# Geometric Impedance Control on SE(3) for Robotic Manipulators

arXiv: https://arxiv.org/abs/2211.07945 · HTML: https://mlsanity.com/paper/2211.07945/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2022.

## Built on by (most cited first, 5 of 5)

- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)
- [SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey](https://mlsanity.com/paper/2503.09829/) (2025)
- [MIMIC-D: Multi-modal Imitation for MultI-agent Coordination with Decentralized Diffusion Policies](https://mlsanity.com/paper/2509.14159/) (2025)
- [Partially Equivariant Reinforcement Learning in Symmetry-Breaking Environments](https://mlsanity.com/paper/2512.00915/) (2025)
- [CompVLA: A Variable Compliance Vision-Language-Action Model for Contact-rich Manipulation](https://mlsanity.com/paper/2609.23614/) (2026)

## Abstract (arXiv)

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.