Autonomous dynamic systems (ADS) have become a key area of research in the field of robotics, aiming to enable robots to acquire human-like operational skills and perform complex tasks in dynamic environments without external intervention. Despite significant progress, current technologies have yet to enable robots to fully achieve autonomous skill transfer in real-world applications. The prevailing approach to bridge this gap is Learning from Demonstration (LfD), where robots learn by observing and imitating expert demonstrations. Dynamic systems-based methods, particularly those utilizing Lyapunov stability theory, have shown great potential in effectively encoding human motor skills, ensuring the stability, accuracy, and generalization of learned behaviors during the learning process. This survey provides an overview of the recent advancements in dynamic systems for skill transfer, focusing on methods that enable robots to replicate human actions, as demonstrated by experts. We present a classification of existing dynamic systems approaches, highlight landmark studies, and discuss their key features, advantages, and limitations. This paper also explores the applications of these methods and identifies major challenges that remain in both theoretical and practical aspects of robot skill learning
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