Quaternion Sliding Variables in Manipulator Control

TL;DR

This paper introduces two quaternion-based sliding variables for manipulator end-effector orientation control, offering singularity-free, globally convergent error dynamics that avoid unwinding, enhancing full operational envelope movement.

Contribution

It proposes novel quaternion sliding variables for manipulator control that are globally stable and free of singularities, improving upon existing orientation representations.

Findings

Both sliding variables are free of singularities.

The stability results are global, not just almost global.

The approach enables full operational envelope movement without unwinding.

Abstract

We present two quaternion-based sliding variables for controlling the orientation of a manipulator's end-effector. Both sliding variables are free of singularities and represent global exponentially convergent error dynamics that do not exhibit unwinding when used in feedback. The choice of sliding variable is dictated by whether the end-effector's angular velocity vector is expressed in a local or global frame, and is a matter of convenience. Using quaternions allows the end-effector to move in its full operational envelope, which is not possible with other representations, e.g., Euler angles, that introduce representation-specific singularities. Further, the presented stability results are global rather than almost global, where the latter is often the best one can achieve when using rotation matrices to represent orientation.