Rigid Body Spacecraft Attitude Synchronization Using Higher Order Interactions With Hypergraphs

A new strategy for attitude synchronization of a network of N rigid body spacecraft is proposed on TSO(3)N using feedback of relative attitudes in the form of rotation matrices and relative angular velocities. In addition to leveraging pairwise interactions according to an undirected and connected ring lattice communication topology, the proposed strategy additionally utilizes higher order interactions corresponding to more than two spacecraft (e.g. a triplet) according to directed hyperedges in the communication topology in order to destabilize non-consensus equilibria and enlarge the region of attraction of the consensus manifold. As an alternative to previously proposed nonlinear feedback control protocols based on pairwise interactions only, it is shown that the use of higher order interactions with linear feedback control can provide similar bene�ts in terms of achieving attitude synchronization.