Geometric Robot Dynamic Identification: A Convex Programming Approach

Recent work has shed light on the often unreliable performance of constrained least-squares estimation methods for robot mass-inertial parameter identification, particularly for high degree-of-freedom systems subject to noisy and incomplete measurements. Instead, differential geometric identification methods have proven to be significantly more accurate and robust. These methods account for the fact that the mass-inertial parameters reside in a curved Riemannian space, and allow perturbations in the mass-inertial properties to be measured in a coordinate-invariant manner. Yet, a continued drawback of existing geometric methods is that the corresponding optimization problems are inherently nonconvex, have numerous local minima, and are computationally highly intensive to solve. In this paper, we propose a convex formulation under the same coordinate-invariant Riemannian geometric framework that directly addresses these and other deficiencies of the geometric approach. Our convex formulation leads to a globally optimal solution, reduced computations, faster and more reliable convergence, and easy inclusion of additional convex constraints. The main idea behind our approach is an entropic divergence measure that allows for the convex regularization of the inertial parameter identification problem. Extensive experiments with the 3-DoF MIT Cheetah leg, the 7-DoF AMBIDEX tendon-driven arm, and a 16-link articulated human model show markedly improved robustness and generalizability vis-a-vis existing vector space methods while ensuring fast, guaranteed convergence to the global solution.