🤖 AI Summary
This work addresses the challenge of learning complex (including periodic) motion plans from kinesthetic demonstrations while simultaneously ensuring safety, stability, and robustness. We propose an online motion generation framework that integrates neural ordinary differential equations (NODEs) with control-theoretic principles. Specifically, we introduce the first NODE architecture incorporating control Lyapunov functions (CLFs) and control barrier functions (CBFs) within its online correction module, coupled with dynamic goal generation and online quadratic programming (QP). This enables reactive, safe, and asymptotically stable motion planning—without reliance on a single fixed attractor. Evaluations on the LASA handwriting dataset and intricate periodic trajectories demonstrate significant improvements over baseline methods. Physical experiments on a Franka Emika robot validate strong disturbance rejection and physical safety in real-world wiping and stirring tasks.
📝 Abstract
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. The project’s web-page is https://sites.google.com/view/lfd-neural-ode/home.
