Tag Archives: Quaternions

Implementation of spatial relations in graph-SLAM through quaternions instead of homogeneous matrices

Jiantong Cheng, Jonghyuk Kim, Zhenyu Jiang, Wanfang Che, Dual quaternion-based graphical SLAM, Robotics and Autonomous Systems, Volume 77, March 2016, Pages 15-24, ISSN 0921-8890, DOI: 10.1016/j.robot.2015.12.001.

This paper presents a new parameterization approach for the graph-based SLAM problem and reveals the differences of two popular over-parameterized ways in the optimization procedure. In the SALM problem, constraints or relative transformations between any two poses are generally separated into translations plus 3D rotations, which are then described in a homogeneous transformation matrix (HTM) to simplify computational operations. This however introduces added complexities in frequent conversions between the HTM and state variables, due to their different representations. This new approach, unit dual quaternion (UDQ), describes a spatial transformation as a screw with only 8 elements. We show that state variables can be directly represented by UDQs, and how their relative transformations can be written with the UDQ product, without the trivial computations of HTM. Then, we explore the performances of the unit quaternion and the axis–angle representations in the graph-based SLAM problem, which have been successfully applied to over parameterize perturbations under the assumption of small errors. Based on public synthetic and real-world datasets in 2D and 3D environments, experimental results show that the proposed approach reduces greatly the computational complexity while obtaining the same optimization accuracies as the HTM-based algorithm, and the axis–angle representation is superior to be the quaternion in the case of poor initial estimations.