共查询到20条相似文献，搜索用时 15 毫秒
1.
H. J. Peng Q. Gao Z. G. Wu W. X. Zhong 《Celestial Mechanics and Dynamical Astronomy》2011,110(4):319-342
In this paper, from a Hamiltonian point of view, the nonlinear optimal control problems are transformed into nonlinear two-point
boundary value problems, and a symplectic adaptive algorithm based on the dual variational principle is proposed for solving
the nonlinear two-point boundary value problem. The state and the costate variables within a time interval are approximated
by using the Lagrange polynomial and the costate variables at two ends of the time interval are taken as independent variables.
Then, based on the dual variational principle, the nonlinear two-point boundary value problems are replaced by a system of
nonlinear equations which can preserve the symplectic structure of the nonlinear optimal control problem. Furthermore, the
computational efficiency of the proposed symplectic algorithm is improved by using the adaptive multi-level iteration idea.
The performance of the proposed algorithm is tested by the problems of Astrodynamics, such as the optimal orbital rendezvous
problem and the optimal orbit transfer between halo orbits. 相似文献
2.
A new approach is presented for the problem of planar optimal impulsive rendezvous of a spacecraft in an inertial frame near
a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a related
characteristic-value function and this related optimization problem can be solved in closed form. The solution of this problem
is shown to approach the solution of the original problem in the limit as the boundary conditions approach those of a circular
orbit. Using a form of primer-vector theory the problem is formulated in a way that leads to relatively easy calculation of
the optimal velocity increments. A certain vector that can easily be calculated from the boundary conditions determines the
number of impulses required for solution of the optimization problem and also is useful in the computation of these velocity
increments. Necessary and sufficient conditions for boundary conditions to require exactly three nonsingular non-degenerate
impulses for solution of the related optimal rendezvous problem, and a means of calculating these velocity increments are
presented. A simple example of a three-impulse rendezvous problem is solved and the resulting trajectory is depicted. Optimal
non-degenerate nonsingular two-impulse rendezvous for the related problem is found to consist of four categories of solutions
depending on the four ways the primer vector locus intersects the unit circle. Necessary and sufficient conditions for each
category of solutions are presented. The region of the boundary values that admit each category of solutions of the related
problem are found, and in each case a closed-form solution of the optimal velocity increments is presented. Similar results
are presented for the simpler optimal rendezvous that require only one-impulse. For brevity degenerate and singular solutions
are not discussed in detail, but should be presented in a following study. Although this approach is thought to provide simpler
computations than existing methods, its main contribution may be in establishing a new approach to the more general problem. 相似文献
3.
James D. Thorne 《Celestial Mechanics and Dynamical Astronomy》2011,110(1):31-42
Orbital maneuver transfer time optimization is traditionally accomplished using direct numerical sampling to find the mission
design with the lowest delta-v requirements. The availability of explicit time series solutions to the Lambert orbit determination
problem allows for the total delta-v of a series of orbital maneuvers to be expressed as an algebraic function of only the
individual transfer times. The delta-v function is then minimized for a series of maneuvers by finding the optimal transfer
times for each orbital arc. Results are shown for the classical example of the Hohmann transfer, a noncoplanar transfer as
well as an interplanetary fly-by mission to the asteroids Pallas and Juno. 相似文献
4.
A solution to the fixed-time minimum-fuel two-impulse rendezvous problem for the general non-coplanar elliptical orbits is
provided. The optimal transfer orbit is obtained using the constrained multiple-revolution Lambert solution. Constraints consist
of lower bound for perigee altitude and upper bound for apogee altitude. The optimal time-free two-impulse transfer problem
between two fixed endpoints implies finding the roots of an eighth order polynomial, which is done using a numerical iterative
technique. The set of feasible solutions is determined by using the constraints conditions to solve for the short-path and
long-path orbits semimajor axis ranges. Then, by comparing the optimal time-free solution with the feasible solutions, the
optimal semimajor axis for the two fixed-endpoints transfer is identified. Based on the proposed solution procedure for the
optimal two fixed-endpoints transfer, a contour of the minimum cost for different initial and final coasting parameters is
obtained. Finally, a numerical optimization algorithm (e.g., evolutionary algorithm) can be used to solve this global minimization
problem. A numerical example is provided to show how to apply the proposed technique. 相似文献
5.
Alessandro A. Quarta Giovanni Mengali 《Celestial Mechanics and Dynamical Astronomy》2009,105(4):361-377
This paper studies the problem of a spacecraft subject to an outward radial thrust, with constant modulus, that may be switched
on or off at suitable time intervals. The problem is to find the optimal strategy to guarantee the possibility of transferring
the spacecraft from an initial to a final position in a given time interval using the least amount of thrust level. The problem
is solved in an optimal framework, using an indirect approach. A number of different mission scenarios are studied in detail:
escape missions, flyby missions and rendezvous missions. In the latter case the spacecraft uses a hybrid system comprising
an high thrust propulsion system for the final impulsive maneuver. The optimal switching strategy allows one to substantially
decrease the thrust level when compared to the continuous case (without thrust modulation). 相似文献
6.
The theory of optimal control is applied to obtain minimum-time trajectories for solar sail spacecraft for interplanetary
missions. We consider the gravitational and solar radiation forces due to the Sun. The spacecraft is modelled as a flat sail
of mass m and surface area A and is treated dynamically as a point mass. Coplanar circular orbits are assumed for the planets. We obtain optimal trajectories
for several interrelated problem families and develop symmetry properties that can be used to simplify the solution-finding
process. For the minimum-time planet rendezvous problem we identify different solution branches resulting in multiple solutions
to the associated boundary value problem. We solve the optimal control problem via an indirect method using an efficient cascaded
computational scheme. The global optimizer uses a technique called Adaptive Simulated Annealing. Newton and Quasi-Newton Methods
perform the terminal fine tuning of the optimization parameters. 相似文献
7.
Riccardo Bevilacqua Jason S. Hall Marcello Romano 《Celestial Mechanics and Dynamical Astronomy》2010,106(1):69-88
A novel two-phase hybrid controller is proposed to optimize propellant consumption during multiple spacecraft rendezvous maneuvers
in Low Earth Orbit. This controller exploits generated differentials in aerodynamic drag on each involved chaser spacecraft
to effect a propellant-free trajectory near to the target spacecraft during the first phase of the maneuver, and then uses
a fuel optimal control strategy via continuous low-thrust engines to effect a precision dock during the second phase. In particular,
by varying the imparted aerodynamic drag force on each of the chaser spacecraft, relative differential accelerations are generated
between each chaser and the target spacecraft along two of the three translational degrees of freedom. In order to generate
this required differential, each chaser spacecraft is assumed to include a system of rotating flat panels. Additionally, each
chaser spacecraft is assumed to have continuous low-thrust capability along the three translational degrees of freedom and
full-axis attitude control. Sample simulations are presented to support the validity and robustness of the proposed hybrid
controller to variations in the atmospheric density along with different spacecraft masses and ballistic coefficients. Furthermore,
the proposed hybrid controller is validated against a complete nonlinear orbital model to include relative navigation errors
typical of carrier-phase differential GPS (CDGPS). Limitations of the proposed controller appear relative to the target spacecraft’s
orbit eccentricity and a general characterization of the atmospheric density. Bounds on these variables are included to provide
a framework within which the proposed hybrid controller can effect an extremely low propellant rendezvous of multiple chaser
spacecraft to a desired target spacecraft. 相似文献
8.
Bruce A. Conway Christian M. Chilan Bradley J. Wall 《Celestial Mechanics and Dynamical Astronomy》2007,97(2):73-86
The space mission planning process is considered as a hybrid optimal control problem. Hybrid optimal control problems are
problems that include categorical variables in the problem formulation. For example, an interplanetary trajectory may consist
of a sequence of low thrust arcs, impulses and planetary flybys. However, for each choice of the structure of the mission,
for example, for a particular choice of the number of planetary flybys to be used, there is a corresponding optimal trajectory.
It is not a priori clear which structure will yield the most efficient mission. In this work we present a mathematical framework
for describing such problems and solution methods for the hybrid optimal control problem based on evolutionary principles
that have the potential for being a robust solver of such problems. As an example, the methods are used to find the optimal
choice of three asteroids to visit in sequence, out of a set of eight candidate asteroids, in order to minimize the fuel required. 相似文献
9.
Mission to asteroids and comets has been the hot spot of deep space exploration in the new century. The choice of a suitable target, which involves both scientific value and technical feasibility, becomes a difficult task to accomplish due to limited energy and technology. The aim of this paper is to provide an approach to selecting a target and evaluating accessibility for rendezvous with a Near-Earth Asteroid mission, taking into account scientific value and engineering feasibility. Firstly, according to the orbital characteristics and physical properties of Near-Earth asteroids, we make a summary of some of the most frequent factors influencing the target selection of scientific significance. When selecting the target for a space mission, these factors can be regarded as the scientific motivations. Then in order to avoid the possibility that some high priority targets for science would be discarded due to requiring too high an energy budget by using a classical direct transfer strategy, we calculate the transfer trajectory for rendezvous with candidates by using the planetary swingby technique and the global optimal two-impulse method. Finally, through a comparison between the scientific relevance of each possible target and the corresponding estimate of energy needed for rendezvous missions, the ranking of some candidates is identified. 相似文献
10.
定点在日-地(月)系L1点附近的探测器的发射及维持 总被引：1，自引：0，他引：1
在限制性三体问题中共线平动点附近的运动虽然是不稳定的,但可以是有条件稳定的,该动力学特征使得一些有特殊目的的探测器只需消耗较少的能量即可定点在这些点附近(如ISEE-3、SOHO).以日-地(月)系的L1点为例,根据其附近的运动特征,探讨定点探测器的发射与轨道控制问题,给出了相应的数值模拟结果,为工程上的实现提供理论依据. 相似文献
11.
Homotopy methods have been widely utilized to solve low-thrust orbital transfer problems, however, it is not guaranteed that the optimal solution can be obtained by the existing homotopy methods. In this paper, a new homotopy method is presented, by which the optimal solution can be found with probability one. Generalized sufficient conditions, which are derived from the parametrized Sard’s theorem, are first developed. A new type of probability-one homotopy formulation, which is custom-designed for solving minimum-time low-thrust trajectory optimization problems and satisfies all these sufficient conditions, is then constructed. By tracking the continuous zero curve initiated by an initial problem with known solution, the optimal solution of the original problem is guaranteed to be solved with probability one. Numerical demonstrations in a three-dimensional time-optimal low-thrust orbital transfer problem with 43 revolutions is presented to illustrate the applications of the method. 相似文献
12.
A strategy is formulated to design optimal time-fixed impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interiorL
1 libration point of the Sun-Earth/Moon barycenter system. The adjoint equation in terms of rotating coordinates in the elliptic restricted three-body problem is shown to be of a distinctly different form from that obtained in the analysis of trajectories in the two-body problem. Also, the necessary conditions for a time-fixed two-impulse transfer to be optimal are stated in terms of the primer vector. Primer vector theory is then extended to non-optimal impulsive trajectories in order to establish a criterion whereby the addition of an interior impulse reduces total fuel expenditure. The necessary conditions for the local optimality of a transfer containing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. Determination of the location, orientation, and magnitude of each additional impulse is accomplished by the unconstrained minimization of the cost function using a multivariable search method. Results indicate that substantial savings in fuel can be achieved by the addition of interior impulsive maneuvers on transfers between libration-point orbits.An earlier version was presented as Paper AAS 92–126 at the AAS/AIAA Spaceflight Mechanics Meeting, Colorado Springs, Colorado, February 24–26, 1992. 相似文献
13.
Camilla Colombo Massimiliano Vasile Gianmarco Radice 《Celestial Mechanics and Dynamical Astronomy》2009,105(1-3):75-112
In this paper an optimisation algorithm based on Differential dynamic programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution. 相似文献
14.
J.-B. Caillau B. Daoud J. Gergaud 《Celestial Mechanics and Dynamical Astronomy》2012,114(1-2):137-150
The circular restricted three-body problem is considered to model the dynamics of an artificial body submitted to the attraction of two planets. Minimization of the fuel consumption of the spacecraft during the transfer, e.g. from the Earth to the Moon, is considered. In the light of the controllability results of Caillau and Daoud (SIAM J Control Optim, 2012), existence for this optimal control problem is discussed under simplifying assumptions. Thanks to Pontryagin maximum principle, the properties of fuel minimizing controls is detailed, revealing a bang-bang structure which is typical of L1-minimization problems. Because of the resulting non-smoothness of the Hamiltonian two-point boundary value problem, it is difficult to use shooting methods to compute numerical solutions (even with multiple shooting, as many switchings on the control occur when low thrusts are considered). To overcome these difficulties, two homotopies are introduced: One connects the investigated problem to the minimization of the L2-norm of the control, while the other introduces an interior penalization in the form of a logarithmic barrier. The combination of shooting with these continuation procedures allows to compute fuel optimal transfers for medium or low thrusts in the Earth–Moon system from a geostationary orbit, either towards the L 1 Lagrange point or towards a circular orbit around the Moon. To ensure local optimality of the computed trajectories, second order conditions are evaluated using conjugate point tests. 相似文献
15.
Alessandro A. Quarta Giovanni Mengali 《Celestial Mechanics and Dynamical Astronomy》2011,109(2):147-166
The aim of this paper is to analyze the optimal trajectories of a spacecraft subjected to a modulated radial thrust, whose
magnitude is inversely proportional to the square of the distance from the primary body. This case is representative of a
Sun-facing solar sail with a passive attitude control system. In this study the sailcraft is assumed to perform a finite number
of reorientation maneuvers to set the propelling acceleration to zero and generate suitable coasting arcs along the trajectory.
Accordingly, the resulting generalized orbit is a sequence of either propelled or ballistic conic arcs, whose main characteristics
(in terms of semimajor axis, eccentricity, and perihelion radius) can be calculated in closed form. As a result, the sailcraft
optimal performance can be studied using an analytical approach. In particular, some compact relationships are drawn and discussed
that allow one to find the optimal sailcraft characteristics required to reach a prescribed final orbit. 相似文献
16.
The smallness parameter of the approximation method is defined in terms of the non-dimensional initial distance between target and chaser satellite. In the case of a circular target orbit, compact analytical expressions are obtained for the interception travel time up to third order. For eccentric target orbits, an explicit result is worked out to first order, and the tools are prepared for numerical evaluation of higher order contributions. The possible transfer orbits are examined within Lambert’s theorem. For an eventual rendezvous it is assumed that the directions of the angular momenta of the two orbits enclose an acute angle. This assumption, together with the property that the travel time should vanish with vanishing initial distance, leads to a condition on the admissible initial positions of the chaser satellite. The condition is worked out explicitly in the general case of an eccentric target orbit and a non-coplanar transfer orbit. The condition is local. However, since during a rendezvous maneuver, the chaser eventually passes through the local space, the condition propagates to non-local initial distances. As to quantitative accuracy, the third order approximation reproduces the elements of Mars, in the historical problem treated by Gauss, to seven decimals accuracy, and in the case of the International Space Station, the method predicts an encounter error of about 12 m for an initial distance of 70 km. 相似文献
17.
Two-point boundary value problems appear frequently in space trajectory design. A remarkable example is represented by the
Lambert’s problem, where the conic arc linking two fixed positions in space in a given time is to be characterized in the
frame of the two-body problem. Classical methods to numerically solve these problems rely on iterative procedures, which turn
out to be computationally intensive in case of lack of good first guesses for the solution. An algorithm to obtain the high
order expansion of the solution of a two-point boundary value problem is presented in this paper. The classical iterative
procedures are applied to identify a reference solution. Then, differential algebra is used to expand the solution of the
problem around the achieved one. Consequently, the computation of new solutions in a relatively large neighborhood of the
reference one is reduced to the simple evaluation of polynomials. The performances of the method are assessed by addressing
typical applications in the field of spacecraft dynamics, such as the identification of halo orbits and the design of aerocapture
maneuvers. 相似文献
18.
A new second-order solution to the two-point boundary value problem for relative motion about orbital rendezvous in one orbit
period is proposed. First, nonlinear differential equations to describe the relative motion between a chaser and a target
are presented considering the second-order terms in the gravity. Then, by regarding the second-order terms as external accelerations,
we establish second-order state transition equations. Moreover, the J2 perturbations effects can also be considered in the
state transition equations. Last, the initial relative velocity to fulfill a rendezvous is determined by solving the state
transition equations. Numerical simulations show that the new second-order state transition equations are accurate. The second-order
solution to the two-point boundary value problem on eccentric orbits is valid even if the relative range is farther than 500 km. 相似文献
19.
Kathryn E. Davis Rodney L. Anderson Daniel J. Scheeres George H. Born 《Celestial Mechanics and Dynamical Astronomy》2011,109(3):241-264
This paper presents a method to construct optimal transfers between unstable periodic orbits of differing energies using invariant
manifolds. The transfers constructed in this method asymptotically depart the initial orbit on a trajectory contained within
the unstable manifold of the initial orbit and later, asymptotically arrive at the final orbit on a trajectory contained within
the stable manifold of the final orbit. Primer vector theory is applied to a transfer to determine the optimal maneuvers required
to create the bridging trajectory that connects the unstable and stable manifold trajectories. Transfers are constructed between
unstable periodic orbits in the Sun–Earth, Earth–Moon, and Jupiter-Europa three-body systems. Multiple solutions are found
between the same initial and final orbits, where certain solutions retrace interior portions of the trajectory. All transfers
created satisfy the conditions for optimality. The costs of transfers constructed using manifolds are compared to the costs
of transfers constructed without the use of manifolds. In all cases, the total cost of the transfer is significantly lower
when invariant manifolds are used in the transfer construction. In many cases, the transfers that employ invariant manifolds
are three times more efficient, in terms of fuel expenditure, than the transfer that do not. The decrease in transfer cost
is accompanied by an increase in transfer time of flight. 相似文献
20.
Strategies for plane change of Earth orbits using lunar gravity and derived trajectories of family G
C. F. de Melo E. E. N. Macau O. C. Winter 《Celestial Mechanics and Dynamical Astronomy》2009,103(4):281-299
The dynamics of the circular restricted three-body Earth-Moon-particle problem predicts the existence of the retrograde periodic
orbits around the Lagrangian equilibrium point L1. Such orbits belong to the so-called family G (Broucke, Periodic orbits
in the restricted three-body problem with Earth-Moon masses, JPL Technical Report 32–1168, 1968) and starting from them it
is possible to define a set of trajectories that form round trip links between the Earth and the Moon. These links occur even
with more complex dynamical systems as the complete Sun-Earth-Moon-particle problem. One of the most remarkable properties
of these trajectories, observed for the four-body problem, is a meaningful inclination gain when they penetrate into the lunar
sphere of influence and accomplish a swing-by with the Moon. This way, when one of these trajectories returns to the proximities
of the Earth, it will be in a different orbital plane from its initial Earth orbit. In this work, we present studies that
show the possibility of using this property mainly to accomplish transfer maneuvers between two Earth orbits with different
altitudes and inclinations, with low cost, taking into account the dynamics of the four-body problem and of the swing-by as
well. The results show that it is possible to design a set of nominal transfer trajectories that require ΔV
Total less than conventional methods like Hohmann, bi-elliptic and bi-parabolic transfer with plane change. 相似文献