# Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overview

arXiv: https://arxiv.org/abs/2403.19916 · HTML: https://mlsanity.com/paper/2403.19916/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 56 of its 215 references that are in the map.
- First posted on arXiv 29 Mar 2024.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)
- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 30 of 56)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Imitation Learning for Complex Manipulation Tasks from Virtual Reality Teleoperation](https://mlsanity.com/paper/1710.04615/) (2017)
- [HG-DAgger: Interactive Imitation Learning with Human Experts](https://mlsanity.com/paper/1810.02890/) (2018)
- [Imitation from Observation: Learning to Imitate Behaviors from Raw Video via Context Translation](https://mlsanity.com/paper/1707.03374/) (2017)
- [Scaling Up and Distilling Down: Language-Guided Robot Skill Acquisition](https://mlsanity.com/paper/2307.14535/) (2023)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [VideoDex: Learning Dexterity from Internet Videos](https://mlsanity.com/paper/2212.04498/) (2022)
- [EnsembleDAgger: A Bayesian Approach to Safe Imitation Learning](https://mlsanity.com/paper/1807.08364/) (2018)
- [Off-Policy Imitation Learning from Observations](https://mlsanity.com/paper/2102.13185/) (2021)
- [Variable Impedance Control in End-Effector Space: An Action Space for Reinforcement Learning in Contact-Rich Tasks](https://mlsanity.com/paper/1906.08880/) (2019)
- [Neural Dynamic Policies for End-to-End Sensorimotor Learning](https://mlsanity.com/paper/2012.02788/) (2020)
- [Towards More Generalizable One-shot Visual Imitation Learning](https://mlsanity.com/paper/2110.13423/) (2021)
- [Dynamic Movement Primitives in Robotics: A Tutorial Survey](https://mlsanity.com/paper/2102.03861/) (2021)
- [Retrospectives on the Embodied AI Workshop](https://mlsanity.com/paper/2210.06849/) (2022)
- [Task-Relevant Adversarial Imitation Learning](https://mlsanity.com/paper/1910.01077/) (2019)
- [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021)
- [ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flows](https://mlsanity.com/paper/2010.13129/) (2020)
- [Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularization](https://mlsanity.com/paper/1907.13122/) (2019)
- [Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems](https://mlsanity.com/paper/2005.13143/) (2020)
- [Residual Learning from Demonstration: Adapting DMPs for Contact-rich Manipulation](https://mlsanity.com/paper/2008.07682/) (2020)
- [Robot Cooking with Stir-fry: Bimanual Non-prehensile Manipulation of Semi-fluid Objects](https://mlsanity.com/paper/2205.05960/) (2022)
- [ProDMPs: A Unified Perspective on Dynamic and Probabilistic Movement Primitives](https://mlsanity.com/paper/2210.01531/) (2022)
- [CRIL: Continual Robot Imitation Learning via Generative and Prediction Model](https://mlsanity.com/paper/2106.09422/) (2021)
- [Learning Contracting Vector Fields For Stable Imitation Learning](https://mlsanity.com/paper/1804.04878/) (2018)
- [Variable impedance control and learning -- A review](https://mlsanity.com/paper/2010.06246/) (2020)
- [Hierarchical Neural Dynamic Policies](https://mlsanity.com/paper/2107.05627/) (2021)
- [Learning Riemannian Stable Dynamical Systems via Diffeomorphisms](https://mlsanity.com/paper/2211.03169/) (2022)
- [Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approach](https://mlsanity.com/paper/2102.12668/) (2021)
- [Diffeomorphically Learning Stable Koopman Operators](https://mlsanity.com/paper/2112.04085/) (2021)
- [Merging Position and Orientation Motion Primitives](https://mlsanity.com/paper/2003.11507/) (2020)

## Built on by (most cited first, 3 of 3)

- [Information-Theoretic Graph Fusion with Vision-Language-Action Model for Policy Reasoning and Dual Robotic Control](https://mlsanity.com/paper/2508.05342/) (2025)
- [A context-adaptive policy framework for robust and reactive robotic manipulation via uncertainty-aware imitation learning](https://mlsanity.com/paper/2410.24035/) (2024)
- [TamedPUMA: safe and stable imitation learning with geometric fabrics](https://mlsanity.com/paper/2503.17432/) (2025)

## Abstract (arXiv)

Imitation Learning (IL), also referred to as Learning from Demonstration (LfD), holds significant promise for capturing expert motor skills through efficient imitation, facilitating adept navigation of complex scenarios. A persistent challenge in IL lies in extending generalization from historical demonstrations, enabling the acquisition of new skills without re-teaching. Dynamical system-based IL (DSIL) emerges as a significant subset of IL methodologies, offering the ability to learn trajectories via movement primitives and policy learning based on experiential abstraction. This paper emphasizes the fusion of theoretical paradigms, integrating control theory principles inherent in dynamical systems into IL. This integration notably enhances robustness, adaptability, and convergence in the face of novel scenarios. This survey aims to present a comprehensive overview of DSIL methods, spanning from classical approaches to recent advanced approaches. We categorize DSIL into autonomous dynamical systems and non-autonomous dynamical systems, surveying traditional IL methods with low-dimensional input and advanced deep IL methods with high-dimensional input. Additionally, we present and analyze three main stability methods for IL: Lyapunov stability, contraction theory, and diffeomorphism mapping. Our exploration also extends to popular policy improvement methods for DSIL, encompassing reinforcement learning, deep reinforcement learning, and evolutionary strategies.