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.