Flyaround Orbit Design for Autonomous Rendezvous Based on Relative Orbit Elements

Abstract

I N RECENT years, there has been considerable interest in spacecraft formation flying, due to the advantages of autonomy, flexibility, and relatively low cost, which is mostly required in the future space missions. One important application is autonomous rendezvous and proximity operation to a cooperative or noncooperative target in space [1–4], where two spacecraft should be ensured to fly in close formation in order to accomplish inspection, servicing, or capture at the specified time [5]. To implement autonomous rendezvous, it is essential to study the relative motion of one spacecraft (referred to as the chaser) with respect to another reference spacecraft (referred to as the target). The relative motion problems have been treated in many references. For instance, early in 1960, the first study on the relative motion of satellite clusters was performed by Clohessy and Wiltshire [6]. The authors presented the linearized equations of relative motion under circular-orbit assumption, well known as Clohessy–Wiltshire equations. Thereafter, Lawden [7] and Tschauner and Hempel [8] first derived the relative motion equations for eccentric orbits. The effects of the reference orbit eccentricity, the gravity perturbation J2, drag, and solar radiation pressure on the relativemotion are shown in [9–13]. Additionally, in these studies, along with developing the relative motion dynamics, the relative trajectory design is also presented to specify six initial conditions for relative position and velocity components, also seen in [14–17]. However, further studies should be developed on two issues. On one hand, these studies mostly used relative position and velocity components to describe the analytic solution and to design the relative orbit. However, it is difficult to intuitively know the size, location, and orientation of the relative trajectory with respect to the target orbit from the relative position and velocity components. Lovell and Tragesser [18] first introduced a set of relative orbit elements to replace the position and velocity components through a simple coordinate transformation. Nevertheless, especially for the description of the orientation of relative trajectory plane, the use of the relative orbit elements is not intuitive enough. Hence, we introduce one new relative orbit element to describe intuitively the orientation of the relative trajectory plane. On the other hand, most of these studies seldom provided the practical considerations such as the requirements of the vehicle’s solar power generation and communications subsystems and thus cannot exploit the relationship of the relative orbit elements and the specified mission design. Reference [19] first investigates the relative orbit design while considering the relative navigation pointing and sun pointing constraints, especially optimizing the solar collection. However, the author illustrates the problem mainly based on one simple example and its simulation. Instead, the objective of our research is to provide thorough theoretical derivation for a general case. In this Note, flyaround orbit design during autonomous rendezvous for a cooperative target or noncooperative target is considered. The rest of this Note is organized as follows. In Sec. II, the relative dynamics is characterized and the relative orbit elements are introduced to describe intuitively the relative trajectory. Section III provides the chaser’s desired attitude constraints to satisfy relative navigation pointing and sun pointing requirements. Then the flyaround orbit design is mainly investigated to specify the initial conditions of relative orbit elements, especially the initial phase angle on the consideration of maximizing the solar power collection of the chaser. Conclusions and future work are given in Sec. IV.