Learning Stable Vector Fields on Lie Groups
This work addresses a domain-specific problem for robotics by extending stable vector field learning to non-Euclidean spaces, representing an incremental improvement over previous Euclidean-based methods.
The paper tackles the problem of learning stable vector fields for robot motions in non-Euclidean manifolds like Lie Groups, which is necessary for full robot poses including orientations, and demonstrates performance in simulated and real robotics tasks for SE(2) and SE(3).
Learning robot motions from demonstration requires models able to specify vector fields for the full robot pose when the task is defined in operational space. Recent advances in reactive motion generation have shown that learning adaptive, reactive, smooth, and stable vector fields is possible. However, these approaches define vector fields on a flat Euclidean manifold, while representing vector fields for orientations requires modeling the dynamics in non-Euclidean manifolds, such as Lie Groups. In this paper, we present a novel vector field model that can guarantee most of the properties of previous approaches i.e., stability, smoothness, and reactivity beyond the Euclidean space. In the experimental evaluation, we show the performance of our proposed vector field model to learn stable vector fields for full robot poses as SE(2) and SE(3) in both simulated and real robotics tasks.