Black swans, defined as extreme or unexpected behaviors in a dynamical system, occur in many nonlinear control systems including rigid body attitude control. In this talk the connection between the well-known Kuramoto model of coupled phase oscillators on the N-torus, including with input delay, and attitude consensus control on SO(3)N will be explored in terms of their similar unexpected non-consensus behaviors for certain communication graph topologies. A strategy to attain consensus or balanced configurations on these manifolds with continuous control and almost global asymptotic stability will be presented, and the strategy of bipartite consensus for multi-agent systems with both cooperative and antagonistic interactions will be applied to the attitude consensus control problem without the use of attitude parameterizations. Finally, this framework will be applied to the problem of 6-DOF spacecraft formation flying in low Earth orbit.
Eric Butcher is a professor of aerospace and mechanical engineering with joint appointments in electrical and computer engineering and the applied mathematics GIDP at the University of Arizona and currently serves as an associate editor for the Journal of the Astronautical Sciences.