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Coverage analysis is an essential process when designing a satellite constellation, and the variations of global revisit characteristics are usually elusive in discontinuous coverage problems. In dealing with this, a general method for analyzing the global revisit characteristics of constellations with repeating ground track orbits is proposed in this paper. Firstly, a two-dimensional map based analytical model for the point coverage of constellations is introduced. Then, the variations of revisit characteristics along both the parallel and meridian are analyzed based on the presented analytical model. Finally, numerical examples are carried out. On the one hand, the proposed analytical model for point coverage is demonstrated to be of high precision. On the other hand, all possible positions where the discontinuous changes of revisit characteristics occur can be analytically obtained, which can reveal the discontinuous variations of revisit characteristics along both the parallel and meridian, and can also ensure that all possible global or regional revisit characteristics are counted for a given constellation. The proposed method can contribute to constellation design and coverage performance analysis. • An analytical model for the coverage calculation of satellite constellations is developed. • Conditions for the appearance of the discontinuous changes of global revisit characteristics are deduced analytically. • Variations of the revisit characteristics of satellite constellations along both the parallel and meridian are revealed. [ABSTRACT FROM AUTHOR]

A three-impulse point return orbit design method is proposed for the manned lunar high-latitude exploration mission. First, considering the restrictions of the reentry corridor and the landing point simultaneously, the constraint conditions of the point return orbit are analyzed. Second, a serial orbit design strategy is presented. In the initial calculation, by decoupling the three-impulse transfer and the lunar escape, a two-segment patched method based on the pseudo-perilune parameters is proposed to determine the three-impulse point return orbit. The three-impulse transfer segment is backward designed by combining maneuvering at the special points with the Lambert problem in the hybrid orbit model, while the lunar escape segment is forward solved by introducing a comprehensive conic method. In the accurate solution, the result of the initial calculation serves as the initial value to perform the backward and forward integration for two segments in the high-fidelity model, respectively. The simulation examples verify the effectiveness and feasibility of this strategy, and show the advantages of high accuracy of the initial calculation and low velocity increment consumption. Finally, a large amount of simulations are conducted by applying this strategy, and the orbit characteristics are discussed. The research conclusions can provide a reference for the design of the point return orbit scheme for the manned lunar exploration mission. • Two-segment patched method for designing the three-impulse point return orbit. • New three-impulse transfer method with low impulse consumption. • Comprehensive conic method for generating the lunar escape segment. [ABSTRACT FROM AUTHOR]

In the design of multitarget interplanetary missions, there are always many options available, making it often impractical to optimize in detail each transfer trajectory in a preliminary search phase. Fast and accurate estimation methods for optimal transfers are thus of great value. In this paper, deep feed-forward neural networks are employed to estimate optimal transfer costs to three types of optimization problems: the transfer time of time-optimal low-thrust transfers, the fuel consumption of fuel-optimal low-thrust transfers, and the total Δ v of minimum- Δ v J 2 -perturbed multi-impulse transfers. To generate the training data, both considered categories of low-thrust trajectories are optimized using the indirect method, and the J 2 -perturbed multi-impulse trajectories are optimized using J 2 homotopy and particle swarm optimization. The hyper-parameters of deep networks are determined by grid search, random search, and the tree-structured Parzen estimators approach. Results show that deep networks are capable of estimating the final mass or time of optimal transfers with a mean relative error of less than 0.5% for low-thrust transfers and less than 4% for multi-impulse transfers. Our results are also compared with other off-the-shelf machine-learning algorithms and the generalization capabilities of the developed deep networks for predicting cases well outside the training data are investigated. Applications in multitarget mission design are also investigated. • The mean relative error for low-thrust transfers is less than 0.5%. • The mean relative error for J 2 -perturbed multi-impulse transfers is less than 4%. • Deep networks are superior to other algorithms. • Deep networks show an excellent extrapolation capability. • Applications in multitarget mission design are investigated. [ABSTRACT FROM AUTHOR]

The epistemic uncertainties caused by insufficient knowledge of the atmosphere, aerodynamic coefficient, and entry state render the entry process challenging, as they not only result in the deviation of the preplanned trajectory, but also may lead to the nonsatisfaction of path constraints. Herein, a robust epistemic uncertainty optimization (REUO) method based on evidence is proposed to solve the Mars entry trajectory optimization problem under epistemic uncertainty. A two-loop nested robust optimization (RO) model is formulated, in which the outer-loop optimization searches the optimal control while the inner-loop optimization calculates the extremal trajectory performances within each focal element (FE) to evaluate the evidence level. To solve the path constraint violation problem under uncertainties, the constraint design based on limitation bounds is considered in the RO model. The polynomial chaos expansion (PCE) is employed to obtain the approximate analytic function of the trajectory performance under uncertainties. Thereafter, the optimization based on ordinary stochastic entry dynamics in the inner loop is replaced by a simple parameter optimization of the analytic functions, which can be readily and rapidly solved. The REUO method is tested in a specific Mars entry mission. The simulation results show that the proposed method can identify the most robust solutions with the optimal trajectory performance under epistemic uncertainties. • Robust trajectory optimization model under epistemic uncertainty is formulated. • A robust epistemic uncertainty optimization method based on evidence is proposed. • Employment of nonintrusive PCE technique improves the optimization efficiency. [ABSTRACT FROM AUTHOR]

This study proposes a high-precision fixed-thrust free return orbit design method for a manned lunar mission centred on the rendezvous and docking with the lunar space station. Future manned lunar landing missions based on the lunar space station will require different spacecraft to achieve rendezvous and docking with it in different mission stages. Adopting the perilune parameters to design the Earth–Moon flight trajectory would be more convenient for decoupling in this kind of series missions. Thus, a new set of pseudo-parameters representing the perilune motion states is defined, and based on these, a hybrid multi-conic method is then proposed to design the free return orbit for manned spacecraft. The new method is more accurate than the traditional four-phase patched-conic method, and can produce initial values with a higher converging speed for a high-precision trajectory iteration design. Then, a fast and high-precision continuation method for the fixed-thrust trajectory is proposed based on the impulse-based solutions, and the gravity loss of the impulse-thrust transfer is analysed. Finally, the general characteristics and launch window of the free return orbit, as well as the reachable domain of the pseudo-perilune parameters, are analysed using the hybrid multi-conic method. The results will provide a theoretical basis for future missions planning. • New set of perilune pseudo-parameters for perilune motion states is defined. • Hybrid multi-conic method for designing free-return orbit. • High-precision fixed-thrust continuation method for impulse transformation. [ABSTRACT FROM AUTHOR]

The controllable set of contingency return trajectories for crewed lunar missions is studied on the basis of interval analysis. Firstly, in the light of the statement of the contingency return trajectory departing from the low lunar orbit, the mathematical model of the controllable set problem is presented. Secondly, based on interval analysis and contingency return trajectory design, a controllable set algorithm is put forward by combining a modified branch and bound method. Thirdly, using numerical simulations, the accuracy of this algorithm is verified by comparing with the results acquired from the classical brute force method. In addition, the comparison indicates this algorithm has higher calculation efficiency. Finally, the controllable set parameter characteristic analysis of contingency return trajectories is performed. The investigation conclusions can supply a decision basis for the plan and selection of a contingency return scheme in the future crewed lunar missions. • Mathematical model of controllable set of the contingency return trajectories. • Controllable set algorithm of the contingency return trajectories based on interval analysis. • Controllable set parameter characteristic analysis. [ABSTRACT FROM AUTHOR]

The return multi-flight-phase trajectory optimization of reusable launch vehicle is the key problem of vertical takeoff and vertical landing (VTVL) technologies. In order to solve the problem of ac-curate pinpoint soft landing in the high-dimensional parameter space composed of complex multi-variables and multi-constraints, this paper proposes a strategy of automatic parameter identification and classification and adaptive allocation of optimization algorithms based on clustering analysis. Firstly, state transition matrix of the terminal constraint variables relative to the design variables in the high-dimensional parameter space is obtained, which describes the sensitivity of the terminal constraint variables to the perturbation of the design variables. Then, K-means clustering algorithm is used to classify the sensitivity of the data elements in the state transition matrix, and the linear and nonlinear constraint variables and design variables together with linear state transition matrix are obtained according to the given linearity criterion. Finally, different optimization algorithms are allocated adaptively according to the linear and nonlinear characteristics of different parameter variables. Numerical simulation shows that the proposed algorithm can effectively deal with complex landing constraints, which has well accuracy, convergence and computational efficiency, and reduces the dimension and complexity of parameter space for the return trajectory optimization problem. Besides, the proposed algorithm is suitable for different return missions and has good adaptability and high expansibility. • A new VTVL reusable launch vehicle is studied. • A novel trajectory optimization strategy is presented for return multi-flight-phase. • A new method for parameter characteristics analysis is proposed to reduce dimension. • An adaptive allocation strategy is proposed to enhance adaptability and robustness. • The proposed algorithm has sufficient adaptability to handle VTVL return missions. [ABSTRACT FROM AUTHOR]

In this paper, the methods and results from Tsinghua University and Shanghai Institute of Satellite Engineering for the 11th Global Trajectory Optimization Competition (GTOC11) are presented. To deal with the complicated "Dyson Sphere" building problem, a three-stage procedure is conducted. First, the pre-analysis is performed to reduce search space. It is found that two-impulse maneuvers between asteroid flybys are near-optimal, the semi-major axis of the "Dyson Ring" should be better at 1.0–1.5 AU, and the larger arrival mass asteroids tend to be selected. Second, the globally optimal trajectory design problem is further divided into two sub-problems, the mothership trajectory design and the asteroid assignment to the "Dyson Ring" power stations. For the first problem, beam search is used to obtain numerous single mothership trajectories based on a pre-constructed flyby trajectory database of 3–8 asteroids. The overall trajectories and asteroids visited are obtained by selecting 10 mothership trajectories with a genetic algorithm. For the second problem, we build a database of optimal rendezvous times for all the 83,453 asteroids at different phase angles to reach power stations of different radii and phase angles, then a greedy algorithm is proposed to obtain the asteroid arrival schedule based on all the asteroids visited by motherships. Finally, local optimization of asteroid sequence and flyby epochs is conducted. The activation time adjustment in combination with indirect continuous-thrust trajectory optimization is used based on the global optimization result. In the final submission, motherships fly by 388 asteroids, and the minimum mass of twelve power stations reaches 94% of the theoretical upper bound, which is defined using the minimum-time orbital transfers with free initial and target phases. • The winning result submitted for GTOC 11 is discussed. • Solving the flyby by the rendezvous in combination with geometric corrections. • Optimizing the flyby times in asteroid chains to solve the time-dependent problems. • An exponential form of the heuristic function is used in beam search. • A low-thrust solution database is constructed to obtain accurate flight time. [ABSTRACT FROM AUTHOR]