This paper presents a direct 3D visual servo scheme for the automatic alignment of point clouds (respectively, objects) using visual information in the spectral domain. Specifically, we propose an alignment method for 3D models/point clouds that works by estimating the global transformation between a reference point cloud and a target point cloud using harmonic domain data analysis. A 3D discrete Fourier transform (DFT) in $\mathbb{R}^3$ is used for translation estimation and real spherical harmonics in $SO(3)$ are used for rotation estimation. This approach allows us to derive a decoupled visual servo controller with 6 degrees of freedom. We then show how this approach can be used as a controller for a robotic arm to perform a positioning task. Unlike existing 3D visual servo methods, our method works well with partial point clouds and in cases of large initial transformations between the initial and desired position. Additionally, using spectral data (instead of spatial data) for the transformation estimation makes our method robust to sensor-induced noise and partial occlusions. Our method has been successfully validated experimentally on point clouds obtained with a depth camera mounted on a robotic arm.

翻译：本文提出了一种直接三维视觉伺服方案，利用谱域视觉信息实现点云（或物体）的自动对齐。具体而言，我们提出了一种基于谐域数据分析的三维模型/点云对齐方法，通过估计参考点云与目标点云之间的全局变换来实现。其中，使用 $\mathbb{R}^3$ 中的三维离散傅里叶变换（DFT）进行平移估计，并利用 $SO(3)$ 中的实球谐函数进行旋转估计。该方法可推导出一个六自由度的解耦视觉伺服控制器。随后，我们展示了如何将该方法作为机械臂的控制器实现定位任务。与现有三维视觉伺服方法不同，本方法在部分点云场景以及初始位置与期望位置存在较大初始变换时仍能有效工作。此外，采用谱域数据（而非空间域数据）进行变换估计，使方法对传感器噪声和部分遮挡具有较强的鲁棒性。通过在安装在机械臂上的深度相机获取的点云上进行的实验验证，证明了该方法的有效性。