Geometric Impedance Control on SE(3) for Robotic Manipulators

TL;DR

This paper introduces a geometric impedance control method for robotic manipulators on SE(3), leveraging differential geometry to improve stability and trajectory tracking over traditional approaches.

Contribution

It proposes a novel geometric impedance control scheme on SE(3) using a left-invariant metric, enhancing stability and performance in manipulation tasks.

Findings

Outperforms conventional impedance control in trajectory tracking

Ensures closed-loop stability via Lyapunov analysis

Effectively accounts for manipulator's geometric structure

Abstract

After its introduction, impedance control has been utilized as a primary control scheme for robotic manipulation tasks that involve interaction with unknown environments. While impedance control has been extensively studied, the geometric structure of SE(3) for the robotic manipulator itself and its use in formulating a robotic task has not been adequately addressed. In this paper, we propose a differential geometric approach to impedance control. Given a left-invariant error metric in SE(3), the corresponding error vectors in position and velocity are first derived. We then propose the impedance control schemes that adequately account for the geometric structure of the manipulator in SE(3) based on a left-invariant potential function. The closed-loop stabilities for the proposed control schemes are verified using Lyapunov function-based analysis. The proposed control design clearly outperformed a conventional impedance control approach when tracking challenging trajectory profiles.