Station-keeping of Halo Orbits using Convex Optimization-Based Receding Horizon Control
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In this work, we propose a convex optimization-based receding horizon control method for the station-keeping control of halo orbit in Earth-Moon system. we leverage the advantages of convex optimization and receding horizon control and design the method under the high-fidelity ephemeris model, making it feasible to actual mission. Simulation results show that our method reaches low tracking errors and control consumption and produces better performances than linear quadratic regulation method.Keywords:
Leverage (statistics)
Halo orbit
Halo orbit
Radiation Pressure
Two-body problem
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We investigate the effects of halo kinematics on the dynamics of stellar discs by simulating the evolution of isolated disc-halo systems from equilibrium initial conditions. Our main results come from four simulations where the initial disc is identical and the halo is either treated as a rigid potential or is live with isotropic orbits or orbits that preferentially rotate with or counter to the disc. We confirm previous results that bar formation is more vigorous in models with a live halo than a rigid one and is further enhanced when halo orbits preferentially rotate with the disc. We discuss two types of buckling events with different symmetries about the mid plane, one that occurs just as the bar is forming and the other well after the bar has been established. We also show that warps are most easily excited and maintained when the halo is counter-rotating with the disc, in agreement with theoretical predictions. Our most novel result is the discovery of a rotating halo instability, which causes the disc and halo cusp to spiral outward from the centre of mass of the system whether the halo rotates with the disc or counter to it and also occurs in a disc bulge halo system that does not form a bar. We provide a heuristic linear model that captures the essential dynamics of the instability.
Halo orbit
Dynamics
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Halo orbit
Halo effect
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An explicit guidance strategy is developed in order to compensate for the perturbations in a real model or a simulation model. The main idea is to add control at equally spaced time points according to the calculation of the required velocity,which is the key point of the method. The required velocity is computed by solving a three-body Lambert problem (3BLP). The presented method is applied to the Earth-Moon L1 Halo-to-Halo transfer problem where the nominal orbit is obtained from CR3BP,and the simulation is performed taking the bicircular model (BCM) as perturbation model including the solar gravity. It can be easily extended to other systems and transfer types,as well as various dynamics models. Results show that the approach can successfully maintain control of the vehicle and a small amount of propellant are required.
Halo orbit
Orbit (dynamics)
Lagrangian point
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This work presents a study of the dynamics in the vicinity of the stable L2 halo orbits in the Earth-Moon system of the circular restricted three-body problem. These solutions include partially elliptic, partially hyperbolic, and elliptic quasi-halo orbits. The first two types of orbits are 2-dimensional quasi-periodic tori, whereas the elliptic orbits are 3-dimensional quasi-periodic tori. Motivated by the Lunar Gateway, this work computes these orbits to explore the 3-parameter family of solutions lying in the vicinity of the stable halo orbits. An algorithm is presented to quantify the size of the invariant surfaces which gives perspective on the size of the orbits. A stability bifurcation is detected where the partially elliptic tori become partially hyperbolic. A nonlinear behavior of the Jacobi constant is observed which differs from the behavior of the quasi-halo orbits emanating from the unstable halo orbits which makeup the majority of the quasi-halo family. Uses of the orbits in the vicinity of the stable L2 halo orbits are identified, and the results highlight characteristics and structure of the family to broaden the understanding of the dynamical structure of the circular restricted three-body problem.
Dynamics
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Halo orbit
Celestial mechanics
Lagrangian point
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Halo orbit
Orbit (dynamics)
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Sequence (biology)
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Abstract This paper deals with direct transfers from the Earth to Halo orbits related to the translunar point. The gravitational influence of the Sun as a fourth body is taken under consideration by means of the Bicircular Problem (BCP), which is a periodic time dependent perturbation of the Restricted Three Body Problem (RTBP) that includes the direct effect of the Sun on the spacecraft. In this model, the Halo family is quasi-periodic. Here we show how the effect of the Sun bends the stable manifolds of the quasi-periodic Halo orbits in a way that allows for direct transfers.
Halo orbit
Celestial mechanics
Lagrangian point
Periodic orbits
Gravitational potential
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Lagrange L1 Point and Halo Orbits aound it in Sun-Earth(Moon) System play an important role in Kuafu project. Halo Orbits around L1 point can be used in continuous sun observation. This paper computes periodic Halo orbits around L1 point in circular-restricted three bodies problem,composed of Sun-Earth(Moon) -Probe,by means of numerical analytical method,and researchs the feature of these Halo orbits. The results are useful for target orbit design of Kuafu project.
Lagrangian point
Halo orbit
Orbit (dynamics)
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