Point-to-point and periodic motions are ubiquitous in the world of robotics. To master these motions, Autonomous Dynamic System (DS) based algorithms are fundamental in the domain of Learning from Demonstration (LfD). However, these algorithms face the significant challenge of balancing precision in learning with the maintenance of system stability. This paper addresses this challenge by presenting a novel ADS algorithm that leverages neural network technology. The proposed algorithm is designed to distill essential knowledge from demonstration data, ensuring stability during the learning of both point-to-point and periodic motions. For point-to-point motions, a neural Lyapunov function is proposed to align with the provided demonstrations. In the case of periodic motions, the neural Lyapunov function is used with the transversal contraction to ensure that all generated motions converge to a stable limit cycle. The model utilizes a streamlined neural network architecture, adept at achieving dual objectives: optimizing learning accuracy while maintaining global stability. To thoroughly assess the efficacy of the proposed algorithm, rigorous evaluations are conducted using the LASA dataset and a manually designed dataset. These assessments were complemented by empirical validation through robotic experiments, providing robust evidence of the algorithm's performance

翻译：点对点运动和周期运动在机器人学领域无处不在。为掌握这些运动，基于自治动态系统（DS）的算法在示教学习（LfD）领域具有基础性地位。然而，这些算法面临学习精度与系统稳定性保持之间平衡的重大挑战。本文通过提出一种利用神经网络技术的新型ADS算法来解决这一挑战。该算法旨在从示教数据中提取关键知识，确保在点对点运动和周期运动学习过程中的稳定性。针对点对点运动，提出了与给定示教数据对齐的神经李雅普诺夫函数。对于周期运动，该神经李雅普诺夫函数与横向收缩理论结合使用，确保所有生成的运动收敛至稳定极限环。该模型采用简化的神经网络架构，能够有效实现双重目标：在保持全局稳定性的同时优化学习精度。为全面评估所提算法的效能，采用LASA数据集和人工设计数据集进行了严格评估，并通过机器人实验进行实证验证，为算法性能提供了有力证据。