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1.
Low-thrust electric propulsion is increasingly being used for spacecraft missions primarily due to its high propellant efficiency. As a result, a simple and fast method for low-thrust trajectory optimization is of great value for preliminary mission planning. However, few low-thrust trajectory tools are appropriate for preliminary mission design studies. The method presented in this paper provides quick and accurate solutions for a wide range of transfers by using numerical orbital averaging to improve solution convergence and include orbital perturbations. Thus, preliminary trajectories can be obtained for transfers which involve many revolutions about the primary body. This method considers minimum fuel transfers using first-order averaging to obtain the fuel optimum rates of change of the equinoctial orbital elements in terms of each other and the Lagrange multipliers. Constraints on thrust and power, as well as minimum periapsis, are implemented and the equations are averaged numerically using a Gausian quadrature. The use of numerical averaging allows for more complex orbital perturbations to be added in the future without great difficulty. The effects of zonal gravity harmonics, solar radiation pressure, and thrust limitations due to shadowing are included in this study. The solution to a transfer which minimizes the square of the thrust magnitude is used as a preliminary guess for the minimum fuel problem, thus allowing for faster convergence to a wider range of problems. Results from this model are shown to provide a reduction in propellant mass required over previous minimum fuel solutions. 相似文献
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The design of interplanetary trajectories based on patched circular restricted three body models is gradually becoming a valuable alternative to the classical patched conic approach. The main advantage offered by such a model is the possibility to exploit the manifold dynamics to move naturally far from or toward a body. Generally, propulsive maneuvers are required to match these structures. Low-thrust arcs offer the possibility to have a significant propellant mass reduction when moving from manifold to manifold. The aim of this paper is to present a methodology to design low-thrust trajectories between two planetary orbits connecting the manifolds of two circular three body systems. The approach is based on a grid search on the main parameters governing the solution to identify those trajectories moving within the manifold images on given Poincarè sections. The value of the Jacoby constant of the target libration point periodic orbit is chosen as stop condition for the thrusting phases. Ballistic arcs follow up to the proper Poincarè section intersection. A grid search for an Earth to Venus transfer is presented as test case. 相似文献
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《Acta Astronautica》2007,60(8-9):649-657
Here, we investigate an orbital transfer from a low Earth orbit to the geostationary one where the considered criterion to maximize is the final mass. We seek to observe numerically the connections between the impulse transfer and the low-thrust one after giving two computational methods in each cases. We see that the links are very strong and that the impulse transfer can be viewed as the limit of the low-thrust transfer when its number of revolutions increases. 相似文献
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Sandro da Silva Fernandes 《Acta Astronautica》1989,19(12):933-938
The problem of optimal low-thrust, limited power transfer between quasi-circular orbits (e 0) around an oblate planet is analysed. It is assumed that the orbital changes due to thrust acceleration and Earth oblateness are of the same order. A first order solution to the problem is obtained by application of Pontryagin's Maximum Principle. Subsequently, by application of Hori's method for generalized canonical systems, a first order solution in a small parameter ε is derived. Finally, three particular cases of long-time transfer and the orbit maintenance manoeuvre are considered. The results obtained are in agreement and represent an extension of the work done by Marec. 相似文献
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《Acta Astronautica》2007,60(8-9):631-648
This paper investigates the problem of continuous-thrust orbital transfer using orbital elements feedback from a nonlinear control standpoint, utilizing concepts of controllability, feedback stabilizability and their interaction. Gauss's variational equations (GVEs) are used to model the state-space dynamics of motion under a central gravitational field. First, the notion of accessibility is reviewed. It is then shown that the GVEs are globally accessible. Based on the accessibility result, a nonlinear feedback controller is derived which asymptotically steers a spacecraft form an initial elliptic orbit to any given elliptic orbit. The performance of the new controller is illustrated by simulating an orbital transfer between two geosynchronous Earth orbits. It is shown that the low-thrust controller requires less fuel than an impulsive maneuver for the same transfer time. Closed-form, analytic expressions for the new orbital transfer controller are given. Finally, it is proven, based on a topological nonlinear stabilizability test, that there does not exist a continuous closed-loop controller that can transfer a spacecraft onto a parabolic escape trajectory. 相似文献
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V. G. Petukhov 《Cosmic Research》2011,49(2):121-130
The problem of synthesizing stable feedback control is considered based on solving the problem of time minimization for a
multiorbit transfer between noncoplanar elliptic and circular orbits in a Newtonian gravitational field. The problem is solved
using asymptotic properties and symmetries of optimal control in the unperturbed problem. Stability of the obtained control
against external perturbations, deviations of initial conditions, and errors in thrust vector realizations is demonstrated.
The obtained quasioptimal control with feedback can be used as an onboard algorithm of spacecraft control and when performing
design and ballistic analysis. 相似文献
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A low-energy, low-thrust transfer between two halo orbits associated with two coupled three-body systems is studied in this paper. The transfer is composed of a ballistic departure, a ballistic insertion and a powered phase using low-thrust propulsion to connect these two trajectories. The ballistic departure and insertion are computed by constructing the unstable and stable invariant manifolds of the corresponding halo orbits, and a complete low-energy transfer based on the patched invariant manifolds is optimized using the particle swarm optimization (PSO) algorithm on the criterion of smallest velocity discontinuity and limited position discontinuity (less than 1 km). Then, the result is expropriated as the boundary conditions for the subsequent low-thrust trajectory design. The fuel-optimal problem is formulated using the calculus of variations and Pontryagin's Maximum Principle in a complete four-body dynamical environment. Then, a typical bang–bang control is derived and solved using the indirect method combined with a homotopic technique. The contributions of the present work mainly consist of two points. Firstly, the global search method proposed in this paper is simply handled using the PSO algorithm, a number of feasible solutions in a fairly wide range can be delivered without a priori or perfect knowledge of the transfers. Secondly, the indirect optimization method is used in the low-thrust trajectory design and the derivations of the first-order necessary conditions are simplified with a modified controlled, restricted four-body model. 相似文献
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Yu. P. Ulybyshev 《Cosmic Research》2012,50(5):376-390
Approximate numerical methods of optimization are presented for multi-orbit noncoplanar orbit transfers of low-thrust spacecraft. The linear representation of derivatives of boundary parameters is used in the vicinity of a reference trajectory with its discretization into small segments. For each segment a set of pseudo-impulses is introduced, representing possible directions of the thrust vector. In order to solve essentially nonlinear problems, the iterative process of upgrading the reference trajectory is used. At each iteration the linear programming problem of high dimensionality is solved, its boundary conditions being represented in the form of a linear matrix equation. Interval constraints are considered in the form of blocking the propulsion system operation on shadow segments of the orbit, as well as cycling constraints, and constraints on total duration of maneuvers at certain trajectory segments. The results of comparison with solutions obtained by other methods are presented together with examples illustrating the convergence of iterative processes. Optimizations of the trajectories for launching geosynchronous satellites to their orbits and of the trajectories of a noncoplanar transfer from low to high-elliptic Molniya orbit are considered under these constraints. 相似文献
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A. A. Baranov A. F. B. de Prado V. Yu. Razumny Anatoly A. BaranovJr. 《Cosmic Research》2011,49(3):269-279
Four types of optimal solutions are demonstrated to exist for transfers (time of flight is not fixed) between close near-circular
coplanar orbits. One solution is realized with the help of fixed orientation of the propulsion system (PS) along a transversal
in the orbital coordinate system. Another is reached at fixed orientation of the PS in the inertial coordinate system. The
third and fourth types of solutions change the PS orientation in the process of executing the maneuver. Regions of existence
are established for all types of solutions, and algorithms for determination of parameters of these maneuvers are suggested.
The algorithms were used to calculate parameters of the maneuvers of transfer from a launching orbit to a working Sun-synchronous
orbit, and to calculate the maneuvers of supporting the parameters of such an orbit in a specified range. 相似文献
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Low-thrust transfers between preset orbits are considered in the presence of perturbations of different origin. A simple method of finding the transfer trajectory is suggested, based on linearization of motion near reference orbits. The required accuracy of calculations is achieved by way of increasing the number of reference orbits. The method can also be used in the case of a large number of revolutions around the attracting center: no averaging of motion is required in this case. The suggested method is applicable as well, when the final orbit is specified partially and when there are constraints on the thrust direction. The optimal solution to the linearized problem is not optimal for the original problem; closeness of solutions to these two problems is estimated using a numerical example. Capabilities of the method are also illustrated by examples. 相似文献
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V. G. Petukhov 《Cosmic Research》2012,50(3):249-261
The problem of local optimization of interplanetary low-thrust trajectories is considered with the use of the maximum principle
and continuation numerical methods. Two types of problems are analyzed: problems with limited power and problems with limited
thrust. The latter problem is generalized by introducing the dependence of thrust and specific impulse on available electric
power. In order to reduce the problem of optimal control to a boundary value problem, the Pontryagin maximum principle is
used, and then, using the continuation method, this boundary value problem is reduced to the Cauchy problem. Variants of the
continuation method for optimizing low-thrust trajectories are presented in the paper, including a new method of continuation
for the limited thrust problem, which does not require any choice of the initial approximation for boundary values of conjugate
variables. 相似文献
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We consider transfers with low thrust in an arbitrary field of forces. The modified method of transporting trajectory [1–4] is used for optimization of the transfers. The complexity of finding the transporting trajectory of a preset type can be the main obstacle to application of this method. This challenge is solved for the three-body problem in the Hill motion model. Numerical analysis of the method is performed using an example of the transfers to halo-orbits around the solar-terrestrial libration points. 相似文献
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Recent studies have shown the feasibility of an Earth pole-sitter mission using low-thrust propulsion. This mission concept involves a spacecraft following the Earth's polar axis to have a continuous, hemispherical view of one of the Earth's poles. Such a view will enhance future Earth observation and telecommunications for high latitude and polar regions. To assess the accessibility of the pole-sitter orbit, this paper investigates optimum Earth pole-sitter transfers employing low-thrust propulsion. A launch from low Earth orbit (LEO) by a Soyuz Fregat upper stage is assumed after which solar electric propulsion is used to transfer the spacecraft to the pole-sitter orbit. The objective is to minimize the mass in LEO for a given spacecraft mass to be inserted into the pole-sitter orbit. The results are compared with a ballistic transfer that exploits manifold-like trajectories that wind onto the pole-sitter orbit. It is shown that, with respect to the ballistic case, low-thrust propulsion can achieve significant mass savings in excess of 200 kg for a pole-sitter spacecraft of 1000 kg upon insertion. To finally obtain a full low-thrust transfer from LEO up to the pole-sitter orbit, the Fregat launch is replaced by a low-thrust, minimum time spiral, which provides further mass savings, but at the cost of an increased time of flight. 相似文献
17.
Exploration of the inner planets of the Solar System is vital to significantly enhance the understanding of the formulation of the Earth and other planets. This paper therefore considers the development of novel orbits of Mars, Mercury and Venus to enhance the opportunities for remote sensing of these planets. Continuous acceleration is used to extend the critical inclination of highly elliptical orbits at each planet and is shown to require modest thrust magnitudes. This paper also presents the extension of existing sun-synchronous orbits around Mars. However, unlike Earth and Mars, natural sun-synchronous orbits do not exist at Mercury or Venus. This research therefore also uses continuous acceleration to enable circular and elliptical sun-synchronous orbits, by ensuring that the orbit's nodal precession rate matches the planets mean orbital rate around the Sun, such that the lighting along the ground-track remains approximately constant over the mission duration. This property is useful both in terms of spacecraft design, due to the constant thermal conditions, and for comparison of images. Considerably high thrust levels are however required to enable these orbits, which are prohibitively high for orbits with inclinations around 90°. These orbits therefore require some development in electric propulsion systems before becoming feasible. 相似文献
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Trajectories of spacecraft with electro-jet low-thrust engines are studied for missions planning to deliver samples of matter from small bodies of the Solar System: asteroids Vesta and Fortuna, and Martian moon Phobos. Flight trajectories are analyzed for the mission to Phobos, the limits of optimization of payload spacecraft mass delivered to it are determined, and an estimate is given to losses in the payload mass when a low-thrust engine with constant outflow velocity is used. The model of an engine with ideally regulated low thrust is demonstrated to be convenient for calculations and analysis of flight trajectories of a low-thrust spacecraft. 相似文献