On the rotational Cucker-Smale model: optimal formation configuration and adaptive gains design

In the present paper we consider the attitude synchronization problem for a formation of spacecraft flying in free space. In particular, we consider the same control laws of [1] and we expand on the results presented there. First, we review the adaptive gains definition for one of the controls and we modify it in order to lighten the computational load (without compromising the performance). Secondly, given the limitations imposed by the formation dimension and configuration, we explore the parameters spaces for both controls in search for gains providing the best performances (in terms of synchronization time). Finally, following these analyses, we study the dependence of the synchronization time from the formation configuration, considered as a function of the latter dimension and of the graph structure