Explicit Nonlinear Rotational Controllers Using the Fundamental Equation

In this paper, we present two explicitly generated nonlinear controllers for rest-to-rest rigid body rotational maneuvers in terms of quaternions. The controllers are brought about by applying the fundamental equation of constrained motion to both the rotational dynamics and rotational control of rigid bodies. The first controller yields asymptotic stability at a desired orientation while allowing the stabilization to occur exactly along a pre-selected trajectory for three of the four components that make-up the quaternion. The second controller provides global stability at the desired orientation allowing stable motion to occur from any point in quaternion space. Numerical examples are provided showing the qualitative behavior that both rotational controllers yield when applied to a rigid body.© 2009 ASME