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.Comment: This paper has been accepted for publication at the IEEE Conference
on Decision and Control (CDC), 2023. Copyright @ IEE