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Attitude tracking on the unit sphere of dimension $3$ based on sliding modeis considered in this paper. The tangent bundle of Lagrangian dynamics thatdescribes the rotational motion of a rigid body is first shown to be a Liegroup, and then a sliding surface that emerged on it is defined. Next, asliding-mode controller is designed for attitude tracking that relies on anintrinsic error defined on the Lie group. Almost global asymptotic stability ofthe closed loop is demonstrated using the Lyapunov analysis. Numericalsimulations are included to compare the performance of the sliding modecontroller designed on the Lie group with that designed in the embeddingEuclidean space.

Geometric Tracking on $\mathcal{S}^{3}$ Based on Sliding Mode Control