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$\mathbb{R}^{3}$is used for the translation estimation, and the real spherical harmonics in$\boldsymbol{SO}(3)$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.

Handling object deformations for robotic grasping is still a major problem to solve. In this paper, we propose an efficient learning-free solution for this problem where generated grasp hypotheses of a region of an object are adapted to its deformed configurations. To this end, we investigate the applicability of functional map (FM) correspondence, where the shape matching problem is treated as searching for correspondences between geometric functions in a reduced basis. For a user selected region of an object, a ranked list of grasp candidates is generated with local contact moment (LoCoMo) based grasp planner. The proposed FM-based methodology maps these candidates to an instance of the object that has suffered arbitrary level of deformation. The best grasp, by analysing its kinematic feasibility while respecting the original finger configuration as much as possible, is then executed on the object. We have compared the performance of our method with two different state-of-the-art correspondence mapping techniques in terms of grasp stability and region grasping accuracy for 4 different objects with 5 different deformations.

This paper presents a spectral correlation-based method (SpectGRASP) for robotic grasping of arbitrarily shaped, unknown objects. Given a point cloud of an object, SpectGRASP extracts contact points on the object’s surface matching the hand configuration. It neither requires offline training nor a-priori object models. We propose a novel Binary Extended Gaussian Image (BEGI), which represents the point cloud surface normals of both object and robot fingers as signals on a 2-sphere. Spherical harmonics are then used to estimate the correlation between fingers and object BEGIs. The resulting spectral correlation density function provides a similarity measure of gripper and object surface normals. This is highly efficient in that it is simultaneously evaluated at all possible finger rotations in SO(3). A set of contact points are then extracted for each finger using rotations with high correlation values. We then use our previous work, Local Contact Moment (LoCoMo) similarity metric, to sequentially rank the generated grasps such that the one with maximum likelihood is executed. We evaluate the performance of SpectGRASP by conducting experiments with a 7-axis robot fitted with a parallel-jaw gripper, in a physics simulation environment. Obtained results indicate that the method not only can grasp individual objects, but also can successfully clear randomly organized groups of objects. The SpectGRASP method also outperforms the closest state-of-the-art method in terms of grasp generation time and grasp-efficiency.