Diversity and validity of stable-unstable transitions in the algorithmic weak stability boundary

Sousa-Silva, P. A.; Terra, Maisa O.

doi:10.1007/s10569-012-9418-y

Cited by 11 publications

(8 citation statements)

References 22 publications

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“…Generally speaking, DEMR performs better than all of the algorithms except SHADE. Among the 25 test functions, DEMR is significantly better than CMA-ES, LBBO, GL-25, SaDE, MPEDE, and SHADE in 15,11,16,12,10, and 9 functions, respectively, while the numbers of functions where CMA-ES, LBBO, GL-25, SaDE, MPEDE, and SHADE perform significantly better are 6, 7, 6, 10, 8, and 13. And for the remaining functions, DEMR provides error values comparable to those of the compared algorithms.…”

Section: Experiments On Benchmarkmentioning

confidence: 96%

“…This type of low-energy transfer trajectory is mainly achieved by taking advantage of the invariant manifold structures associated with the 3D halo orbits (or 2D Lyapunov orbits) in the vicinity of the libration points in the Sun-Earth system and Earth-Moon system and can be modelled as two coupled CR3BPs. In fact, the Japanese Hiten mission was a paradigmatic example for a class of low-energy Earth-to-Moon orbits obtained by considering the gravitational effects of the Earth, the Moon, and the Sun on the motion of the spacecraft simultaneously [8,9,14,15] and was later found to be related to the hyperbolic invariant manifolds of the CR3BP by employing the patched threebody approximation [5,16,17]. Gómez et al [18] had also presented the use of the restricted three-body problem's invariant manifold structural to design the low-energy transfer orbit in detail.…”

Section: Introductionmentioning

confidence: 99%

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Enhanced Hybrid Differential Evolution for Earth-Moon Low-Energy Transfer Trajectory Optimization

Zhang

Peng

Dai

et al. 2018

International Journal of Aerospace Engineering

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It is known that the optimization of the Earth-Moon low-energy transfer trajectory is extremely sensitive with the initial condition chosen to search. In order to find the proper initial parameter values of Earth-Moon low-energy transfer trajectory faster and obtain more accurate solutions with high stability, in this paper, an efficient hybridized differential evolution (DE) algorithm with a mix reinitialization strategy (DEMR) is presented. The mix reinitialization strategy is implemented based on a set of archived superior solutions to ensure both the search efficiency and the reliability for the optimization problem. And by using DE as the global optimizer, DEMR can optimize the Earth-Moon low-energy transfer trajectory without knowing an exact initial condition. To further validate the performance of DEMR, experiments on benchmark functions have also been done. Compared with peer algorithms on both the Earth-Moon low-energy transfer problem and benchmark functions, DEMR can obtain relatively better results in terms of the quality of the final solutions, robustness, and convergence speed.

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Section: Experiments On Benchmarkmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Enhanced Hybrid Differential Evolution for Earth-Moon Low-Energy Transfer Trajectory Optimization

Zhang

Peng

Dai

et al. 2018

International Journal of Aerospace Engineering

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“…Otherwise the point is redeemed as unstable. (Some of these ideas are also suggested in [11].) The main result of this paper is that the WSB points, which make the transition from the weakly stable to the weakly unstable regime, are the points on the stable manifold of the Lyapunov orbit for the corresponding energy level.…”

Section: Introductionmentioning

confidence: 94%

“…We remark that, since the stability/instability criteria, as described above, are concerned with the behavior of trajectories for finite time, they inherently introduce 'artifacts', i.e., points with very similar trajectories that are categorized differently with respect to these criteria. See [4,11].…”

Section: Introductionmentioning

confidence: 99%

Geometry of Weak Stability Boundaries

Belbruno

Gidea

Topputo

2012

Qual. Theory Dyn. Syst.

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The notion of a weak stability boundary has been successfully used to design low energy trajectories from the Earth to the Moon. The structure of this boundary has been investigated in a number of studies, where partial results have been obtained. We propose a generalization of the weak stability boundary. We prove analytically that, in the context of the planar circular restricted three-body problem, under certain conditions on the mass ratio of the primaries and on the energy, the weak stability boundary about the heavier primary coincides with a branch of the global stable manifold of the Lyapunov orbit about one of the Lagrange points

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“…The Weak Stability Boundary ∂W can therefore be introduced: it identifies the separatrix between those points in the phase space leading to capture orbits and those leading to different behaviours, such as escape orbits. In order to identify an initial point on the WSB, a bisection method defined in polar coordinates has been here implemented, as discussed in Topputo and Belbruno (2009): the possible Cantor-like structure of the Stable Set, discussed in Sousa and Terra (2012), has been here neglected. This work is focused on the identification of the closure of both the Stable Set (i.e., the Weak Stability Boundary), and of the Unstable Set.…”

Section: Ballistic Capturementioning

confidence: 99%

A flow-informed strategy for ballistic capture orbit generation

Manzi

Topputo

2021

Celest Mech Dyn Astr

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Ballistic capture is a phenomenon by which a spacecraft approaches its target body, and performs a number of revolutions around it, without requiring manoeuvres in between. Capture orbits are characterized by specific dynamics, defining regions that guide transport phenomena. Because of the limitations associated with existing approaches, the development of heuristics informed by Lagrangian Coherent Structures appears desirable. In fact, such structures identify transport barriers in dynamical systems, separating regions with qualitatively different dynamics. In this work, different flow-informed approaches are presented, and their relations with ballistic capture are discussed. A new heuristic, the time-varying strainline, is introduced. This new tool is applied to compute ballistic capture orbits around Mars. Different degrees of model fidelity have been investigated, mainly in order to test the robustness of the proposed technique with respect to different features of the underlying dynamical model. We show that time-varying strainlines are useful in identifying ballistic capture orbits.

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Diversity and validity of stable-unstable transitions in the algorithmic weak stability boundary

Cited by 11 publications

References 22 publications

Enhanced Hybrid Differential Evolution for Earth-Moon Low-Energy Transfer Trajectory Optimization

Enhanced Hybrid Differential Evolution for Earth-Moon Low-Energy Transfer Trajectory Optimization

Geometry of Weak Stability Boundaries

A flow-informed strategy for ballistic capture orbit generation

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