Feasible-Orbit-Set Generation for Launch Vehicles

In this paper we present a real-time feasible-orbit-set generation algorithm for the launch vehicle. The feasible-orbit-set is obtained by solving its max-volume inscribed polyhedron. In order to calculate the boundary points of the feasible-orbit-set, a series of optimal control problems are formulated, which include maximizing the position and velocity along the specified direction in the orbital plane. To solve this problem in real-time, the thrust direction equality constraint is convexified by the lossless relaxation technique and the terminal orbital terminal constraint is linearized, establishing standard second-order cone programming problems. An iterative second-order cone programming algorithm is designed to solve the original four-type nonlinear optimal control problems. The algorithm has stable convergency that is practically independent of the initial guess. The result of the ISOCP is given, which shows that ISOCP works well in optimality and convergency. The result of the feasible-orbit-set generation algorithm is also given, showing that the algorithm is efficient and reliable.