Stable and Accurate Robot Trajectory Tracking Using Variable-Stiffness Euclideanizing Flow

Imitation learning based on dynamical systems (DSs) can generate real-time motion planning with intrinsic stability and robustness, providing significant advantages in highly uncertain dynamic environments. However, most DS approaches tend to deviate from their original integral curves when subjected to perturbations, limiting their applicability in scenarios that require tracking specific reference trajectories or passing through critical path points. To address this issue, this article proposes a variable stiffness Euclidean flow. Using diffeomorphic mapping, complex demonstrated trajectories are transformed into straight-line trajectories, eliminating the need for the integration process typically required to obtain integral curves. Furthermore, a gradient system based on these straight-line trajectories is designed to converge to the demonstrated trajectories, creating symmetric attractor-like behavior around the demonstrated trajectory. When applied to the original system, this approach preserves the desired velocity of the demonstrated trajectory. The effectiveness of the proposed method is demonstrated using standard datasets and real robot experiments. More videos and model details are available on the project website (https://anonymous.4open.science/w/EFVSDS-WebPage-5D06/).