The non-commutative nature of 3D rotations poses well-known challenges in generalizing planar problems to three-dimensional ones, even more so in contact-rich tasks where haptic information (i.e., forces/torques) is involved. In this sense, not all learning-based algorithms that are currently available generalize to 3D orientation estimation. Non-linear filters defined on $\mathbf{\mathbb{SO}(3)}$ are widely used with inertial measurement sensors; however, none of them have been used with haptic measurements. This paper presents a unique complementary filtering framework that interprets the geometric shape of objects in the form of superquadrics, exploits the symmetry of $\mathbf{\mathbb{SO}(3)}$, and uses force and vision sensors as measurements to provide an estimate of orientation. The framework's robustness and almost global stability are substantiated by a set of experiments on a dual-arm robotic setup.

翻译：三维旋转的非交换特性为将平面问题推广至三维问题带来了众所周知的挑战，在涉及触觉信息（即力/力矩）的接触密集型任务中尤为如此。从这个意义上说，并非所有现有的基于学习的算法都能推广至三维姿态估计。定义在 $\mathbf{\mathbb{SO}(3)}$ 上的非线性滤波器已广泛用于惯性测量传感器，但尚未有研究将其与触觉测量结合。本文提出了一种独特的互补滤波框架，该框架以超二次曲面的形式解释物体的几何形状，利用 $\mathbf{\mathbb{SO}(3)}$ 的对称性，并采用力传感器与视觉传感器作为测量手段以提供姿态估计。通过在一套双臂机器人系统上进行的一系列实验，验证了该框架的鲁棒性与近乎全局稳定性。