# Continuous Manifold-Decomposed Impedance Retargeting for Contact-Rich Imitation Learning

arXiv: https://arxiv.org/abs/2609.15716 · HTML: https://mlsanity.com/paper/2609.15716/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Robot manipulation imitation learning, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Placed in

- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

## Builds on (most cited first, 16 of 16)

- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Temporal Convolutional Networks for Action Segmentation and Detection](https://mlsanity.com/paper/1611.05267/) (2016)
- [MimicGen: A Data Generation System for Scalable Robot Learning using Human Demonstrations](https://mlsanity.com/paper/2310.17596/) (2023)
- [OKAMI: Teaching Humanoid Robots Manipulation Skills through Single Video Imitation](https://mlsanity.com/paper/2410.11792/) (2024)
- [Adaptive Compliance Policy: Learning Approximate Compliance for Diffusion Guided Control](https://mlsanity.com/paper/2410.09309/) (2024)
- [ForceMimic: Force-Centric Imitation Learning with Force-Motion Capture System for Contact-Rich Manipulation](https://mlsanity.com/paper/2410.07554/) (2024)
- [MimicTouch: Leveraging Multi-modal Human Tactile Demonstrations for Contact-rich Manipulation](https://mlsanity.com/paper/2310.16917/) (2023)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [Bi-ACT: Bilateral Control-Based Imitation Learning via Action Chunking with Transformer](https://mlsanity.com/paper/2401.17698/) (2024)
- [Physics-Driven Data Generation for Contact-Rich Manipulation via Trajectory Optimization](https://mlsanity.com/paper/2502.20382/) (2025)
- [ImMimic: Cross-Domain Imitation from Human Videos via Mapping and Interpolation](https://mlsanity.com/paper/2509.10952/) (2025)
- [Learning Variable Compliance Control From a Few Demonstrations for Bimanual Robot with Haptic Feedback Teleoperation System](https://mlsanity.com/paper/2406.14990/) (2024)
- [Contact-rich SE(3)-Equivariant Robot Manipulation Task Learning via Geometric Impedance Control](https://mlsanity.com/paper/2308.14984/) (2023)
- [TRACT: Temporally Routed Action Chunks with Chronological Phase Authority for Contact-Rich Manipulation](https://mlsanity.com/paper/2607.29285/) (2026)
- [Condition-based Design of Variable Impedance Controllers from User Demonstrations](https://mlsanity.com/paper/2209.10244/) (2022)
- [MDIR: A Task-Manifold Impedance Retargeting Method for Contact-Rich Teleoperation](https://mlsanity.com/paper/2607.29271/) (2026)

## Abstract (arXiv)

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.