用几何代数方法高效解析机器人惯性基参数，提升识别精度与速度。
A Geometric Method for Base Parameter Analysis in Robot Inertia Identification Based on Projective Geometric Algebra
- 基于投影几何代数重构动力学模型，导出可闭式求解的系数。
- 提出三项基础原理，实现基参数自动识别，算法复杂度理论最优。
- 在4类机器人上验证有效，尤其对并联机构表现鲁棒高效。
本文提出一种新颖的几何方法，用于解析确定机器人系统的基惯性参数。通过投影几何代数重写刚体动力学，构建了名为“四面点（TP）”的新识别模型。基于刚体TP模型，推导出识别模型中回归矩阵系数的闭式表达式，并具有清晰的几何意义。从动力学模型直接出发，提出了三项基础分析原则：共点原则、定点原则和平面旋转原则。据此开发了自动确定所有基参数的算法。核心算法——动力学回归矩阵零空间生成器（DRNG），在完成O(N)预处理后，理论上达到O(1)复杂度，其中N为刚体数量。所提方法及算法在四种机器人系统上得到验证：Puma560、Unitree Go2、2RRU-1RRS并联机构（PKM）和2PRS-1PSR PKM。所有案例中，算法均成功识别出完整的基参数集。特别地，该方法在并联机构案例中表现出高度鲁棒性与计算效率。综合演示表明，该方法具有通用性、鲁棒性和高效性。
原文摘要 · Abstract (English)
This paper proposes a novel geometric method for analytically determining the base inertial parameters of robotic systems. The rigid body dynamics is reformulated using projective geometric algebra, leading to a new identification model named ``tetrahedral-point (TP)" model. Based on the rigid body TP model, coefficients in the regresoor matrix of the identification model are derived in closed-form, exhibiting clear geometric interpretations. Building directly from the dynamic model, three foundational principles for base parameter analysis are proposed: the shared points principle, fixed points principle, and planar rotations principle. With these principles, algorithms are developed to automatically determine all the base parameters. The core algorithm, referred to as Dynamics Regressor Nullspace Generator (DRNG), achieves $O(1)$-complexity theoretically following an $O(N)$-complexity preprocessing stage, where $N$ is the number of rigid bodies. The proposed method and algorithms are validated across four robots: Puma560, Unitree Go2, a 2RRU-1RRS parallel kinematics mechanism (PKM), and a 2PRS-1PSR PKM. In all cases, the algorithms successfully identify the complete set of base parameters. Notably, the approach demonstrates high robustness and computational efficiency, particularly in the cases of PKMs. Through the comprehensive demonstrations, the method is shown to be general, robust, and efficient.
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