Shijie Xu

Impulsive Control for Formation Flight About Libration Points

The concept of formation flight of multiple spacecraft, near the libration points of the sun-Earth system, offers many possibilities for space exploration. This study focuses on the use of impulsive control to maintain formation flight in the circular restricted three-body problem. Two specific tasks are accomplished in this paper. First, the tangent targeting method, based on a two-level differential correction, is formulated to fully exploit the predetermined error bound. A comparison between the tangent targeting method and traditional targeting method shows that the number of maneuvers can be significantly reduced and the length of time between successive maneuvers can be greatly increased by using the tangent targetingmethod. The study of the practical convergence of the algorithm is also discussed. The second task is the proposal of a tangent targeting method-based formationkeeping strategy for handling uncertainty introduced by the thrust implementation error. A tradeoff between the formation-keeping accuracy and the number of maneuvers is achieved. Monte Carlo analysis, including 100 trials, demonstrates the effectiveness of this strategy.

Stability of the classical type of relative equilibria of a rigid body in the J2 problem

The motion of a point mass in the J2 problem is generalized to that of a rigid body in a J2 gravity field. The linear and nonlinear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, are studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. The conditions of nonlinear stability of the relative equilibria are derived with the energy-Casimir method through the projected Hessian matrix of the variational Lagrangian. With the stability conditions obtained, both the linear and nonlinear stability of the relative equilibria are investigated in details in a wide range of the parameters of the gravity field and the rigid body. We find that both the zonal harmonic J2 and the characteristic dimension of the rigid body have significant effects on the linear and nonlinear stability. Similar to the classical attitude stability in a central gravity field, the linear stability region is also consisted of two regions that are analogues of the Lagrange region and the DeBra-Delp region respectively. The nonlinear stability region is the subset of the linear stability region in the first quadrant that is the analogue of the Lagrange region. Our results are very useful for the studies on the motion of natural satellites in our solar system.

Stochastic Optimal Maneuver Strategies for Transfer Trajectories

AbstractAfter being initially launched into the parking orbit, a spacecraft usually implements several maneuvers to insert its nominal orbit as the geostationary orbit for global communication, a Halo orbit to survey the solar wind, and an adjacent orbit to rendezvous with other spacecraft. The transfer problem between two different trajectories is very important in academic research and practical engineering. Trajectory correction maneuvers are necessary to keep actual flight trajectories near the nominal ones because of the errors produced by control maneuvers, measurements, launching, and modeling. However, an inappropriate strategy costs more time and fuel and may even result in mission failure. This study investigates optimal maneuver strategies from the stochastic control viewpoint to track interesting and typical trajectories, including the Halo-transfer and Lambert rendezvous orbits. This study proposes an improved correction algorithm to eliminate modeling errors for reference transfer trajectori...

Earth-to-Moon Low Energy Transfer Using Time-dependent Invariant Manifolds

This paper investigates time-dependent invariant manifolds in the Sun-Earth-Moon bicircular problem (BCP) using Lagrangian coherent structures (LCSs) as substitutes. LCSs, which are defined as ridges of finite-time Lyapunov exponent (FTLE) fields, are proving to be excellent platforms for studies of stable and unstable manifolds in flows with arbitrary time dependence. A preliminary assertion of this paper is achieved numerically: timedependent invariant manifolds in the BCP are not only separatrices, but also invariant sets. Dichotomy is utilized to extract LCSs for the purpose of improving computational efficiency. A series of LCSs, with regularly spaced energy, are then extracted to illustrate the configuration of time-dependent invariant manifold on specified section. Finally, the application on constructing Earth-Moon low energy transfer in non-autonomous system is presented.

On the construction of low-energy cislunar and translunar transfers based on the libration points

There exist cislunar and translunar libration points near the Moon, which are referred to as the LL1 and LL2 points, respectively. They can generate the different types of low-energy trajectories transferring from Earth to Moon. The time-dependent analytic model including the gravitational forces from the Sun, Earth, and Moon is employed to investigate the energy-minimal and practical transfer trajectories. However, different from the circular restricted three-body problem, the equivalent gravitational equilibria are defined according to the geometry of the instantaneous Hill boundary due to the gravitational perturbation from the Sun. The relationship between the altitudes of periapsis and eccentricities is achieved from the Poincaré mapping for all the captured lunar trajectories, which presents the statistical feature of the fuel cost and captured orbital elements rather than generating a specified Moon-captured segment. The minimum energy required by the captured trajectory on a lunar circular orbit is deduced in the spatial bi-circular model. The idea is presented that the asymptotical behaviors of invariant manifolds approaching to/traveling from the libration points or halo orbits are destroyed by the solar perturbation. In fact, the energy-minimal cislunar transfer trajectory is acquired by transiting the LL1 point, while the energy-minimal translunar transfer trajectory is obtained by transiting the LL2 point. Finally, the transfer opportunities for the practical trajectories that have escaped from the Earth and have been captured by the Moon are yielded by the transiting halo orbits near the LL1 and LL2 points, which can be used to generate the whole of the trajectories.

Homoclinic/Heteroclinic Connections of Equilibria and Periodic Orbits of Contact Binary Asteroids

In this paper, homoclinic/heteroclinic connections of equilibrium points of two different types (that is, equilibrium points with one-dimensional unstable/stable manifolds together with two-dimensi...

Fault-Tolerant Decoupling Control for Spacecraft with SGCMGs Based on an Active-Disturbance Rejection-Control Technique

AbstractThis paper describes a fault-tolerant decoupling-control algorithm for spacecraft incorporating single-gimbal control moment gyroscopes (SGCMGs), simultaneously considering the SGCMG rotor ...

Bounded Motions near Contact Binary Asteroids by Hamiltonian Structure-Preserving Control

This paper is devoted to stabilizing motions near a special type of equilibrium point of contact binary asteroids by Hamiltonian structure-preserving control. Aiming at noncollinear equilibrium poi...