# Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies

arXiv: https://arxiv.org/abs/2309.01884 · HTML: https://mlsanity.com/paper/2309.01884/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Robot learning from demonstration, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 19 of its 63 references that are in the map.
- First posted on arXiv 5 Sep 2023.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [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)
- [BC-Z: Zero-Shot Task Generalization with Robotic Imitation Learning](https://mlsanity.com/paper/2202.02005/) (2022)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [One-Shot Visual Imitation Learning via Meta-Learning](https://mlsanity.com/paper/1709.04905/) (2017)
- [Task-Free Continual Learning](https://mlsanity.com/paper/1812.03596/) (2018)
- [Vision-Based Multi-Task Manipulation for Inexpensive Robots Using End-To-End Learning from Demonstration](https://mlsanity.com/paper/1707.02920/) (2017)
- [BundleTrack: 6D Pose Tracking for Novel Objects without Instance or Category-Level 3D Models](https://mlsanity.com/paper/2108.00516/) (2021)
- [Bridging Multi-Task Learning and Meta-Learning: Towards Efficient Training and Effective Adaptation](https://mlsanity.com/paper/2106.09017/) (2021)
- [PaCo: Parameter-Compositional Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2210.11653/) (2022)
- [Modular Lifelong Reinforcement Learning via Neural Composition](https://mlsanity.com/paper/2207.00429/) (2022)
- [K for the Price of 1: Parameter-efficient Multi-task and Transfer Learning](https://mlsanity.com/paper/1810.10703/) (2018)
- [TaSIL: Taylor Series Imitation Learning](https://mlsanity.com/paper/2205.14812/) (2022)
- [Learning Stable Vector Fields on Lie Groups](https://mlsanity.com/paper/2110.11774/) (2021)
- [Temporal Logic Imitation: Learning Plan-Satisficing Motion Policies from Demonstrations](https://mlsanity.com/paper/2206.04632/) (2022)
- [Learning Task-Parameterized Skills from Few Demonstrations](https://mlsanity.com/paper/2201.09975/) (2022)
- [The State of Industrial Robotics: Emerging Technologies, Challenges, and Key Research Directions](https://mlsanity.com/paper/2010.14537/) (2020)
- [Inferring Versatile Behavior from Demonstrations by Matching Geometric Descriptors](https://mlsanity.com/paper/2210.08121/) (2022)

## Built on by (most cited first, 10 of 10)

- [Transfer Learning in Robotics: An Upcoming Breakthrough? A Review of Promises and Challenges](https://mlsanity.com/paper/2311.18044/) (2023)
- [The Art of Imitation: Learning Long-Horizon Manipulation Tasks from Few Demonstrations](https://mlsanity.com/paper/2407.13432/) (2024)
- [Elastic Motion Policy: An Adaptive Dynamical System for Robust and Efficient One-Shot Imitation Learning](https://mlsanity.com/paper/2503.08029/) (2025)
- [The Unreasonable Effectiveness of Discrete-Time Gaussian Process Mixtures for Robot Policy Learning](https://mlsanity.com/paper/2505.03296/) (2025)
- [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)
- [Distributionally Robust Policy and Lyapunov-Certificate Learning](https://mlsanity.com/paper/2404.03017/) (2024)
- [Trajectory Adaptation using Large Language Models](https://mlsanity.com/paper/2504.12755/) (2025)
- [KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planning](https://mlsanity.com/paper/2509.09074/) (2025)
- [A context-adaptive policy framework for robust and reactive robotic manipulation via uncertainty-aware imitation learning](https://mlsanity.com/paper/2410.24035/) (2024)
- [A Robust Task-Level Control Architecture for Learned Dynamical Systems](https://mlsanity.com/paper/2511.09790/) (2025)

## Abstract (arXiv)

Dynamical System (DS) based Learning from Demonstration (LfD) allows learning of reactive motion policies with stability and convergence guarantees from a few trajectories. Yet, current DS learning techniques lack the flexibility to generalize to new task instances as they ignore explicit task parameters that inherently change the underlying trajectories. In this work, we propose Elastic-DS, a novel DS learning, and generalization approach that embeds task parameters into the Gaussian Mixture Model (GMM) based Linear Parameter Varying (LPV) DS formulation. Central to our approach is the Elastic-GMM, a GMM constrained to SE(3) task-relevant frames. Given a new task instance/context, the Elastic-GMM is transformed with Laplacian Editing and used to re-estimate the LPV-DS policy. Elastic-DS is compositional in nature and can be used to construct flexible multi-step tasks. We showcase its strength on a myriad of simulated and real-robot experiments while preserving desirable control-theoretic guarantees. Supplementary videos can be found at https://sites.google.com/view/elastic-ds