Low-thrust trajectory optimization in a full ephemeris model

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.

Opportunities search of transfer between interplanetary halo orbits in ephemeris model

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.

Trajectory design for the Moon departure libration point mission in full ephemeris model

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.

Design and optimization of a trajectory for Moon departure Near Earth Asteroid exploration

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.

Solar sailing trajectory optimization with planetary gravity assist

Significant propellant mass saving can be obtained with the use of complex multiple intermediate flyby maneuvers for conventional propulsion systems,and trip time also decreases for a portion of the proper solar sail missions.This paper discusses the performance of gravity assist(GA)in the time-optimal control problem of solar sailing with respect to sail lightness number and the energy difference between the initial and final orbit in the rendezvous problem in a two-body model,in which the GA is modeled as a substantial change in the velocity of the sailcraft at the GA time.In addition,this paper presents a method to solve the time-optimal problem of solar sailing with GA in a full ephemeris model,which introduces the third body’s gravity in a dynamic equation.This study builds a set of inner constraints that can describe the GA process accurately.Finally,this study presents an example for evaluating the accuracy and rationality of the two-body model’s simplification of GA by comparison with the full ephemeris model.

Close relative motion on distant retrograde orbits

Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions.However,as the reference DROs are obtained through numerical methods,the close relative motions on DROs are non-analytical,which severely limits the design of relative trajectories.In this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs.The linear dynamics of relative motion on DRO is established at first.The preliminary forms of the general solutions are obtained based on the Floquet theory.And the general solutions are classified as different modes depending on their periodic components.A new parameterization is applied to each mode,which allows us to explore the geometries of quasi-periodic modes in detail.In each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series.In this way,the analytical bounded relative motion on DRO is obtained.Based on the analytical expression,the characteristics of different modes are comprehensively analyzed.The natural periodic mode is always located on the single side of the target spacecraft on DRO and is appropriate to be the parking orbits of the rendezvous and docking.On the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period.The fly-around formation can support observations to targets on DRO from multiple viewing angles.And the fly-around formation is validated in a more practical ephemeris model.

Leveraging quasi-periodic orbits for trajectory design in cislunar space

Incorporating quasi-periodic orbits into the preliminary design process offers a wide range of options to meet mission constraints and address the challenges in a complex trade space.In this investigation,linear stability and quasi-periodic orbit family continuation schemes are examined to meet various types of constraints.Applications in eclipse avoidance and transfer design are examined by leveraging quasi-periodic orbits and their associated hyperbolic manifolds in the lunar region.Solutions are transitioned to an ephemeris model to validate that geometries are maintained in higher-fidelity models.When the natural dynamical structures associated with quasi-periodic orbits are leveraged,novel trajectory solutions can emerge.