This paper presents a spectral domain registration-based visual servoing scheme that works on 3D point clouds. Specifically, we propose a 3D model/point cloud alignment method, which works by finding a global transformation between reference and target point clouds using spectral analysis. A 3D Fast Fourier Transform (FFT) in R3 is used for the translation estimation, and the real spherical harmonics in SO(3) are used for the rotations estimation. Such an approach allows us to derive a decoupled 6 degrees of freedom (DoF) controller, where we use gradient ascent optimisation to minimise translation and rotational costs. We then show how this methodology can be used to regulate a robot arm to perform a positioning task. In contrast to the existing state-of-the-art depth-based visual servoing methods that either require dense depth maps or dense point clouds, our method works well with partial point clouds and can effectively handle larger transformations between the reference and the target positions. Furthermore, the use of spectral data (instead of spatial data) for transformation estimation makes our method robust to sensor-induced noise and partial occlusions. We validate our approach by performing experiments using point clouds acquired by a robot-mounted depth camera. Obtained results demonstrate the effectiveness of our visual servoing approach.

翻译：本文提出一种基于谱域配准的视觉伺服方案，该方案适用于三维点云。具体而言，我们提出一种三维模型/点云对齐方法，通过谱分析在参考点云与目标点云之间寻找全局变换。其中，采用R3空间中的三维快速傅里叶变换（FFT）进行平移估计，并利用SO(3)空间中的实球谐函数进行旋转估计。该方法使我们能够推导出一个解耦的六自由度（DoF）控制器，通过梯度上升优化算法最小化平移与旋转代价。随后展示了如何将此方法应用于机械臂定位任务的调节控制。与现有最先进的基于深度图像的视觉伺服方法（需密集深度图或密集点云）不同，本方法在部分点云场景下仍能有效工作，并可稳健处理参考位置与目标位置间的大尺度变换。此外，采用谱域数据（而非空间域数据）进行变换估计，使本方法对传感器噪声和局部遮挡具有鲁棒性。我们通过搭载于机械臂的深度相机采集点云数据开展实验验证，结果证明了所提视觉伺服方法的有效性。