Survey of SO(3)-based spacecraft attitude error description methods

To address the issues of mathematical complexity and lack of physical clarity in manifold-based spacecraft attitude modeling methods, this paper conducts a comprehensive analysis of spacecraft attitude error description methods and their characteristics on manifolds. Firstly, a rigid-body spacecraft attitude model is established based on the three-dimensional special orthogonal group (SO(3)) on manifolds. Subsequently, three common error description methods on SO(3) are presented from the perspectives of Riemannian manifolds and Lie groups. The different algebraic characteristics among these three error description frameworks are then analyzed using differential geometry theory and numerical simulation tools. Finally, based on a geometric proportional-derivative (PD) controller, the response characteristics of the three error description methods under the same control law are verified through simulations, providing theoretical support for the design and engineering application of attitude controllers.