Finite-Time Attitude Trajectory Tracking Control of Rigid Spacecraft

In this paper, we investigate the finite-time attitude tracking control problem for a rigid spacecraft on the special orthogonal group (
$SO(3)$
). The exponential coordinates, derived from the exponential and logarithmic maps of Lie group, are utilized to describe the attitude tracking error on
$SO(3)$
almost globally unique except for a zero measure set on which the logarithmic map is double valued. To avoid this issue, a novel nonsingular sliding surface is designed to guarantee that the attitude tracking error will never reach the zero measure set and provide fixed-time stability during the sliding phase. Then, a novel continuous second-order sliding mode control scheme is developed to force the system state to reach the desired sliding surface in finite time. The salient feature of the proposed control scheme is that it significantly suppresses the chattering phenomenon. In addition, to address the lack of angular velocity measurements, a finite-time observer is proposed to recover the unknown angular velocity information in finite time. Then, an observer-based finite-time output feedback control strategy is obtained. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed control scheme.