Efficient Graph-SLAM optimization using unit dual-quaternions

This paper presents a new parameterization 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 has been widely used in pose-graph optimizations. In this paper, we investigate the use of unit dual-quaternion for SLAM problem, providing a unified representation of the robot poses with computational and storage benefits. Although unit dual-quaternion has been widely used in robot kinematics and navigation (known also as Michel Chasles´ theorem), it has not been well utilised in the graph SLAM optimization. In this work, we re-parameterize the graph SLAM problem with dual-quaternions, investigating the optimization 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 map accuracies compared to the homogeneous transform matrix-based one.