Technique of target selection and profiles of transfer trajectory for Chinese asteroid exploring mission are studied systemically.A complete set of approaches to selecting mission targets and designing the transfer trajectory is proposed.First,when selecting a target for mission,some factors regarded as the scientific motivations are discussed.Then,when analyzing the accessibility of targets,instead of the classical strategy,the multiple gravity-assist strategy is provided.The suitable and possible targets,taking into account scientific value and technically feasible,are obtained via selection and estimation.When designing the transfer trajectory for exploring asteroid mission,an approach to selecting gravity-assist celestial body is proposed.Finally,according to the mission constraints,the trajectory profile with 2-years △V-EGA for exploring asteroid is presented.Through analyzing the trajectory profile,unexpected result that the trajectory would pass by two main-belts asteroids is found.So,the original proposal is extended to the multiple flybys mission.It adds the scientific return for asteroid mission.
CUI PingYuan1,QIAO Dong1,CUI HuTao2 & LUAN EnJie3 1 School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China
In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the first-level search procedure is performed under the conditions of the initial time of escape manifold trajectory of the Sun-Earth halo orbit and the terminal time of capture manifold of the target planet fixed,by solving the optimal two-impulsive heliocentric trajectory to connect the two manifold trajectories.The contour map,helpful to the understanding of the global characteristics of the transfer opportunities,taking the initial time of escape manifold and the terminal time of capture manifold as variables,the optimal velocity increment of the first-level search as objective function,is used for the second-level search.Finally,taking the Earth-Mars and Earth-Venus halo to halo transfers for example,the transfer opportunities in 2015-2017 are searched.The results show the effectiveness of the proposed method and reveal the property of quasi-period of transfer opportunities between interplanetary halo orbits.
The lunar probe may still have some remaining fuel after completing its predefined Moon exploration mission and is able to carry out some additional scientific or technological tasks after escaping from the Moon orbit.The Moon departure mission for the lunar probe is the focus of this paper.The possibility of the spacecraft orbiting the Moon to escape the Moon's gravitational pull is analyzed.The trajectory design for the Earth-Moon system libration point mission is studied in a full ephemeris dynamical model,which considers the non-uniform motion of the Moon around the Earth,the gravity of the Sun and planets and the finite thrust of the onboard engine.By applying the Particle Swarm Optimization algorithm,the trajectory design for the transfer from the Moon-centered orbit to the L1 halo orbit,the station-keeping strategies for the Earth-Moon halo orbit and the construction of homoclinic and heteroclinic orbits are investigated.Taking the tracking conditions and engineering constraints into account,two feasible schemes for the Moon departure libration point mission for the lunar probe are presented.
The periodic or quasi-periodic orbits around collinear Lagrange points present many properties that are advantageous for space missions. These Lagrange point orbits are exponentially unstable. On the basis of an analytical method, an orbit control strategy that is designed to eliminate the dominant unstable components of Lagrange point orbits is developed. The proposed strategy enables the derivation of the analytical expression of nonlinear control force. The control parameter of this strategy can be arbitrarily selected provided that the parameter is considerably lower than the negative eigenvalue of motion equations, and that the energy required keeps the same order of magnitude. The periodic or quasi-periodic orbit of controlled equations remains near the periodic or quasi-periodic orbit of uncontrolled equations.
The lunar probe often has some remaining fuel on completing the predefined Moon exploration mission and may carry out some additional tasks from the Moon orbit using the fuel.The possibility for the lunar probe to escape from the Moon and the Earth is analyzed.Design and optimization of the trajectory from the Moon orbit to the Near Earth Asteroids (NEAs) using the spacecraft's residual fuel is studied.At first,the semi-major axis,inclinations and the phase relations with the Earth of all the numbered NEAs are investigated to preliminarily select the possible targets.Based on the Sun-centered two-body problem,the launch window and the asteroid candidates are determined by calculating the minimum delta-v for two-impulse rendezvous mission and one-impulse flyby mission,respectively.For a precise designed trajectory,a full ephemeris dynamical model,which includes gravities of the Sun,the planets and the Moon,is adopted by reading the JPL ephemeris.The departure time,arrival time,burning time duration and thrust angles are set as variables to be designed and optimized.The optimization problem is solved via the Particle Swarm Optimization (PSO) algorithm.Moreover,two feasible NEA flyby missions are presented.
An analytical method is proposed to find geometric structures of stable,unstable and center manifolds of the collinear Lagrange points.In a transformed space,where the linearized equations are in Jordan canonical form,these invariant manifolds can be approximated arbitrarily closely as Taylor series around Lagrange points.These invariant manifolds are represented by algebraic equations containing the state variables only without the help of time.Thus the so-called geometric structure of these invariant manifolds is obtained.The stable,unstable and center manifolds are tangent to the stable,unstable and center eigenspaces,respectively.As an example of applicability,the invariant manifolds of L 1 point of the Sun-Earth system are considered.The stable and unstable manifolds are symmetric about the line from the Sun to the Earth,and they both reach near the Earth,so that the low energy transfer trajectory can be found based on the stable and unstable manifolds.The periodic or quasi-periodic orbits,which are chosen as nominal arrival orbits,can be obtained based on the center manifold.
Low thrust propulsion and gravity assist (GA) are among the most promising techniques for deep space explorations.In this paper the two techniques are combined and treated comprehensively,both on modeling and numerical techniques.Fuel optimal orbit rendezvous via multiple GA is first formulated as optimal guidance with multiple interior constraints and then the optimal necessary conditions,various transversality conditions and stationary conditions are derived by Pontryagin's Maximum Principle (PMP).Finally the initial orbit rendezvous problem is transformed into a multiple point boundary value problem (MPBVP).Homotopic technique combined with random searching globally and Particle Swarm Optimization (PSO),is adopted to handle the numerical difficulty in solving the above MPBVP by single shooting method.Two scenarios in the end show the merits of the present approach.
Rendezvous in circular or near circular orbits has been investigated in great detail,while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored.Among the various optimization methods proposed for fuel optimal orbital rendezvous,Lawden's primer vector theory is favored by many researchers with its clear physical concept and simplicity in solution.Prussing has applied the primer vector optimization theory to minimum-fuel,multiple-impulse,time-fixed orbital rendezvous in a near circular orbit and achieved great success.Extending Prussing's work,this paper will employ the primer vector theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous.Based on linearized equations of relative motion on elliptical reference orbit (referred to as T-H equations),the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar,coaxial elliptical orbits with arbitrary large eccentricity.A parameter adjustment method is developed for the prime vector to satisfy the Lawden's necessary condition for the optimal solution.Finally,the optimal multiple-impulse rendezvous solution including the time,direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem.The rendezvous error of the linearized equation is also analyzed.The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentricity case and is large for the higher eccentricity.For better rendezvous accuracy of high eccentricity orbits,a combined method of multiplier penalty function with the simplex search method is used for local optimization.The simplex search method is sensitive to the initial values of optimization variables,but the simulation results show that initial values with the primer vector theory,and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence,because the optimal results obtained by the primer vector t
