Intrinsic geometric super-twisting control on Lie groups with application to spacecraft attitude tracking

Spacecraft control requires globally consistent formulations and robustness against model uncertainties and external disturbances. While a general intrinsic sliding-mode framework on Lie groups is available for first-order reaching, existing higher-order geometric sliding-mode formulations are predominantly developed for specific configuration groups or application models. This paper addresses the complementary problem of formulating a multivariable Super-Twisting reaching mechanism directly within a general Lie-group mechanical framework. The algorithm is formulated on the Lie algebra through covariant derivatives and builds upon the existing state-space Lie group structure. A strict Lyapunov analysis establishes finite-time convergence to the second-order sliding set and provides constructive gain conditions. Under suitable matching and regularity assumptions, exact rejection of matched disturbances is obtained, while the sliding dynamics ensure almost-global asymptotic tracking. The method is specialized to spacecraft attitude dynamics on SO(3) and assessed under nominal, disturbed, uncertain, and sampled-data conditions.