  With the increased application of model-based whole-body control in legged
robots, there has been a resurgence of research interest into methods for
accurate system identification. An important class of methods focuses on the
inertial parameters of rigid-body systems. These parameters consist of the
mass, first mass moment (related to center of mass location), and rotational
inertia matrix of each link. The main contribution of this paper is to
formulate physical-consistency constraints on these parameters as Linear Matrix
Inequalities (LMIs). The use of these constraints in identification can
accelerate convergence and increase robustness to noisy data. It is critically
observed that the proposed LMIs are expressed in terms of the covariance of the
mass distribution, rather than its rotational moments of inertia. With this
perspective, connections to the classical problem of moments in mathematics are
shown to yield new bounding-volume constraints on the mass distribution of each
link. While previous work ensured physical plausibility or used convex
optimization in identification, the LMIs here uniquely enable both advantages.
Constraints are applied to identification of a leg for the MIT Cheetah 3 robot.
Detailed properties of transmission components are identified alongside link
inertias, with parameter optimization carried out to global optimality through
semidefinite programming.
