In this paper, a comparison analysis between geometric impedance controls (GICs) derived from two different potential functions on SE(3) for robotic manipulators is presented. The first potential function is defined on the Lie group, utilizing the Frobenius norm of the configuration error matrix. The second potential function is defined utilizing the Lie algebra, i.e., log-map of the configuration error. Using a differential geometric approach, the detailed derivation of the distance metric and potential function on SE(3) is introduced. The GIC laws are respectively derived from the two potential functions, followed by extensive comparison analyses. In the qualitative analysis, the properties of the error function and control laws are analyzed, while the performances of the controllers are quantitatively compared using numerical simulation.

翻译：本文针对机器人操作器在SE(3)空间中由两种不同势函数导出的几何阻抗控制进行了比较分析。第一种势函数定义于李群之上，利用构型误差矩阵的Frobenius范数；第二种势函数则基于李代数定义，即构型误差的对数映射。采用微分几何方法，详细介绍了SE(3)上距离度量和势函数的推导过程。分别从两种势函数导出几何阻抗控制律，并进行了全面的比较分析。在定性分析中，对误差函数和控制律的特性进行了分析；通过数值仿真定量比较了控制器的性能。