The paper analyzes the rotation averaging problem as a minimization problem for a potential function of the corresponding gradient system. This dynamical system is one generalization of the famous Kuramoto model on special orthogonal group SO(3), which is known as the non-Abelian Kuramoto model. We have proposed a novel method for finding weighted and unweighted rotation average. In order to verify the correctness of our algorithms, we have compared the simulation results with geometric and projected average using real and random data sets. In particular, we have discovered that our method gives approximately the same results as geometric average.

翻译：本文将平均旋转问题分析为相应梯度系统潜在功能的最小化问题。 这个动态系统是著名的Kuramoto特殊正统组SO(3)模型(称为非Abelian Kuramoto模型)的概括。 我们提出了一种新颖的方法来寻找加权和未加权的旋转平均值。 为了验证我们的算法的正确性, 我们用真实和随机数据集将模拟结果与几何和预测平均数进行了比较。 我们发现我们的方法与几何平均数大致相同。