Attitude control strategies overcoming the topological obstruction on SO(3)

Abstract

Global tracking strategies are presented for the attitude dynamics of a rigid body. Due to the inherent topological restriction, it is impossible to achieve global attractivity with any continuous attitude control system on the special orthogonal group. Recently, the topological restriction has been dealt with switching between multiple configuration error functions according to the hybrid system framework. This paper proposes an alternative attitude control strategy to achieve exponential stability where the region of attraction covers the entire special orthogonal group. This is achieved by the novel ideal of adjusting the desired attitude trajectory via a conjugacy class. The unique contribution is that the topological restriction in attitude controls is addressed without introducing discontinuities with respect to time.