To efficiently and accurately design satellite constellations equipped with Reentry Glide Vehicles (RGVs), new analytical solutions are developed for calculating their coverage performance. Specifically, a new coverage model is established by approximating the Reentry Reachable Domain (RRD). However, the computation of real-time relative distances between satellites and targets, which is essential for coverage analysis based on this model, imposes a significant computational burden. To address this challenge, a coverage analysis method based on two-dimensional map theory is proposed. This method represents the coverage conditions of a target as a fixed area on a two-dimensional map and transforms the satellite trajectory into a series of parallel lines. By determining the intersection points between these lines and the area boundaries, the coverage analytical solutions for a target point are derived. On this basis, coverage theorems are presented for rapid calculation of the constellation coverage performance for an area. Simulation results demonstrate the effectiveness and high precision of the proposed analytical solutions.

This paper deals with the problem of guidance law design for the single moving mass controlled reentry vehicle when impact angle constraints and maneuvering target are taken into consideration. More specifically, a modified rolling guidance law is proposed with the interactive virtual target and the landing point prediction strategy. First, considering the fact that the roll channel can be controlled directly, the relative motion between the single moving mass controlled reentry vehicle and the target is described by the error angle between the relative velocity and the line-of-sight. Second, a nonlinear error angle command is given to reduce the rotation rate. To satisfy impact angle constraints, an interactive virtual target is presented and the “S” formed velocity of the virtual target is given to abate the error angle tracking difficulty at the final stage of the reentry phase. Then, the landing point prediction strategy is employed and the motion variation trend is also taken into consideration. As the maneuvering target is replaced with the predicted landing point, the error angle tracking difficulty caused by the target velocity decreases, which is helpful to meet impact angle constraints and improve guidance accuracy at the same time. Finally, the finite-time rolling guidance law is proposed and proved via Lyapunov stability theorem. Compared with the existing method, lower-speed rotation, smaller missing distance and less impact angle errors are obtained, which can be demonstrated by numerical simulations.

For the solid rocket with depletion shutdown system, effective energy management is significant to meet terminal constraints by exhausting excess energy. Several traditional energy management algorithms cannot satisfy the altitude constraint and path constraints are not sufficiently considered. The velocity adjustment capability of these algorithms is limited and the uncertainties are not considered. Based on the on-line programming of velocity capability curve, Spline-Line Energy Management (SLEM) guidance algorithm is proposed. It introduces lateral maneuvers to further consume the available velocity on the basis of longitudinal energy management. After expressing the constraints as several algebraic equations, the closed-loop guidance problem is converted to solving a system of nonlinear equations about the curve parameters in real time. The advantage is that the altitude constraint can be satisfied theoretically. The overload and control variable change rate and amplitude constraints are also considered during the flight by constructing the feasible boundary of velocity capability curve. To improve the robustness, it is further extended by estimating the actual uncertainties. The effectiveness and advantages of SLEM are demonstrated by simulations and comparisons with other energy management algorithms. Simulation results show that the proposed approach can satisfy multiple constraints with high precision under the condition of uncertainties.

The shape approximation method has been proven to be rapid and practicable in resolving low-thrust trajectory; however, it still faces the challenges of large deviation from the optimal solution and inability to satisfy the specific flight time and fuel mass constraints. In this paper, a modified shape approximation low-thrust model is presented, and a novel constrained optimization algorithm is developed to solve this problem. The proposed method aims at settling the bi-objective optimization orbit involving the twin objectives of minimum flight time and low fuel consumption and enhancing the accuracy of optimized orbit. In particular, a transformed high-order polynomial model based on finite Fourier series is proposed, which can be characterized as a multi-constraint optimization problem. Then, a novel optimization algorithm is specifically developed to optimize the large-scale multi-constraint dynamical equations of shape trajectory. The key performance indicators of the index include minimum flight time, low fuel consumption and bi-objective optimization of the two. Simulation results prove that this approach possesses both the high precision achievable by numerical methods and low computational complexity offered by shape approximation techniques. Besides, the Pareto front of the fuel-time bi-objective optimization orbit is firstly introduced to analyze an intact optimal solution set. Furthermore, we have demonstrated that our proposed approach is appropriate to generate the preliminary orbit for pseudo-spectral method.