A four-DOF Lagrangian approach to attitude tracking

Abstract

This paper presents a novel Lagrangian approach to attitude tracking for rigid bodies. The 4-DOF Lagrangian dynamics presented in this paper describes the rotational rigid motion on the unit sphere. Energy conservation property is explored, which holds on the entire unit quaternion group. This enables one to address the full attitude control problem where the attitude may evolve on the entire rotation group and to design controllers to track any desired attitude by leveraging the rich literature on energy-shaping based control methodology in Euclidean space. Global exponential tracking on the unit quaternion group is achieved using a simple potential function. In addition, the adaptive technique is used to deal with unknown on-orbit torque disturbances and uncertainties of the inertia matrix. Simulations are included to illustrate the theoretical results.