New Control Laws for the Attitude Stabilization of Rigid Bodies

Abstract This paper introduces a new class of globally asymptotically stabilizing feedback control laws for the complete (i.e., dynamics and kinematics) attitude motion of a rotating rigid body. Control laws are given in terms of two new parameterizations of the rotation group derived using stereographic projection. The stabilizing properties of the proposed controllers are proved using Lyapunov functions which involve a quadratic plus a logarithmic term. An Interesting feature of the proposed Lyapunov functions is that they often lead to controllers that are linear with respect to the kinematic parameters.

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