The interest in the periodic orbits of the restricted three-body problem continues to grow for their significant practical application.This paper focuses on the interplanetary transfers between periodic orbits of two ...The interest in the periodic orbits of the restricted three-body problem continues to grow for their significant practical application.This paper focuses on the interplanetary transfers between periodic orbits of two different three-body systems,whose invariant manifolds have no intersection in phase space.A novel design method is proposed to obtain the optimal transfer employing the invariant manifolds and planetary gravity assist.The periapsis Poincare map is used to analyze the periapsides of invariant manifolds.On the basis of hyperbola approximation,the impulses performed on the periapsis of invariant manifolds are calculated with a simple iterative algorithm.The propellant-efficient escape and capture trajectories can be found by comparing the impulses magnitudes corresponding to different invariant manifolds,which can provide the appropriate initial guess for optimization.Further,the trajectory design is formulated as an unconstrained optimization problem under the perturbed restricted three-body model.An efficient algorithm combining simplex method and differential correction is adopted to obtain the optimal solution.The validity of the proposed approach is demonstrated through several interplanetary low energy transfer trajectories.展开更多
The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject ...The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft＇s own electric propulsion only, and the gravity assist （GA） is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body＇s gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.展开更多
In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi...In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-kin-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.展开更多
基金supported by the National Basic Research Program of China ("973" Program) (Grant No. 2012CB720000)the National Natural Science Foundation of China (Grant No. 11102021)Foundation of Science and Technology on Space Intelligent Control Laboratory
文摘The interest in the periodic orbits of the restricted three-body problem continues to grow for their significant practical application.This paper focuses on the interplanetary transfers between periodic orbits of two different three-body systems,whose invariant manifolds have no intersection in phase space.A novel design method is proposed to obtain the optimal transfer employing the invariant manifolds and planetary gravity assist.The periapsis Poincare map is used to analyze the periapsides of invariant manifolds.On the basis of hyperbola approximation,the impulses performed on the periapsis of invariant manifolds are calculated with a simple iterative algorithm.The propellant-efficient escape and capture trajectories can be found by comparing the impulses magnitudes corresponding to different invariant manifolds,which can provide the appropriate initial guess for optimization.Further,the trajectory design is formulated as an unconstrained optimization problem under the perturbed restricted three-body model.An efficient algorithm combining simplex method and differential correction is adopted to obtain the optimal solution.The validity of the proposed approach is demonstrated through several interplanetary low energy transfer trajectories.
文摘The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft＇s own electric propulsion only, and the gravity assist （GA） is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body＇s gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.
基金supported by the National Natural Science Foundation of China(Grant11372311)the grant from the State key Laboratory of Astronautic Dynamics(2014-ADL-DW0201)
文摘In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-kin-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.
