Further Passivity Results for the Attitude Control Problem

In this paper we establish passivity for the system which describes the attitude motion of a rigid body in terms of minimal three-dimensional kinematic parameters. In particular, we show that linear, asymptotically stabilizing controllers and control laws without angular velocity measurements follow naturally from these passivity properties. The results of this paper extend similar results for the case of the (nonminimal) Euler parameters. Keywords--- Attitude control, passivity, stabilization, CayleyRodrigues parameters, Modified Rodrigues parameters. I. Introduction Recently it has been shown [1],[2],[3] that there exist linear asymptotically stabilizing control laws for the attitude motion of a rigid body using minimal, three-dimensional parameterizations for the kinematics. In [1] linear control laws were derived in terms of the classical Cayley-Rodrigues parameters [4] and the nonstandard Modified Rodrigues parameters [1],[4] In the present paper we show that the existence of l..