The design of observers for formation-flying control

In this paper a method for estimating the relative orbit is proposed. The method requires a minimum number of simple sensors. The design of observers for formation-flying control, which is formulated as a control problem of tracking the target satellite, is treated. If the equations of the relative motion of the target and the chaser satellites are rewritten in the Local Vertical/Local Horizontal (LVLH) coordinate system, a nonlinear control system of the sixth order is obtained. It is very well known that such a control problem can be solved by a (linear or nonlinear) state controller. The formation-flying models are reviewed and analysed with respect to their observability according to the measured quantities. Based on the results of the observability analysis two state observers enabling an estimation of all the states are proposed in the paper: a simple observer of the linearised system and a nonlinear observer. Since cheap, small satellites are targeted, the application of cheap sensors is studied. In addition, the possibility of measuring the three relative position coordinates of the chaser satellite with a camera and a compass is given with some simulation results demonstrating the suppression of the measurement noise, which is significant when using cheap, COTS sensors and cameras.

► Observability analysis of formation flying models.
► Designing state observers based on simple sensors.
► Application of observers in orbit manoeuvres control algorithms.