Unit Dual-Quaternion Parametrisation for Graph SLAM

This paper presents a new parameterisation approach for the graph-based SLAM problem utilising unit dual-quaternion. The rigid-body transformation typically consists of the robot position and rotation, and due to the Lie-group nature of the rotation, a homogeneous transformation matrix (HTM) has been widely used in pose-graph optimizations. In this paper, we investigate the use of unit dual-quaternion (UDQ) for SLAM problem, providing a unified representation of the robot poses with computational and storage benefits. Although UDQ has been widely used in kinematics and navigation (known as Michel Chasles’ theorem or Skrew motion), it has not been well utilised in the graph SLAM optimisation. In this work, we re-parameterise the graph SLAM problem using UDQs, focusing on the optimisation performance and the sensitivity to poor initial estimates. Experimental results on public synthetic and real-world datasets show that the proposed approach significantly reduces the computational complexity, whilst retaining the similar accuracies compared to the HTM-based one. With the poor initial estimates, it is also shown that the rotation vector-based perturbation is more stable than the quaternion-based in recovering the error dual-quaternion.