Distributed control for intrinsic reduced attitude formation with ring inter-agent graph

This paper investigates the reduced attitude formation control problem for a group of rigid-body agents using only relative attitude information. Under both undirected and directed ring inter-agent graph, it is shown that when reversing the sign of a classic consensus control, different formations depending on the parity of the group size are achieved asymptotically. Specifically, the reduced attitudes converge to a pair of antipodal points with even number of agents, and distribute uniformly on a great circle with odd number of agents. To show the effectiveness of the proposed control law, illustrative examples are provided.