Exponential stability of an attitude trajectory tracking controller utilizing unit quaternions

The problem of designing a controller for tracking a desired attitude trajectory by a rigid body is addressed. Such a controller design is not trivial since the orientation space is a Riemannian manifold. In this paper we utilize an attitude error stemming from the Lie Algebra of the unit quaternion space in conjunction with an angular velocity error respecting the manifold’s geometry. Using these errors we design a controller that guarantees exponential convergence to the desired trajectory. The proposed controller with the particular attitude error is shown through simulations to achieve faster convergence to the desired trajectory than other attitude error selections.