Orientation Control with Variable Stiffness Dynamical Systems

TL;DR

This paper introduces a novel control algorithm for robotic orientation that combines motion generation and impedance control in a closed loop, using Lie algebra and unit quaternions to enable reactive, safe, and precise orientation behaviors.

Contribution

It presents a new orientation control method that adapts rotational motion and stiffness in real-time using Lie algebra and quaternion constraints, addressing a gap in existing position-focused approaches.

Findings

Successfully follows complex orientation profiles

Reacts safely to perturbations

Performs physical interaction tasks

Abstract

Recently, several approaches have attempted to combine motion generation and control in one loop to equip robots with reactive behaviors, that cannot be achieved with traditional time-indexed tracking controllers. These approaches however mainly focused on positions, neglecting the orientation part which can be crucial to many tasks e.g. screwing. In this work, we propose a control algorithm that adapts the robot's rotational motion and impedance in a closed-loop manner. Given a first-order Dynamical System representing an orientation motion plan and a desired rotational stiffness profile, our approach enables the robot to follow the reference motion with an interactive behavior specified by the desired stiffness, while always being aware of the current orientation, represented as a Unit Quaternion (UQ). We rely on the Lie algebra to formulate our algorithm, since unlike positions, UQ feature constraints that should be respected in the devised controller. We validate our proposed approach in multiple robot experiments, showcasing the ability of our controller to follow complex orientation profiles, react safely to perturbations, and fulfill physical interaction tasks.