem of optimal aeroassisted symmetric transfer between elliptical orbits is concerned. The complete trajectory is assumed as consisting of two impulsive velocity changes at the beginning and the end of an interior atmospheric subarc, where the vehicle is controlled via the lift coefficient and thrust. The corresponding dynamic equations are built and bounded controls are considered. For the purpose of optimization computation, the equations are normalized. In order to minimize the total fuel consumption, the geocentric radius of initial elliptical transfer orbital perigee and controls during atmospheric flight should all be optimized. It is an optimal control problem which involves additional parameter optimization. To solve the problem, a two-level optimization method denoted by “genetic algorithm + Gauss pseudospectral method” is adopted: the genetic algorithm is used for parameter optimization and the Gauss pseudospectral method is used for optimal control problems. The flow chart of simulation is given. On this basis, the issue of more realistic modeling with two finite-thrust subarcs in the nonatmospheric part of the trajectory is simultaneously addressed. The orbital transfer problem is transformed to three continuous optimal control problems, and the constraints at different times are given, which are respectively solved by using the Gauss pseudospectral method. The obtained numerical results indicate that the optimal thrust control is of bang-bang type. The minimum-fuel trajectory in the atmosphere consists of aeroglide, aerocruise and aeroglide. They are compared with the results of pure impulsive model, and the conclusions that a significant fuel saving will be achieved by synergetic maneuver are drawn.