Abstract
Learning from demonstrations provides effective methods for teaching robot manipulation skills.However,capturing periodic manipulation skills remains challenging with the current techniques.To address this gap,we introduce the neural Liénard system(neural LS),a novel neural network framework that utilizes Liénard-type differential equations to create dynamical systems with stable and distinct limit cycles.We also introduce an innovative technique,which not only manages periodic trajectories across various dimensions but also handles trajectories with intersections,enhancing the capability of the robot for complex tasks.We provide a thorough theoretical analysis of neural LS,focusing on its stability and representational capabilities.Empirical evaluations show that neural LS achieves superior performance in modeling complex limit cycles,surpassing the existing methods.We particularly emphasize its effectiveness in handling high-dimensional periodic motions and trajectories with intersections.In addition,we explore the adaptability and robustness of neural LS.A practical application involving the Franka Emika robot in a drawing task further demonstrates the real-world utility of neural LS,confirming its effectiveness and potential to equip robots with advanced periodic manipulation skills.
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