Modelling and control of satellite formations

Formation flying is a new paradigm in space mission design, aimed at replacing large satellites with multiple small satellites. Some of the proposed benefits of formation flying satellites are: (i) Reduced mission costs and (ii) Multi mission capabilities, achieved through the reconfiguration of formations. This dissertation addresses the problems of initiatialization, maintenance and reconfiguration of satellite formations in Earth orbits. Achieving the objectives of maintenance and reconfiguration, with the least amount of fuel is the key to the success of the mission. Therefore, understanding and utilizing the dynamics of relative motion, is of significant importance.

The simplest known model for the relative motion between two satellites is described using the Hill-Clohessy-Wiltshire(HCW) equations. The HCW equations offer periodic solutions that are of particular interest to formation flying. However, these solutions may not be realistic. In this dissertation, bounded relative orbit solutions are obtained, for models, more sophisticated than that given by the HCW equations. The effect of the nonlinear terms, eccentricity of the reference orbit, and the oblate Earth perturbation, are analyzed in this dissertation, as a perturbation to the HCW solutions. A methodology is presented to obtain initial conditions for formation establishment that leads to minimal maintenance effort.

A controller is required to stabilize the desired relative orbit solutions in the presence of disturbances and against initial condition errors. The tradeoff between stability and fuel optimality has been analyzed for different controllers. An innovative controller which drives the dynamics of relative motion to control-free natural solutions by matching the periods of the two satellites has been developed under the assumption of spherical Earth. A disturbance accommodating controller which significantly brings down the fuel consumption has been designed and implemented on a full fledged oblate Earth simulation. A formation rotation concept is introduced and implemented to homogenize the fuel consumption among different satellites in a formation.

To achieve the various mission objectives it is necessary for a formation to reconfigure itself periodically. An analytical impulsive control scheme has been developed for this purpose. This control scheme has the distinct advantage of not requiring extensive online optimization and the cost incurred compares well with the cost incurred by the optimal schemes.