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.

翻译：模仿学习（IL），也称示教学习（LfD），通过高效模仿获取专家运动技能，在复杂场景的灵活导航中展现出重要潜力。IL领域的一个持续挑战在于如何将历史示教的泛化能力拓展至新技能学习，从而避免重复示教。基于动力系统的模仿学习（DSIL）作为IL方法的重要分支，能够通过运动基元学习和基于经验抽象的策略学习来获取轨迹。本文重点阐述理论范式的融合，将动力系统固有的控制理论原理融入IL，显著增强了在新场景下的鲁棒性、适应性和收敛性。本综述旨在全面概述DSIL方法，涵盖从经典方法到最新前沿技术。我们将DSIL分为自治动力系统与非自治动力系统，系统综述了面向低维输入的传统IL方法与面向高维输入的深度IL前沿方法。此外，我们重点分析并讨论了IL的三种主要稳定性方法：李雅普诺夫稳定性、收缩理论与微分同胚映射。本文还拓展探讨了DSIL的主流策略优化方法，包括强化学习、深度强化学习与进化策略。