Cyclic Spacecraft Formations: Relative Motion Control Using Line-of-Sight Measurements Only
Pini Gurfil, David Mishne · Journal of Guidance Control and Dynamics · 2006
In this paper, we develop a new nonlinear relative spacecraft motion control law based on line-of-sight measurements only. Each spacecraft tracks its neighboring spacecraft to produce a line-af-sight vector measurement, and the last spacecraft tracks again the first spacecraft to create a cyclic formation. We show that cyclic leaderless formations controlled by line-of-sight measurements only are stable in the sense of energy matching. The initial semimajor axis errors relative to a reference semimajor axis all tend to the same value, which is the centroid of the initial semimajor axis errors. The stable behavior is achieved by using both full line-of-sight feedback (range and bearing) and partial line-of-sight feedback (bearing only). We also investigate the case of leader formations, where a designated leader does not track any other spacecraft. In this case, the semimajor axes of all follower spacecraft will converge to the initial semimajor axis of the leader. We also discuss an intermediate case, in which only part of the spacecraft forms a cycle. In this case, the cyclic formation members will determine the semimajor axes of all the other, noncyclic, spacecraft. We use elementary graph theory to describe the resulting formation topologies and conclude the development with an illustrating example.