A Convex Approach for Trajectory Optimization of Super-Synchronous-Transfer-Orbit Large Launch Systems with Time-Position Constraints

Abstract

This paper presents a trajectory optimization algorithm for super-synchronous-transfer-orbit (SSTO) large launch systems by convex optimization. The payload of SSTO launch systems is typically a geostationary equatorial orbit (GEO) satellite, and the time and position of orbital injection are constrained, which is quite different from the case of general satellites. In this paper, the optimal control problem of SSTO large launch systems is formulated considering the terminal constraints including orbital elements and the time-position equation. To improve the computational performance of the algorithm, the terminal orbital element constraints are expressed in the perifocal coordinate system with second-order equations. And then, several convexification techniques and their modified strategies are applied to transform the original trajectory optimization problem into a series of convex optimization problems, which can be solved iteratively with high accuracy and computational efficiency. Considering the time-position constraint of the payload, the flight time updater design method is proposed to correct the error of time during the flight, which lays solid foundation for the subsequent flight phase, guaranteeing that the GEO satellite settles into the required position. Finally, simulation results indicate the high efficiency and accuracy and strong robustness of the proposed algorithm in different special situations including engine failure and time delay. The algorithm proposed in this paper has great development potential and application prospect in onboard trajectory optimization of SSTO launch missions and similar situations.