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.

翻译：本文提出了一种基于SE(3)流形的阻抗控制框架，该框架在实现力跟踪的同时保证无源性。基于统一力-阻抗控制（UFIC）及我们先前在几何阻抗控制（GIC）方面的工作，我们发展了几何统一力-阻抗控制（GUFIC），从微分几何视角将SE(3)流形结构纳入控制器公式化中。与UFIC类似，GUFIC采用能量罐增强技术同时实现力跟踪与阻抗控制，以保障操作器对外部力的无源性。这确保末端执行器与未知环境保持安全接触交互，并跟踪期望的交互力。此外，通过引入速度场和力场，我们解决了UFIC公式化中的非因果实现问题。由于基于SE(3)公式化，所提出的GUFIC继承了GIC中理想的SE(3)不变性与等变性，有助于在将学习算法融入控制律的机器学习应用中提升样本效率。在需要跟踪包含位置与姿态的SE(3)轨迹，同时向表面施加力的仿真场景中，所提出的控制律得到了验证。代码见 https://github.com/Joohwan-Seo/GUFIC_mujoco。