MDIR: A Task-Manifold Impedance Retargeting Method for Contact-Rich Teleoperation

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 $5.8$--$9.4\times$ 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.

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.

Teleoperation for contact-rich manipulation remains challenging, especially when using low-cost, motion-only interfaces that provide no haptic feedback. Virtual reality controllers enable intuitive motion control but do not allow operators to directly perceive or regulate contact forces, limiting task performance. To address this, we propose an augmented reality (AR) visualization of the impedance controller's target pose and its displacement from each robot end effector. This visualization conveys the forces generated by the controller, providing operators with intuitive, real-time feedback without expensive haptic hardware. We evaluate the design in a dual-arm manipulation study with 17 participants who repeatedly reposition a box with and without the AR visualization. Results show that AR visualization reduces completion time by 24% for force-critical lifting tasks, with no significant effect on sliding tasks where precise force control is less critical. These findings indicate that making the impedance target visible through AR is a viable approach to improve human-robot interaction for contact-rich teleoperation.