We propose a sliding surface for systems on the Lie group $SO(3)times mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable equilibrium. The sliding surface is used to design a sliding-mode controller for the attitude control of rigid bodies. The closed-loop system is robust against matched disturbances and does not exhibit the undesired unwinding phenomenon.
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