Learning Stable Nonlinear Dynamical System from One Demonstration

Dynamic systems (DS) methods constitute one of the most commonly employed frameworks for Learning from Demonstration (LfD). The field of LfD aims to enable robots or other agents to learn new skills or behaviors by observing human demonstrations, and DS provide a powerful tool for modeling and reproducing such behaviors. Due to their ability to capture complex and nonlinear patterns of movement, DS have been successfully applied in robotics application. This paper presents a new learning from demonstration method by using the DS. The proposed method ensures that the learned systems achieve global asymptotic stability, a valuable property that guarantees the convergence of the system to an equilibrium point from any initial condition. The original trajectory is initially transformed to a higher-dimensional space and then subjected to a diffeomorphism transformation. This transformation maps the transformed trajectory forward to a straight line that converges towards the zero point. By deforming the trajectories in this way, the resulting system ensures global asymptotic stability for all generated trajectories.