VIDP: Variable Impedance Diffusion Policy for Compliant Robot Manipulation from Diverse Demonstrations
Authors: Hisham Khalil, Neil Fernandes, Thomas M. Kwok, Hsiu-Chin Lin, Yue Hu
Abstract
Contact-rich manipulation requires precise tracking and mechanical compliance, where variable impedance control can improve robustness in task success, whereas static compliance cannot adapt to varying contact constraints. Variable impedance skills can be learned from demonstrations, avoiding complex modeling, but compliance is a hidden variable in force-agnostic kinematic data. While existing methods infer compliance from trajectory variations, these variations may reflect geometric adaptation and not intentional compliance when subject to changing spatial layouts. Therefore, this letter introduces Variable Impedance Diffusion Policy (VIDP), an imitation learning-based variable impedance control framework leveraging a Task-Parameterized Directionality-Aware Mixture Model (TP-DAMM) to extract physically consistent trajectory distributions from diverse demonstrations. By mapping distributions to stiffness profiles, VIDP jointly predicts pose actions and task compliance without force sensors. Real-world experiments show that VIDP significantly outperforms fixed-impedance baselines in task success rate while reducing interaction forces with respect to high stiffness controllers and tracking errors with respect to low stiffness baselines.
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: no 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 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 open-sourced. The reference Cartesian impedance controller supports task-dependent compliance by rotating translational and rotational stiffness and damping, 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 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.
CMDIR extends Manifold-Decomposed Impedance Retargeting (MDIR) to transform fixed-impedance demonstrations into continuous variable-impedance controllers, which can also serve as structured supervision for imitation learning. Continuous Task-Manifold Impedance Representation (TMIR) pairs an evolving task frame with controller instructions. Demo-relative Compromise dynamics retain moving-basis transport and control/physical metric mismatch, yielding displacement, reaction-impulse, and perturbation-sensitivity criteria. Quality-to-Fast automatically compiles a solver structure from development paths within a predefined finite space, re-instantiates that structure for each demonstration, and certifies the resulting candidate by multi-resolution evaluation. Across 225 retargeted-controller trials in three real contact tasks, full CMDIR improves mean task-proxy retention and reduces mean pose deviation, force fluctuation, and peak force relative to discrete MDIR. FastMPO achieves a 5.8--9.4× speedup over C-MPO with comparable closed-loop outcomes. Downstream experiments demonstrate learnability of the complete TMIR supervision interface; lower force fluctuation and peak force are observed among successful executions, while completion reliability remains uneven across tasks and environments.
Vision-language-action models tell a robot where to move, but not how hard to push. Contact-rich tasks depend on that second quantity, compliance, yet no widely used demonstration interface records it. The obstacle is identifiability as realized pose and measured force cannot separate the operator's intended equilibrium from their stiffness, so VR controllers, SpaceMouse and handheld grippers cannot supply compliance supervision even in principle. Prior compliance-output policies work around this with hand-specified task structure, privileged simulation contact state, or dedicated force and tactile hardware. Four-channel bilateral teleoperation removes the ambiguity directly by using the leader arm as a separate measurement of the intended equilibrium, making per-axis stiffness identifiable by regression using only the joint-torque sensing already on the manipulator. This yields per-timestep, direction-dependent compliance labels at zero annotation cost, which we use to fine-tune a VLA to emit stiffness alongside pose. On a Franka Research 3 wiping task, ours is the only policy of five whose contact force changes when the instruction asks for a firm wipe rather than a normal one (6.4N (normal) to 9.1N (firm) RMS, Cohen's d = 0.89, p = 0.023