Point Cloud Registration for Assembly using Conformal Geometric Algebra

Abstract

This thesis is a collection of five journal papers and one conference paper. The thesis is on pose alignment and point correspondence estimation for 3D point clouds, and inverse kinematics of industrial robots. The approaches proposed in this thesis are based on conformal geometric algebra, which is an extension of Euclidean geometry which enables efficient descrition of geometric objects such as line, plane and sphere geometry, as well the calculation of the intersection between such objects. The thesis presents a novel approach for the initial alignment between two point clouds called the Curvature-Based Descriptor. The curvature-based descriptor is a descriptor which describes the local curvature around a point in the point cloud. The local curvature is expressed with two spheres generated using conformal geometric algebra. The thesis also presents preprocessing steps which are used to segment the point cloud to extract only the parts of the point cloud that are necessary for the alignment, and a keypoint extraction method which extracts certain points from the point cloud, making the point correspondence more accurate. The inverse kinematics presented in this thesis is an analytic solution which uses conformal geometric algebra. The solution is presented for the Kuka KR6 R900 sixx robot and the Universal Robots UR5 robot. All singularities and all configurations are accounted for in the solutions. The thesis has several experimental results. These experiments are presented in each paper, and show the results from various methods performing point cloud alignment. The results show that it is possible to achieve a sub-millimeter accuracy for position estimation of an object using state-of-the-art methods when using both 3D and 2D cameras combined. The results also show that the curvature-based alignment method, after applying the preprocessing steps presented in the thesis, achieve a sub-millimeter accuracy on its own, an accuracy that is not achieved with any of the other 3D alignment methods.