Pose-Following with Dual Quaternions

TL;DR

This paper introduces a novel dual quaternion-based control law for pose-following, enabling a rigid body to follow a spatial path with stable, full-body motion control and self-regulation of progress along the path.

Contribution

It extends existing pose-tracking methods into a pose-following control law with proven stability, applicable to full-body motion control in spatial paths.

Findings

Control law is almost globally asymptotically stable.

Validated in spatial and planar case studies.

Demonstrates benefits over traditional pose-tracking methods.

Abstract

This work focuses on pose-following, a variant of path-following in which the goal is to steer the system's position and attitude along a path with a moving frame attached to it. Full body motion control, while accounting for the additional freedom to self-regulate the progress along the path, is an appealing trade-off. Towards this end, we extend the well-established dual quaternion-based pose-tracking method into a pose-following control law. Specifically, we derive the equations of motion for the full pose error between the geometric reference and the rigid body in the form of a dual quaternion and dual twist. Subsequently, we formulate an almost globally asymptotically stable control law. The global attractivity of the presented approach is validated in a spatial example, while its benefits over pose-tracking are showcased through a planar case-study.