Optimal reconfiguration manoeuvres in formation flying missions

Most of the current formation flying systems are intended to work in a single, stable orbital configuration acquired shortly after the launch. However, the formation flying concept lends itself to be used in a flexible manner, by introducing the possibility of changing the relative configuration of the platforms, i.e. to reconfigure the formation. Instead of maintaining a single relative geometry, the change in configuration helps to achieve multiple objectives. Several examples of missions gaining from a reconfiguration capability have been already identified (as some space-based distributed telescopes, the TPF – Terrestrial Pathfinder, and variable aperture/geometry radar missions), and it is expected that the concept will be increasingly applied in the future. Obviously, the reconfiguration has to be achieved by minimizing the control effort, by approximately distributing such an effort in a uniform manner among platforms, and – above all – by ensuring the safety of the maneuvers, avoiding any risk of collision. Within such a range of constraints, reconfiguration moves as an optimization process, opening the path to several ways to tackle the problem. This paper investigates a solution based on the Pontryagin Maximum Principle, looking primarily to the reduction of the required control effort. An important asset of this solution is its applicability to eccentric orbits, which are especially appealing for some of the astronomical missions interested to the reconfiguration opportunity. The proposed solution is described in theory and then applied in simulations of several mission scenarios – at different altitude ranges and to different configurations – to show its potential applicability and advantages.