Homogeneous Finite-time Tracking Control on Lie Algebra so(3)

An attitude tracking problem for a full-actuated rigid body in 3-D is studied using a model of rotation dynamics on the Lie group SO (3). A generalized homogeneous control is adopted to achieve tracking of a smooth attitude trajectory in a finite-time. The attitude dynamics on the Lie algebra so(3) is utilized to design the homogeneous control, since SO (3) is not a vector space. A switch control is proposed for achieving global finite-time tracking by combining a global asymptotic control with local homogeneous control. The simulations illustrate the performance of the proposed control algorithm.