Research on the rigid body pose estimation using dual quaternions

Abstract

The dual quaternion is the simplest and most effective mathematical tool to describe the translational and rotational motion of a general rigid body. Its computation and updating require screw vector. The relative pose information need to be updated when measuring the pose of the rigid body. In the traditional algorithm, it generally focuses on attitude updating, but less research on position updating. The rotation vector algorithm is used to represent the quaternion to update the attitude of the rigid body, but it cannot update the position. Because any general rigid body motion can be realized by rotation about a certain axis and translation along this axis, this article proposes an algorithm to update the position and attitude of the rigid body’s relative motion based on the screw vector. The rotation vector and screw vector are introduced in the rigid body motion and update the quaternion and dual quaternion, respectively; then, the relative pose information of the leader–follower rigid body based on the screw vector algorithm is deduced. The single-sample, two-sample, and three-sample algorithms are compared and simulated, and the simulation results show that this method not only overcomes the deficiencies associated with the separate updating of position and attitude using a traditional algorithm but also has higher precision than the traditional algorithm.