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

Yingbai Hu, Fares J. Abu-Dakka, Fei Chen, Xiao Luo, Zheng Li, Alois Knoll, Weiping Ding

TL;DR

This survey addresses imitation learning through a fusion with dynamical systems (DSIL), spanning non-autonomous mp-based approaches (e.g., DMP) and autonomous DSIL (ADSIL) to deep IL. It organizes methods by input dimensionality and stability framework, detailing Lyapunov, contraction theory, and diffeomorphism mappings, and surveys policy-improvement techniques including PI-2, evolution strategies, and deep RL. It presents a taxonomy of DSIL, analyzes stability guarantees, and connects classical mp-based models with modern deep IL, providing a 213-paper synthesis of methods, applications, and challenges. The work highlights practical implications for robust generalization, safe policy improvement, and scalable learning in robotics, offering guidelines and future directions for stability-aware, data-efficient DSIL systems.

Abstract

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.

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

TL;DR

This survey addresses imitation learning through a fusion with dynamical systems (DSIL), spanning non-autonomous mp-based approaches (e.g., DMP) and autonomous DSIL (ADSIL) to deep IL. It organizes methods by input dimensionality and stability framework, detailing Lyapunov, contraction theory, and diffeomorphism mappings, and surveys policy-improvement techniques including PI-2, evolution strategies, and deep RL. It presents a taxonomy of DSIL, analyzes stability guarantees, and connects classical mp-based models with modern deep IL, providing a 213-paper synthesis of methods, applications, and challenges. The work highlights practical implications for robust generalization, safe policy improvement, and scalable learning in robotics, offering guidelines and future directions for stability-aware, data-efficient DSIL systems.

Abstract

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.
Paper Structure (25 sections, 1 theorem, 37 equations, 14 figures, 11 tables, 4 algorithms)

This paper contains 25 sections, 1 theorem, 37 equations, 14 figures, 11 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. mp learning with low dimension input
  3. ndsil
  4. Autonomous dynamical system imitation learning
  5. Stable dsil
  6. Lyapunov stability
  7. Contraction theory
  8. Diffeomorphism mapping
  9. Policy learning with dynamical system
  10. Dynamical system with pi2
  11. Dynamical system with evolutionary strategies
  12. Dynamical system with deep RL
  13. Dynamical system with other RL methods
  14. Deep imitation learning
  15. Applications
  16. ...and 10 more sections

Key Result

Theorem 1

A ds is locally asymptotically stable at the fixed-point $x^* \in \Omega$ within the positive invariant neighborhood $\Omega \subset \mathbb{R}^d$ of $x^*$ if and only if there exists a continuous and continuously differentiable function $V : \Omega \to \mathbb{R}$ that satisfies the following cond

Figures (14)

  • Figure 1: A taxonomy of existing directions for ds.
  • Figure 2: The imitation performance of ndsil utilizing dmp is evaluated on a dataset containing 20 instances of human handwriting motions. The black '$\cdot$' and '*' symbols denote the initial and goal points, respectively. The blue dashed line represents the demonstration, while the solid brown line illustrates the reproduced imitation.
  • Figure 3: Different potential functions obstacle avoidance performance of ndsil in dmp ginesi2021dynamic.
  • Figure 4: The robot performs the grasping task via lfd employing seds hu2022robot. Left: the robot converges from the random initial position to the goal position. Right: the robot converges towards a different goal position, suggesting a switch during the task.
  • Figure 5: Imitation performance of clfdm on 20 human handwriting motions dataset khansari2014learning. The blue streamlines denote the dynamic flow of the energy function. The purple dashed lines represent the demonstrations, and the solid red lines are the imitation reproduction.
  • ...and 9 more figures

Theorems & Definitions (1)

  • Theorem 1