We propose a Dynamical System (DS) approach to learn complex, possibly periodic motion plans from kinesthetic demonstrations using Neural Ordinary Differential Equations (NODE). To ensure reactivity and robustness to disturbances, we propose a novel approach that selects a target point at each time step for the robot to follow, by combining tools from control theory and the target trajectory generated by the learned NODE. A correction term to the NODE model is computed online by solving a quadratic program that guarantees stability and safety using control Lyapunov functions and control barrier functions, respectively. Our approach outperforms baseline DS learning techniques on the LASA handwriting dataset and complex periodic trajectories. It is also validated on the Franka Emika robot arm to produce stable motions for wiping and stirring tasks that do not have a single attractor, while being robust to perturbations and safe around humans and obstacles.

翻译：本文提出一种动力学系统方法，利用神经常微分方程从动觉示教中学习复杂的可能周期性运动规划。为确保对扰动的反应性与鲁棒性，我们提出一种创新方法：在每一时间步为目标跟踪选择目标点，通过融合控制理论工具与由学习型神经ODE生成的目标轨迹实现。通过求解二次规划在线计算对神经ODE模型的修正项，该二次规划分别利用控制李雅普诺夫函数与控制障碍函数保证稳定性与安全性。我们的方法在LASA手写数据集与复杂周期性轨迹上优于基线DS学习技术，并在Franka Emika机器人臂上通过擦拭与搅拌任务验证了其能生成无单一吸引子的稳定运动，同时具备对扰动的鲁棒性及在人机/障碍物环境下的安全性。