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 feedback based on relative attitude information. Under both undirected and directed cycle graph topologies, it is shown that reversing the sign of a classic consensus protocol yields asymptotical convergence to formations whose shape depends on the parity of the group size. Specifically, in the case of even parity the reduced attitudes converge asymptotically to a pair of antipodal points and distribute equidistantly on a great circle in the case of odd parity. Moreover, when the inter-agent graph is an undirected ring, the desired formation is shown to be achieved from almost all initial states

Robust synchronization of heterogeneous robot swarms on the sphere

Synchronization on the sphere is important to certain control applications in swarm robotics. Of recent interest is the Lohe model, which generalizes the Kuramoto model from the circle to the sphere. The Lohe model is mainly studied in mathematical physics as a toy model of quantum synchronization. The model makes few assumptions, wherefore it is well-suited to represent a swarm. Previous work on this model has focused on the cases of complete and acyclic networks or the homogeneous case where all oscillator frequencies are equal. This paper concerns the case of heterogeneous oscillators connected by a non-trivial network. We show that any undesired equilibrium is exponentially unstable if the frequencies satisfy a given bound. This property can also be interpreted as a robustness result for small model perturbations of the homogeneous case with zero frequencies. As such, the Lohe model is a good choice for control applications in swarm robotics