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 article presents a particle filter for pose estimation using unit dual quaternion kinematics. The eight-parameter unit dual quaternion is used for global representation of the pose, whereas the six parameters of the dual modified Rodrigues parameters (MRPs) are used for local pose representation in the state-space model. The dual MRPs enable estimates of the mean and the covariance to be calculated from the particles without violating the algebraic constraint of the unit dual quaternion. For verification of the filter and comparison with state of the art, we consider pose measurements available in the form of unit dual quaternions. Angular velocity and specific force measurements from a body-mounted inertial measurement unit are also considered in the filtering. We show through simulations that the suggested particle filter has comparable accuracy with a previously proposed unscented Kalman filter based on unit dual quaternions. We also consider a practical application where the pose of an arbitrary rigid object is estimated using a sequence of point clouds from a 3-D camera. A model point cloud of the object is displaced with the unit dual quaternion associated with each particle, and a fitting score is calculated between the displaced model point cloud and the measured point cloud from the 3-D camera. The likelihoods of the fitting scores are calculated from an exponential distribution and are used to update the weights of the particles. The system was verified in an experiment where the motion of a swinging payload hanging from a crane was estimated using a 3-D camera.
This paper presents a method for pose estimation of a rigid body using unit dual quaternions where pose measurements from point clouds are filtered with a multiplicative extended Kalman filter (MEKF). The point clouds come from a 3D camera fixed to the moving rigid body, and then consecutive point clouds are aligned with the Iterative Closest Point (ICP) algorithm to obtain pose measurements. The unit constraint of the dual quaternion is ensured in the filtering process with the Dual Quaternion MEKF (DQ-MEKF), where the measurement updates are performed using the dual quaternion product so that the result is a unit dual quaternion. In addition, we use the Cayley transform for the discrete time propagation of the DQ-MEKF estimate, eliminating the need for normalization and projection of the resulting unit dual quaternion. The ICP algorithm is initialized with the time propagated state of the filter to give faster and more accurate pose measurements. To further improve the accuracy of the initialization, angular velocity measurements from a gyroscope fixed to the camera are included in the filter. The proposed method has been tested in experiments using a Kinect v2 3D camera mounted rigidly on a KUKA KR6 robotic arm, while a customized ICP algorithm was successfully implemented on a Graphical Processing Unit (GPU) system.
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