Monte Carlo Pose Estimation with Quaternion Kernels and the Bingham Distribution

Abstract

Abstract-The success of personal service robotics hinges upon reliable manipulation of everyday household objects, such as dishes, bottles, containers, and furniture. In order to accurately manipulate such objects, robots need to know objects' full 6-DOF pose, which is made difficult by clutter and occlusions. Many household objects have regular structure that can be used to effectively guess object pose given an observation of just a small patch on the object. In this paper, we present a new method to model the spatial distribution of oriented local features on an object, which we use to infer object pose given small sets of observed local features. The orientation distribution for local features is given by a mixture of Binghams on the hypersphere of unit quaternions, while the local feature distribution for position given orientation is given by a locally-weighted (Quaternion kernel) likelihood. Experiments on 3D point cloud data of cluttered and uncluttered scenes generated from a structured light stereo image sensor validate our approach.

Bingham Distribution-Based Linear Filter for Online Pose Estimation

“…Henebeck et al have recently developed a Bingham distribution-based recursive filtering approach for orientation estimation [9]. Glover et al [10] use Bingham distribution to describe the orientation features, while Hanebeck et al use this distribution for planar pose estimation [8]. Our work takes inspiration from these works for modeling the uncertainty in the orientation using Bingham distribution.…”

“…Our work takes inspiration from these works for modeling the uncertainty in the orientation using Bingham distribution. The use of Bingham distribution to model uncertainties in rotation parameters is a very valuable tool that has been largely under-utilized by the robotics community, as also noted by [10]. One of the important reasons for this, is the difficulty in computing the normalization constant as well as performing expensive convolution operation over the distributions [3]; which are both avoided in our approach.…”

“…The Bingham distribution is widely used to analyze paleomagnetic data [17], computer vision [12] and directional statistics [3] and recently in robotics [18,9,10,8].…”

“…Secondly, prior works deal with non-linear measurement models, hence resorting to unscented filtering. This results in computation of the normalization constant which is known to be expensive [10,18]. Our approach uses a linear model (as developed by Srivatsan et.…”

Tracking the spin on a ping pong ball with the quaternion Bingham filter

“…The Bingham distribution is commonly used as a distribution on 3-D rotations as unit quaternions [2], [9], [18]. Its density function (PDF) is given by…”