This paper shows how the recently developed formulation of conformal geometric algebra can be used for analytic inverse kinematics of two six-link industrial manipulators with revolute joints. The paper demonstrates that the solution of the inverse kinematics in this framework relies on the intersection of geometric objects like lines, circles, planes and spheres, which provides the developer with valuable geometric intuition about the problem. It is believed that this will be very useful for new robot geometries and other mechanisms like cranes and topside drilling equipment. The paper extends previous results on inverse kinematics using conformal geometric algebra by providing consistent solutions for the joint angles for the different configurations depending on shoulder left or right, elbow up or down, and wrist flipped or not. Moreover, it is shown how to relate the solution to the Denavit-Hartenberg parameters of the robot. The solutions have been successfully implemented and tested extensively over the whole workspace of the manipulators.

This paper presents a method for coarse alignment of point clouds by introducing a new descriptor based on the local curvature. The method is developed for model fitting a CAD model for use in robotic assembly. The method is based on selecting keypoints depending on shape factors calculated from the local covariance matrix of the surface. A descriptor is then calculated for each keypoint by fitting two spheres that describe the curvature of the surface. The spheres are calculated using conformal geometric algebra, which gives a convenient and efficient description of the geometry. The keypoint descriptors for the model and the observed point cloud are then compared to estimate the corresponding keypoints, which are used to calculate the displacement. The method is tested in several experiments. One experiment is for robotic assembly, where objects are placed on a table and their position and orientation is estimated using a 3D CAD model.

Abstract. This paper presents an approach for detecting primitive geometric objects in point clouds captured from 3D cameras. Primitive objects are objects that are well defined with parameters and mathematical relations, such as lines, spheres and ellipsoids. RANSAC, a robust parameter estimator that classifies and neglects outliers, is used for object detection. The primitives considered are modeled, filtered and fitted using the conformal model of geometric algebra. Methods for detecting planes, spheres and cylinders are suggested. Least squares fitting of spheres and planes to point data are done analytically with conformal geometric algebra, while a cylinder is fitted by defining a nonlinear cost function which is optimized using a nonlinear least squares solver. Furthermore, the suggested object detection scheme is combined with an octree sampling strategy that results in fast detection of multiple primitive objects in point clouds.

This paper presents a descriptor for course alignment of point clouds using conformal geometric algebra. The method is based on selecting keypoints depending on shape factors to identify distinct features of the object represented by the point cloud, and a descriptor is then calculated for each keypoint by fitting two spheres that describe the local curvature. The method for estimating the point correspondences is to a larger extent based on geometric arguments than the method of Kleppe et al. (IEEE Trans Autom Sci Eng, 2017), which results in improved performance. The accuracy of the curvature-based descriptor is validated in experiments, and is shown to compare favorably to stateof-the-art methods in an experiment on course alignment of industrial parts to be assembled with robots.

2D and 3D computer vision systems are frequently being used in automated production to detect and determine the position of objects. Accuracy is important in the production industry, and computer vision systems require structured environments to function optimally. For 2D vision systems, a change in surfaces, lighting and viewpoint angles can reduce the accuracy of a method, maybe even to a degree that it will be erroneous, while for 3D vision systems, the accuracy mainly depends on the 3D laser sensors. Commercially available 3D cameras lack the precision found in high-grade 3D laser scanners, and are therefore not suited for accurate measurements in industrial use. In this paper, we show that it is possible to identify and locate objects using a combination of 2D and 3D cameras. A rough estimate of the object pose is first found using a commercially available 3D camera. Then, a robotic arm with an eye-in-hand 2D camera is used to determine the pose accurately. We show that this increases the accuracy to < 1 mm and < 1 • . This was demonstrated in a real industrial assembly task where high accuracy is required.