Rotate the compliance directions
The diagonal gains set the soft and stiff task directions. \(\mathbf{R}_{\mathrm{task}}\) rotates both stiffness matrices as the path bends.
A Modular Framework for Online Variable Impedance with Arbitrarily Oriented Compliance Axes
Eastern Institute of Technology, Ningbo
The paper proposes a robot-agnostic compliant-control framework that extends the ROS control ecosystem with standardized joint and Cartesian command interfaces. It addresses a key limitation of existing control software: the lack of reusable infrastructure for implementing compliant-control algorithms across different manipulators while preserving a common interface to higher-level applications. A plugin-based architecture separates controller infrastructure from control-law implementation. Generic wrappers use existing hardware abstractions to interface with different manipulators, while runtime-loaded plugins implement only the control law. Command interfaces support updates of joint- and Cartesian-space references, stiffness and damping gains, nullspace targets, and feedforward terms, enabling variable impedance and diverse compliant-control formulations. Robot kinematics and dynamics are computed from URDF models using Pinocchio. The architecture facilitates the development of compliant-control strategies and enables the same implementation to be deployed across platforms unchanged. The complete framework, including reference controllers, high-level task interfaces, and example configurations for various manipulators, is available as open-source software. The reference Cartesian impedance controller supports task-dependent compliance by rotating translational and rotational stiffness and damping matrices, allowing the principal compliance directions to be updated online according to local task geometry rather than remaining fixed in the robot base or TCP frame. This is particularly important in contact-rich manipulation, where the desired directions of motion, constraints, and compliance directions may vary continuously throughout task execution. Real-robot experiments demonstrate task-dependent compliance in contact-rich manipulation, while simulations show portability across manipulators with distinct kinematic and dynamic characteristics.
High-level policies, teleoperation, and shared-autonomy systems often issue sparse action chunks or task-level corrections. A dependable low-level layer must turn those coarse commands into smooth, stable, and physically consistent interaction.
Compliant controllers commonly bundle the control law with middleware, model access, and vendor-specific hardware code. That makes a new control strategy costly to prototype and difficult to reuse.
The pipeline scaffolds the command and state buses, provides a model template for the control law, and compiles it into a loadable plugin for the generic ROS 2 wrapper.
Even mature robot-specific controllers are hard to transfer when dynamics and hardware access come from vendor APIs. URDF-backed models and common ROS 2 effort interfaces leave only description, naming, launch, and hardware configuration to change.




Contact-rich tasks need different behavior over time: compliance during search and alignment, followed by higher stiffness along constrained directions once contact is established.
The diagonal gains set the soft and stiff task directions. \(\mathbf{R}_{\mathrm{task}}\) rotates both stiffness matrices as the path bends.
High stiffness
Lower normal stiffness
Low normal, high tangential stiffness
Increase compliance temporarily
High stiffness
Real-robot tests on a Franka FR3 demonstrate geometry-aware behavior in contact-rich manipulation.
The end effector establishes contact and follows a curved feature while the moving compliance frame keeps the soft direction aligned with the local surface normal.
The same command and controller follow a curved feature placed at a different position, demonstrating tolerance to fixture-placement error without reteaching the reference path.
Task-aligned compliance accommodates contact and pose uncertainty while the robot engages and manipulates the rotary connector.
A PVC quick connector approaches with angular misalignment. Task-aligned compliance lets contact forces guide self-alignment and prevent binding during insertion.
The robot inserts an electrical plug while compliant translational and rotational directions accommodate small pose errors and protect the connector during contact.
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