Feedback Linearizing Controllers on SO(3) using a Global Parametrization

We present a methodology for studying the stabilization problem of a fully-actuated rotating rigid body. Since a rigid body attitude is represented by a rotation matrix in three dimensions, we exploit this fact and use each element of the rotation matrix as a parameter. This nine-parameter representation is global as well as unique, and results in a simplified set of nonlinear differential equations. We apply feedback linearization to design both local and almost global controllers. We also propose two novel definitions of feedback linearization functions, and prove that they lead to a well-defined vector relative degree and, as a result, almost-globally and locally stable controllers with bounded internal states. Using the proposed methodology, we present detailed examples of two such functions, demonstrating stabilization performance for each resulting controller on a rigid body system.