A Geometric Algorithm for Robust Multibody Inertial Parameter Identification

Notwithstanding the seemingly straightforward nature of the inertial parameter identification problem for multibody systems-the most common formulation is as a linear least-squares estimation problem-existing methods, especially for complex high-dof systems subject to nonpersistent and noisy measurements, tend to be highly sensitive to the choice of initial values, and more often than not converge to ad hoc solutions that lie on arbitrary user-specified boundaries. We argue in this letter that such ill-posed behavior is traceable in large part to the use of the standard Euclidean metric in the regularized least-squares error criterion. We instead make use of the fact that the collection of inertial parameters constitutes a Riemannian manifold with a naturally defined Riemannian metric. By formulating and minimizing a coordinate-invariant error criterion based on this natural Riemannian metric, we show that accuracy and robustness of the identification can be vastly improved. Experiments involving high-dof humanoid structures are presented to validate our method and claims.