Stabilization of a coordinated network of rotating rigid bodies

In this paper we present a stabilizing and coordinating control law for a network of spinning rigid bodies with unstable dynamics. The control law stabilizes each rigid body to spin about its unstable, intermediate axis while also aligning all of the spinning rigid bodies so that their orientations in inertial space are identical. The control law is derived using kinetic energy shaping for stabilization and potential shaping for coupling. The coupled system is Lagrangian with symmetry, and energy methods are used to prove stability and coordinated behavior.