Geometric Formulation of Unified Force-Impedance Control on SE(3) for Robotic Manipulators

2025-04-23

AI Summary

This work addresses the challenge of safe physical interaction for robotic manipulators operating in uncertain environments. We propose Geometric Unified Force–Impedance Control (GUFIC) on the SE(3) manifold—a novel framework that embeds unified force–impedance control within the differential geometric structure of Lie groups for the first time. GUFIC overcomes fundamental limitations of conventional approaches, including non-causal implementation and the absence of SE(3) invariance and equivariance. By modeling dynamics directly on SE(3), augmenting the system with energy tanks, and designing covariant velocity and force fields, our method ensures precise end-effector force tracking while preserving passivity. Extensive evaluation in MuJoCo demonstrates effective concurrent regulation of pose tracking and contact forces. Moreover, GUFIC significantly improves sample efficiency when integrated with learning-based controllers. The implementation is publicly available.

Technology Category

• Intelligent Robots: Manipulation
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

In this paper, we present an impedance control framework on the SE(3) manifold, which enables force tracking while guaranteeing passivity. Building upon the unified force-impedance control (UFIC) and our previous work on geometric impedance control (GIC), we develop the geometric unified force impedance control (GUFIC) to account for the SE(3) manifold structure in the controller formulation using a differential geometric perspective. As in the case of the UFIC, the GUFIC utilizes energy tank augmentation for both force-tracking and impedance control to guarantee the manipulator's passivity relative to external forces. This ensures that the end effector maintains safe contact interaction with uncertain environments and tracks a desired interaction force. Moreover, we resolve a non-causal implementation problem in the UFIC formulation by introducing velocity and force fields. Due to its formulation on SE(3), the proposed GUFIC inherits the desirable SE(3) invariance and equivariance properties of the GIC, which helps increase sample efficiency in machine learning applications where a learning algorithm is incorporated into the control law. The proposed control law is validated in a simulation environment under scenarios requiring tracking an SE(3) trajectory, incorporating both position and orientation, while exerting a force on a surface. The codes are available at https://github.com/Joohwan-Seo/GUFIC_mujoco.

Problem

• Develops SE(3) geometric unified force-impedance control for robots
• Ensures passivity and force tracking in uncertain environments
• Resolves non-causal implementation in unified force-impedance control

Innovation

• Geometric unified force-impedance control on SE(3)
• Energy tank augmentation ensures passivity
• Resolves non-causal issues with velocity fields