Unwinding phenomenon in attitude control

A new exposition of the unwinding phenomenon was presented and a new type of PD controller for attitude control was proposed. The quaternions are often used in practical applications to represent rigid-body attitude. However, the quaternion state space S³ double covers the set of attitudes SO(3) in the sense that each attitude corresponds to two different quaternion vectors. Thus, in the case of feedback control using quaternions, this nonunique representation can give rise to regions of attraction and repulsion in the neighborhood of q∈S³ and-q∈S³, respectively, and cause the unwinding phenomenon of attitude control. A practical attitude control example was presented to illustrate this unstable behavior. A PD-type nonlinear controller was proposed to avoid the unwinding phenomenon. This controller also has an advantage of retuning to the equilibrium state with minimum angle of rotation.