# Elastic Motion Policy: An Adaptive Dynamical System for Robust and Efficient One-Shot Imitation Learning

arXiv: https://arxiv.org/abs/2503.08029 · HTML: https://mlsanity.com/paper/2503.08029/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Real-world robot offline RL, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Placed in

- Offline RL and imitation learning from data / [Real-world robot offline RL](https://mlsanity.com/offlinerl/real-world-robot-offline-rl/)

## Builds on (most cited first, 28 of 28)

- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Grounded SAM: Assembling Open-World Models for Diverse Visual Tasks](https://mlsanity.com/paper/2401.14159/) (2024)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [FoundationPose: Unified 6D Pose Estimation and Tracking of Novel Objects](https://mlsanity.com/paper/2312.08344/) (2023)
- [Universal Manipulation Interface: In-The-Wild Robot Teaching Without In-The-Wild Robots](https://mlsanity.com/paper/2402.10329/) (2024)
- [HG-DAgger: Interactive Imitation Learning with Human Experts](https://mlsanity.com/paper/1810.02890/) (2018)
- [DART: Noise Injection for Robust Imitation Learning](https://mlsanity.com/paper/1703.09327/) (2017)
- [ALOHA Unleashed: A Simple Recipe for Robot Dexterity](https://mlsanity.com/paper/2410.13126/) (2024)
- [EnsembleDAgger: A Bayesian Approach to Safe Imitation Learning](https://mlsanity.com/paper/1807.08364/) (2018)
- [Deeply AggreVaTeD: Differentiable Imitation Learning for Sequential Prediction](https://mlsanity.com/paper/1703.01030/) (2017)
- [NeRF in the Palm of Your Hand: Corrective Augmentation for Robotics via Novel-View Synthesis](https://mlsanity.com/paper/2301.08556/) (2023)
- [Towards More Generalizable One-shot Visual Imitation Learning](https://mlsanity.com/paper/2110.13423/) (2021)
- [Grasping with Chopsticks: Combating Covariate Shift in Model-free Imitation Learning for Fine Manipulation](https://mlsanity.com/paper/2011.06719/) (2020)
- [Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems](https://mlsanity.com/paper/2005.13143/) (2020)
- [CCIL: Continuity-based Data Augmentation for Corrective Imitation Learning](https://mlsanity.com/paper/2310.12972/) (2023)
- [Lyapunov Density Models: Constraining Distribution Shift in Learning-Based Control](https://mlsanity.com/paper/2206.10524/) (2022)
- [Universal Visual Decomposer: Long-Horizon Manipulation Made Easy](https://mlsanity.com/paper/2310.08581/) (2023)
- [One-Shot Imitation Learning with Invariance Matching for Robotic Manipulation](https://mlsanity.com/paper/2405.13178/) (2024)
- [Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Control](https://mlsanity.com/paper/1909.05946/) (2019)
- [One-shot Imitation Learning via Interaction Warping](https://mlsanity.com/paper/2306.12392/) (2023)
- [Stable-BC: Controlling Covariate Shift with Stable Behavior Cloning](https://mlsanity.com/paper/2408.06246/) (2024)
- [Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies](https://mlsanity.com/paper/2309.01884/) (2023)
- [Learning Complex Motion Plans using Neural ODEs with Safety and Stability Guarantees](https://mlsanity.com/paper/2308.00186/) (2023)
- [Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learning](https://mlsanity.com/paper/2310.07902/) (2023)
- [Directionality-Aware Mixture Model Parallel Sampling for Efficient Linear Parameter Varying Dynamical System Learning](https://mlsanity.com/paper/2309.02609/) (2023)
- [SE(3) Linear Parameter Varying Dynamical Systems for Globally Asymptotically Stable End-Effector Control](https://mlsanity.com/paper/2403.16366/) (2024)

## Built on by (most cited first, 5 of 5)

- [Flow with the Force Field: Learning 3D Compliant Flow Matching Policies from Force and Demonstration-Guided Simulation Data](https://mlsanity.com/paper/2510.02738/) (2025)
- [Annotation-Free One-Shot Imitation Learning for Multi-Step Manipulation Tasks](https://mlsanity.com/paper/2509.24972/) (2025)
- [POIL: Point-based One-Shot Imitation Learning with Stable Dynamical Systems](https://mlsanity.com/paper/2609.30404/) (2026)
- [In-Context Learning for Robots: Methods and Applications](https://mlsanity.com/paper/2609.36012/) (2026)
- [TReF-6: Inferring Task-Relevant Frames from a Single Demonstration for One-Shot Skill Generalization](https://mlsanity.com/paper/2509.00310/) (2025)

## Abstract (arXiv)

Behavior cloning (BC) has become a staple imitation learning paradigm in robotics due to its ease of teaching robots complex skills directly from expert demonstrations. However, BC suffers from an inherent generalization issue. To solve this, the status quo solution is to gather more data. Yet, regardless of how much training data is available, out-of-distribution performance is still sub-par, lacks any formal guarantee of convergence and success, and is incapable of allowing and recovering from physical interactions with humans. These are critical flaws when robots are deployed in ever-changing human-centric environments. Thus, we propose Elastic Motion Policy (EMP), a one-shot imitation learning framework that allows robots to adjust their behavior based on the scene change while respecting the task specification. Trained from a single demonstration, EMP follows the dynamical systems paradigm where motion planning and control are governed by first-order differential equations with convergence guarantees. We leverage Laplacian editing in full end-effector space, ℝ3× SO(3), and online convex learning of Lyapunov functions, to adapt EMP online to new contexts, avoiding the need to collect new demonstrations. We extensively validate our framework in real robot experiments, demonstrating its robust and efficient performance in dynamic environments, with obstacle avoidance and multi-step task capabilities. Project Website: https://elastic-motion-policy.github.io/EMP/