Geometric tracking on 𝒮3 based on sliding mode control

Abstract

AbstractAttitude tracking on the unit sphere of dimension 3 based on sliding mode is considered in this article. The tangent bundle of Lagrangian dynamics that describes the rotational motion of a rigid body is first equipped with the structure of a Lie group, then a sliding subgroup emerged on it is defined. Next, a sliding‐mode controller is designed for attitude tracking that relies on an intrinsic error defined on the Lie group. Almost global asymptotic stability of the closed loop is demonstrated using the Lyapunov analysis. Comparisons of the proposed geometric sliding mode controller designed on the nonlinear manifold with one designed in the Euclidean space showed that under the same working conditions the former is more energy efficient, more robust to measurement noises, and has a shorter and smoother transient response.