# GrOMP: Grasped Object Manifold Projection for Multimodal Imitation Learning of Manipulation

arXiv: https://arxiv.org/abs/2512.03347 · HTML: https://mlsanity.com/paper/2512.03347/

## Key facts

- Cited by 1 papers in the map (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 14 of its 21 references that are in the map.
- First posted on arXiv 3 Dec 2025.

## 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, 14 of 14)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [HG-DAgger: Interactive Imitation Learning with Human Experts](https://mlsanity.com/paper/1810.02890/) (2018)
- [Transferable Tactile Transformers for Representation Learning Across Diverse Sensors and Tasks](https://mlsanity.com/paper/2406.13640/) (2024)
- [Diffusion Meets DAgger: Supercharging Eye-in-hand Imitation Learning](https://mlsanity.com/paper/2402.17768/) (2024)
- [Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior](https://mlsanity.com/paper/2307.14619/) (2023)
- [CCIL: Continuity-based Data Augmentation for Corrective Imitation Learning](https://mlsanity.com/paper/2310.12972/) (2023)
- [SQIL: Imitation Learning via Reinforcement Learning with Sparse Rewards](https://mlsanity.com/paper/1905.11108/) (2019)
- [MEGA-DAgger: Imitation Learning with Multiple Imperfect Experts](https://mlsanity.com/paper/2303.00638/) (2023)
- [DropoutDAgger: A Bayesian Approach to Safe Imitation Learning](https://mlsanity.com/paper/1709.06166/) (2017)
- [GelSlim 4.0: Focusing on Touch and Reproducibility](https://mlsanity.com/paper/2409.19770/) (2024)

## Built on by (most cited first, 1 of 1)

- [TAP-VLA: Tactile Annotation Prompting for Vision Language Action Models](https://mlsanity.com/paper/2606.29089/) (2026)

## Abstract (arXiv)

Imitation Learning (IL) holds great potential for learning repetitive manipulation tasks, such as those in industrial assembly. However, its effectiveness is often limited by insufficient trajectory precision due to compounding errors. In this paper, we introduce Grasped Object Manifold Projection (GrOMP), an interactive method that mitigates these errors by constraining a non-rigidly grasped object to a lower-dimensional manifold. GrOMP assumes a precise task in which a manipulator holds an object that may shift within the grasp in an observable manner and must be mated with a grounded part. Crucially, all GrOMP enhancements are learned from the same expert dataset used to train the base IL policy, and are adjusted with an n-arm bandit-based interactive component. We propose a theoretical basis for GrOMP's improvement upon the well-known compounding error bound in IL literature. We demonstrate the framework on four precise assembly tasks using tactile feedback, and note that the approach remains modality-agnostic. Data and videos are available at williamvdb.github.io/GrOMPsite.