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.

该研究论文探讨了在机器人系统中运用惯性参数的建模和识别方法，提出了一种基于线性矩阵不等式的物理一致性约束方法，能够提高收敛速度和抵抗噪声干扰，并且通过标准半定规划实现对底盘组件的参数优化。

基于线性矩阵不等式的惯性参数物理一致性辨识：对质量分配的统计视角

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

This paper presents a new condition, the fully physical consistency for a set
of inertial parameters to determine if they can be generated by a physical
rigid body. The proposed condition ensure both the positive definiteness and
the triangular inequality of 3D inertia matrices as opposed to existing
techniques in which the triangular inequality constraint is ignored. This paper
presents also a new parametrization that naturally ensures that the inertial
parameters are fully physical consistency. The proposed parametrization is
exploited to reformulate the inertial identification problem as a manifold
optimization problem, that ensures that the identified parameters can always be
generated by a physical body. The proposed optimization problem has been
validated with a set of experiments on the iCub humanoid robot.

本文提出了一种新的条件，即完全物理一致性，用于确定一组惯性参数是否可由物理刚体生成；提出的条件保证三维惯性矩阵的正定性和三角不等式。本文还提出了一种新的参数化方法，自然保证惯性参数完全符合物理一致性。利用该参数化方法，将惯性识别问题重新表示为流形优化问题，从而保证识别出的参数始终可以被物理刚体所生成。在 iCub 人形机器人上进行了一系列实验，验证了所提出的优化问题。