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This paper presents a spectral domain registration-based visual servoingscheme that works on 3D point clouds. Specifically, we propose a 3D model/pointcloud alignment method, which works by finding a global transformation betweenreference and target point clouds using spectral analysis. A 3D Fast FourierTransform (FFT) in R3 is used for the translation estimation, and the realspherical harmonics in SO(3) are used for the rotations estimation. Such anapproach allows us to derive a decoupled 6 degrees of freedom (DoF) controller,where we use gradient ascent optimisation to minimise translation androtational costs. We then show how this methodology can be used to regulate arobot arm to perform a positioning task. In contrast to the existingstate-of-the-art depth-based visual servoing methods that either require densedepth maps or dense point clouds, our method works well with partial pointclouds and can effectively handle larger transformations between the referenceand the target positions. Furthermore, the use of spectral data (instead ofspatial data) for transformation estimation makes our method robust tosensor-induced noise and partial occlusions. We validate our approach byperforming experiments using point clouds acquired by a robot-mounted depthcamera. Obtained results demonstrate the effectiveness of our visual servoingapproach.

3D Spectral Domain Registration-Based Visual Servoing