Linear Matrix Inequalities for Physically-Consistent Inertial Parameter Identification: A Statistical Perspective on the Mass Distribution

摘要

With the increased application of model-based whole-body control in leggedrobots, there has been a resurgence of research interest into methods foraccurate system identification. An important class of methods focuses on theinertial parameters of rigid-body systems. These parameters consist of themass, first mass moment (related to center of mass location), and rotationalinertia matrix of each link. The main contribution of this paper is toformulate physical-consistency constraints on these parameters as Linear MatrixInequalities (LMIs). The use of these constraints in identification canaccelerate convergence and increase robustness to noisy data. It is criticallyobserved that the proposed LMIs are expressed in terms of the covariance of themass distribution, rather than its rotational moments of inertia. With thisperspective, connections to the classical problem of moments in mathematics areshown to yield new bounding-volume constraints on the mass distribution of eachlink. While previous work ensured physical plausibility or used convexoptimization 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 linkinertias, with parameter optimization carried out to global optimality throughsemidefinite programming.