Quaternion-based Finite-time Control for Attitude Tracking of the Spacecraft without Unwinding

This paper investigates two finite-time controllers for the attitude tracking control of the spacecraft based on the quaternion by terminal sliding mode control. Because quaternion is unable to represent the set of attitudes both globally and uniquely, it can result in unwinding. Unwinding makes a spacecraft perform an unnecessary large-angle maneuver when a small-angle maneuver in the opposite rotational direction is sufficient to achieve the objective. The first controller converges to the equilibrium without singularity in finite time, while the second one converges to the region near the equilibrium without singularity, chattering and unwinding in finite time. Saturation function is introduced to the first controller to eliminate singularity, while a novel fast terminal sliding mode control is introduced to the second controller to eliminate singularity and unwinding. Theoretical analysis shows that the controllers can make the spacecraft follow a time-varying reference attitude signal in finite time and guarantee the stability of the overall closed-loop system. Numerical simulations also demonstrate the effectiveness of the proposed control schemes.