Computational geometric system identification for the attitude dynamics on SO(3)

A computational approach for system identification for the attitude dynamics of a rigid body is proposed. The estimation and system identification for the rigid body are particularly challenging as they evolve on the compact nonlinear manifold, referred to as the special orthogonal group. Current methods based on local parameterizations or quaternions suffer from inherent singularities or ambiguities associated with them. The proposed method addresses these issues by formulating the system identification problem as an optimization problem on the special orthogonal group. It is solved by a geometric numerical integrator that yields numerical trajectories that are consistent with the geometric structures of Hamiltonian systems on a Lie group. As a result, the proposed method is particularly useful to handle large initial estimation errors that may cause substantial discrepancies between the target attitude trajectories and the initial estimate of them. These are illustrated by numerical examples.