Velocity-Free Attitude Tracking for Lost-in-Space Spacecraft

The inertial reference vectors, such as star vectors and sun vector, are usually assumed to be known in the inertial frame for spacecraft attitude estimation and control problems, and can be measured by onboard sensors. When the information of reference vectors in the inertial frame cannot be obtained for attitude determination and no priori information about the spacecraft attitude is available, i.e., the spacecraft is lost in space, conducting attitude tracking is challenging, especially in the absence of velocity measurements. To address this problem, we develop an attitude tracking method for rigid spacecraft based on the foundational theory of the gradient-based algorithms on Lie groups. Firstly, a gradient-based velocity observer is developed on $SO(3)$, whose state is augmented with inertial reference vectors. At an appropriate time, we use the attitude estimate from the observer to develop an auxiliary inertial frame. Following this, we then develop a gradient-based attitude tracking controller with proportional-derivative (PD) plus feedforward form, to drive the spacecraft towards a specifically designed attitude motion trajectory. With the auxiliary frame, we transform the requirement of absolute desired attitude information with respect to the inertial frame, to that of relative information associated with the artificial reference frame. The proposed observer-controller combination differs from classical algorithms mainly in the sense that the inertial frame is not known a priori and an auxiliary frame is introduced for tracking. Both rigorous analysis of the stability property and simulation results are presented to verify the effectiveness of the proposed algorithm.