A distributed attitude control law for formation flying based on the Cucker-smale model

Abstract

In this paper we consider the attitude synchronization problem for a swarm of spacecrafts flying in formation. Starting from previous works on consensus dynamics, we construct a distributed attitude control law and derive analytically sufficient conditions for the formation to converge asymptotically towards a synchronized, non–accelerating state (possibly defined a priori). Moreover, motivated by the results obtained on a particular consensus model, first introduced by F. Cucker and S. Smale to modellize the translational dynamics of flocks, we numerically explore the dependence of the convergence process on the dimension of the formation and the relative initial conditions of the spacecrafts. Finally, we generalize the class of weights defined by the previous authors in order to dampen the aforementioned effects, thus making our control law suitable for very large formations.