Study On Approach Orbit Design Between Spacecraft And Multiple Constellation Satellites

Space technology becomes more and more important to politics, economy and military, as an ultimate guarantee of nation’s power. A satellite constellation uses multiple satellites located in different orbits working together to implement a common mission. The dissertation studies the problem of designing a spacecraft’s orbit to make a single spacecraft close approach three non-coplanar satellites without orbital maneuver. The spacecraft can realize on-orbit servicing in close range by research findings. The main results achieved in this dissertation are summarized as follows.The orbital design for a spacecraft to achieve the rendezvous with three satellites on circular orbits of equal altitude is discussed theoretically under ideal conditions. 1) According to the numerical search algorithms which taken one or two satellites as reference, the possibility of the rendezvous between a spacecraft and three non-coplanar Walker constellation satellites is verified preliminarily. 2) Using results derived from the numerical search algorithm, the sufficient condition of the rendezvous between a spacecraft and three Walker constellation satellites is put forward. 3) Taking into account contradiction between completeness and time complexity in the numerical search algorithms, the complete orbital design method for rendezvous between a spacecraft and multiple non-coplanar satellites on circular orbits of equal altitude is proposed. As the enumeration space is reduced remarkably, the completeness of the solution is guaranteed with limited computing cost. 4) The complete orbital design method can be simplified by considering the equal orbital height, space and inclination between different orbits of Walker constellation. The necessary and sufficient condition used to calculate the rendezvous orbit analytically is put forward, according to the difference between equispaced and non-equispaced orbital plane. When the relative positions of two groups of objects(each group contains three satellites) are under specific distributions, the characteristics of substitution, rotation symmetry and rotation circulant between two different rendezvous orbits are derived. 5) On the basis of the unique existence lemma and the motional direction lemma of the rendezvous orbit for two satellites, the existence theorem of the rendezvous orbit for three satellites is proposed. In other words, a spacecraft can achieve rendezvous with three non-coplanar satellites located on circular orbits of equal altitude.Two orbital design schemes for a spacecraft to approach three constellation satellites on near round orbits are studied and proposed. Due to the influence of launch error and long period perturbation, the Walker constellation satellite’s orbit, comparing with theoretical orbit, has become an elliptical orbit with small eccentricity. 1) The initial orbit determinated by Lambert algorithm realizes the rendezvous between the spacecraft and the former two constellation satellites, but the distance between the spacecraft and the third constellation satellite is long. Through improvement of the initial orbit by least square method, the distance between the spacecraft and the former two satellites is increased reasonably, while the distance between the spacecraft and the third satellite is decreased effectively, so the spacecraft can close approach three constellation satellites in near round orbits. Compared with the least square method, which fixes the approach time in orbit improvement, the generic and particle swarm optimization algorithms used for orbit improvement have better adaptation and effect. 2) After the near round orbits are projected on the reference sphere, a spacecraft on a circular orbit can achieve rendezvous with them on the reference sphere. If the semimajor axis of constellation satellites is set as the radius of reference sphere, the spacecraft can revisit constellation satellites regularly, thereby the spacecraft’s orbit can act as a lurk orbit. The orbital altitude’s difference by projection can be compensated by a tiny orbital maneuver.The influence of the constrained conditions in orbital design, including orbital perturbation, spacecraft launching and deviation of initial position, are studied and analyzed. 1) The above two schemes of spacecraft’s orbital design have not considered the influence of perturbation in the approach process. At first, by means of hierarchical calculating for the minimum distance between the spacecraft and the constellation satellites, the evolutionary algorithm is also fit for orbit improvement under the existence of orbital perturbation. Then, through analytical derivation and numerical simulation, we can conclude: whether consider the orbital perturbation in the approach process or nor, the spacecraft on the orbit obtained by reference sphere can keep revisiting constellation satellites. 2) Once launch window and corresponding orbit-transfer process for assigned launching site are determined, the spacecraft can be launched into the predesigned target track. 3) Owing to launch and orbit determination bias, the spacecraft and constellation satellites all have deviation comparing with theoretical position. Assuming three position deviation components in orbital coordinate system of the spacecraft(or constellation satellites) obey normal distribution on orbital initial epoch, the three components still obey normal distribution followed by the change of moment. Furthermore, the minimum distance between the spacecraft and the constellation satellites can be enveloped by normal distribution.The choice schemes of approach objects in satellite navigation constellation are studied and proposed. 1) The evaluation criterion of satellite navigation system’s performance is analyzed. 2) A satellite’s contribution for navigation system’s performance is calculated. 3) Considering special period of time and service region, the set of three satellites, which provide the most contribution for navigation system’s performance, are chosen to evaluate the influence for navigation performance in service region.The dissertation theoretically demonstrates the scheme feasibility of a single spacecraft approaches multiple non-coplanar constellation satellites, and the research in this dissertation can provide scheme references and technique support for development of on-orbit servicing technology.