Orientation Uncertainty Characteristics of Some Pose Measuring Systems.

Marek Franaszek,Geraldine S Cheok

doi:10.1155/2017/2696108

Marek Franaszek, Geraldine S Cheok

Open Access

https://doi.org/10.1155/2017/2696108

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Abstract

We investigate the performance of pose measuring systems which determine an object’s pose from measurement of a few fiducial markers attached to the object. Such systems use point-based, rigid body registration to get the orientation matrix. Uncertainty in the fiducials’ measurement propagates to the uncertainty of the orientation matrix. This orientation uncertainty then propagates to points on the object’s surface. This propagation is anisotropic, and the direction along which the uncertainty is the smallest is determined by the eigenvector associated with the largest eigenvalue of the orientation data’s covariance matrix. This eigenvector in the coordinate frame defined by the fiducials remains almost fixed for any rotation of the object. However, the remaining two eigenvectors vary widely and the direction along which the propagated uncertainty is the largest cannot be determined from the object’s pose. Conditions that result in such a behavior and practical consequences of it are presented.

Highlights

The pose of a rigid object is defined by six degrees of freedom (6DOF): three angles describing the object’s orientation matrix R and three components describing the object’s position τ
When the Computer Aided Design (CAD) model of an object is known, the location of any Point of Interest (POI) can be calculated using 6DOF data acquired by pose measuring systems [3]
The angular distribution of the orientation uncertainty propagated to a POI depends generally on the object’s orientation

Summary

Introduction

The pose of a rigid object is defined by six degrees of freedom (6DOF): three angles describing the object’s orientation matrix R and three components describing the object’s position τ (e.g., center of mass or center of bounding box). Accounting for the uncertainty of the measured pose is of great importance in many applications (e.g., propagating uncertainty along different joints in a robot arm or fusing measurements from multiple sensors) and it has been studied for a long time [1]. We are interested in how uncertainty of a single static measurement of a rigid body pose propagates to any Point of Interest (POI) associated with the object (e.g., a point on its surface). When the Computer Aided Design (CAD) model of an object is known, the location of any POI can be calculated using 6DOF data acquired by pose measuring systems [3]. In assembly applications where rigid parts need to be mated using autonomous robotic systems [4,5,6,7,8], uncertainty in pose has to be propagated to the POI

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