A convex approach to trajectory optimization for boost back of vertical take-off/vertical landing reusable launch vehicles

Abstract

In this paper, a convex optimization algorithm is proposed to solve the online trajectory optimization problem of boost back of vertical take-off/vertical landing reusable launch vehicles. To achieve high-precision landing of launch vehicles, trajectory optimization of the boost-back flight phase considering the accuracy of entry is carried out, especially in emergencies. The trajectory optimization problem is formulated as an optimal control problem with minimum fuel consumption, and then it is transformed into a series of convex optimization subproblems, which can be solved by primal-dual interior-point method accurately and rapidly. During the transformation, flip-Radau pseudospectral discretization method, lossless convexification and successive convexification technology are applied. To drive the vehicle to predetermined entry points at the expected velocity, terminal constraints are expressed as orbital constraints of the endpoint in the boost-back flight phase. Considering the influence of Earth's rotation, the right ascension of the ascending node of the target orbit is updated according to the time and true anomaly at the end of the boost-back flight phase. Furthermore, the homotopy method is applied to the situation where there is no good initial guess when emergency happens. The algorithm presented in this paper performs well upon the simulation experiments of mission change and thrust decline. With good accuracy, high computational efficiency, and excellent robustness, the convex approach proposed has a great potential for onboard application in reusable launch vehicles and other space vehicles.