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：我们提出了一种动力学系统方法，通过运动示教学习复杂（可能周期性）的运动规划，该方法采用神经常微分方程（神经ODE）。为确保对扰动的反应性与鲁棒性，我们提出一种新方法，通过结合控制理论工具与由所学神经ODE生成的目标轨迹，在每个时间步为机器人选择一个待跟随的目标点。通过求解二次规划在线计算神经ODE模型的修正项，该修正项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手写数据集和复杂周期轨迹上优于基线DS学习技术，并在Franka Emika机器人臂上通过擦拭和搅拌任务（这些任务不具有单一吸引子）得到验证，能够产生稳定运动，同时具有对扰动的鲁棒性，并在人类与障碍物附近保持安全。