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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. [ABSTRACT FROM AUTHOR]

This brief presents an integrated trajectory planning and attitude control framework for six-degree-of-freedom (6-DOF) hypersonic vehicle (HV) reentry flight. The proposed framework utilizes a bilevel structure incorporating desensitized trajectory optimization and deep neural network (DNN)-based control. In the upper level, a trajectory data set containing optimal system control and state trajectories is generated, while in the lower level control system, DNNs are constructed and trained using the pregenerated trajectory ensemble in order to represent the functional relationship between the optimized system states and controls. These well-trained networks are then used to produce optimal feedback actions online. A detailed simulation analysis was performed to validate the real-time applicability and the optimality of the designed bilevel framework. Moreover, a comparative analysis was also carried out between the proposed DNN-driven controller and other optimization-based techniques existing in related works. Our results verify the reliability of using the proposed bilevel design for the control of HV reentry flight in real time. [ABSTRACT FROM AUTHOR]

Based on the analytical solutions of T-H equations and its state transition matrix form, the open-loop control method of spacecraft impulsive relative hovering was studied， which is promising for practical engineering use. The true anomaly intervals of the hovering impulse were optimized by the nonlinear mathematical programming. Based on the calculation of collision probability, the method of safety analysis and risk management was proposed. The numerical simulations show that the introduced relative hovering method can be used for circular and elliptical reference orbits hovering. Furthermore, the local optimal solution can be obtained by applying the true anomaly intervals optimization method. The maximum collision probability and the minimum relative distance nearly appear at the same time. And, the smaller the relative distance is, the larger the collision probability. [ABSTRACT FROM AUTHOR]