Chen Gao defends his thesis on the dynamics and control of artificial satellites in collinear libration environments

Since the beginning of the 21st century, and following the brilliant achievements obtained during the preceding century in near-Earth artificial satellites and manned spaceflight, the space community has increased its interest in the study and use of the Earth-Moon and the Sun-Earth/Moon environments. In this new deep-space exploration era, space missions developments are putting more emphasis on the accuracy of the required dynamic models and in the use of continuous low-thrust propulsion technologies. Due to the rich dynamic properties of the equilibria of the Restricted Three Body Problem (RTBP), the libration point orbits about them provide advantageous locations, becoming ideal locations for many scientific missions. Fortunately, these invariant dynamical objects of the RTBP persist when adding an appropriate continuous low-thrust propulsion, which opens additional opportunities for observation or communication capabilities of the spacecraft. Moreover, the continuous low-thrust propulsion can help to achieve active orbit control, including station keeping and on-orbit operations, which are of great importance for advanced space missions.

This work is devoted to the study of dynamics and control for continuous low-thrust spacecraft in the realm of collinear libration points. The main new results of the work are the following:

1. Determination and analysis of displaced orbits of a hybrid-sail spacecraft around the L₂ point in the Earth-Moon Elliptic RTBP model. This dynamical model includes the orbital eccentricities of the Earth-Moon system and Sun-Earth/Moon system, as well as the solar radiation pressure acceleration where the inclination of the Moon's orbital plane with respect to the ecliptic plane is considered. The problem is formulated using the linearized dynamics around the L₂ point, whereas the auxiliary electric propulsion is used for orbital stabilization. Taking the orbital eccentricities and the inclination angle as small quantities, and considering first-order approximations, the problem of generating displaced orbits is transformed into that of computing the particular solutions of some algebraic equations. The approximate analytical solutions of the equations are essentially quasi-periodic displaced orbits, whose out-of-plane distances are determined by the sail reflectivity rate and the attitude angles. Due to model errors and the inherent instability of the orbits, a backstepping orbital controller is proposed to ensure precise reference orbital tracking, while the reflectivity rate and orientation of the hybrid-sail spacecraft are optimized in such a way that the overall propellant consumption of the solar electric propulsion system is minimized.

2. Computation and station-keeping of resonant periodic libration point orbits in the Earth-Moon Circular RTBP. To begin with, the orbit and attitude dynamics of a high-fidelity hybrid-sail spacecraft are established, where the reflectivity control devices are taken as actuators. Through the use of a parallel shooting method, combined with a continuation on the solar sail induced acceleration, the families of resonant Lyapunov and halo orbits are investigated. Because of the significant perturbation environment in the Earth-Moon system, an auxiliary solar electric propulsion is necessary for the station-keeping in these perturbed orbits. To achieve high-precision station keeping and to minimize propellant consumption, a coupled orbit-attitude control strategy scheme is proposed. It is composed of three parts: an optimal periodic orbital controller, a solar electric propulsion acceleration optimization and a robust backstepping attitude controller. In particular, nonlinear disturbance observers are incorporated into the orbit as well as the attitude control to enhance the robustness of the procedures in front of force and torque perturbations. In this way, the accuracy of the station keeping is improved significantly.

3. Study of the influence of the solar radiation pressure on the dynamics around the dynamical substitutes of the L₁ and L₂ points in the Earth-Moon Quasi-Bicircular Problem. This model is a periodic perturbation of the RTBP that includes the gravitational effect of the Sun plus the solar radiation pressure acceleration on a solar-sail spacecraft. Starting from the simplest invariant objects in the Quasi-Bicircular Problem, i.e. the dynamical substitutes of the two equilibrium points, as well as the low order Sun resonant periodic orbits with the synodic period of the Sun, the evolution of the families of resonant periodic orbits is investigated when two sail parameters, defining its orientation and efficiency, are varied. The study shows an intricate web of connections between the families. As an important remark, it has been found that for some particular values of the parameters there exists periodic orbits that become stable under the influence of the solar radiation pressure acceleration.

4. Station-keeping of libration point orbits using continuous low-thrust propulsion. Based on the dynamical properties of the phase space near libration point orbits, two families of control procedures are derived using this methodology. The first family is obtained as the limit of impulsive maneuvers, and the second one by means of dynamically reshaping the Floquet modes. Despite following different approaches, the geometrical analysis of both procedures shows that these strategies can reshape the dynamical structures about the libration point orbits and stabilize the motion. With the help of the Jet Transport technique, the control laws can be explicitly written as polynomials in terms of the deviation between the state of the spacecraft and the one at a nominal point on the reference libration point orbit, which opens the possibility of compact on-board implementation. The proposed control laws are geometrically intuitive, suitable to be implemented using a low-thrust propulsion device, and the fuel requirements of the laws are reasonable. The numerical results prove the robustness of the controls in front of measurement uncertainties and large initial orbit injection errors. Not just restricted to the particular problem considered, the new methodology provides a general framework to analyze the geometric behavior of any low-thrust station-keeping control law.