A fast multi-objective optimization design method for emergency libration point orbits transfer between the Sun–Earth and the Earth–Moon systems

Abstract

This paper considers the emergency trajectory design mission of libration point orbit transfer between the Sun-Earth system and the Earth-Moon system. In order to balance the two indexes of transfer time and fuel consumption, Halo orbits and theirinvariant manifolds in the circular restricted three body problem (CRTBP) are combined with low thrust in the bicircular restricted four body problem (BRFBP) to design the transfer trajectories. A fast multi-objective optimization methodbased on surrogate modelwhich is greatly needed especially for emergency transfer missions is proposedto overcome the low-efficacy of original evolutionary multi-objectiveoptimization methods. The advantages of the Sun-Earth manifolds,the Earth-Moon manifoldsand the optimal control methodare fully considered.In the part of numerical simulations, several simple problems with analytical solutions are first employed to validate the proposed fast optimization algorithm,thenthe proposed method is compared with NSGA-II for the same multi-objective transfer problem. Numerical results show that the fast optimization method chooses the expected samplesand has a much higher efficiency than direct multi-objective optimization. The significance of the Sun-Earth manifolds and the Earth-Moon manifolds are considered. Several cases show the complicated relationship between transfer time and fuel consumption.

Solving Multiobjective Constrained Trajectory Optimization Problem by an Extended Evolutionary Algorithm

“…One way to handle this problem is to introduce the lag equation as described in Eq. (8). The function of the lag equation is similar to a first-order filter, that can filter the control input signal and make the trend in the actual control history smoother.…”

“…Generally, this type of problem aims to find the optimal state and control sequences so as to optimize the predefined performance index. Relative works on this topic can be found in various scientific and engineering applications such as agent/robot trajectory planning [3], [4], autonomous vehicle optimal path design [5], and spacecraft optimal control systems [6]- [8]. More precisely, in [2] the author proposed a time-optimal trajectory generation strategy for a multi-body car model.…”

“…Similarly, the low computational cost orbital transfer path was generated by Peng and Wang in [7], wherein an adaptive surrogate optimization technique was constructed. In their follow-up research [8], an emergency transfer trajectory design mission was considered and solved via a fast surrogate-based optimization method. Although many optimization strategies have been designed for trajectory planning problems, it is still challenging to generate the optimal or near optimal state and control trajectories under a highly constrained environment.…”

Multi-Objective Trajectory Planning Method for a Redundantly Actuated Parallel Manipulator Under Hybrid Force and Position Control

“…For this type of problem, the different objectives have a trade-off relationship, so there is no single optimal solution but a set of optimal solutions called the Pareto-optimal solution or noninferior solution. Common optimization algorithms include the MOGA, NPGA, PAES, and NSGA-II, and on this basis, for the trajectory optimization problem, a variety of optimization models are derived to effectively improve the algorithm performance [26][27][28]. In this paper, from the perspective of the solution convergence and diversity, the MOPSO algorithm proposed by Coello et al [29], which has shown outstanding performance, is used.…”

A review of optimization techniques in spacecraft flight trajectory design

“…Weighted-sum method (WS) [85] Physical programming method (PP) [86] Fuzzy physical programming (FPP) [33] Interactive physical programming (IPP) [87] Interactive fuzzy physical programming (IFPP) [88] Goal programming (GP) [89] Fuzzy goal programming (FGP) [75] Fuzzy satisfactory goal programming (FSGP) [32] Adaptive surrogate model (ASM) [90] hard to find a solution that can optimize all the objectives, it is then interesting to find all the pareto-optimal solutions and create the pareto-optimal set.…”