Dual-quaternion-based variable structure control: A new approach and application

Dual quaternion is a more efficient tool without singularity to describe rigid-body transformation than other tools, such as homogeneous transformation matrix. In this paper, we propose a new variable structure control (VSC) based on unit dual quaternion Lie-group for the transformation of rigid-bodies in configuration space. We set up the dynamic model of the rigid-body motion represented by unit dual quaternion after the geometric structure of dual quaternion is revealed, and then propose a new unit-dual-quaternion-based VSC controller, including a new switching function and a new reaching law. At last, the proposed controller is specified into the configuration space of planar robot and applied with the dynamic model of the NuBot omni-directional mobile robot in simulation to show its effectiveness.