Learning Stable Vector Fields on Lie Groups

TL;DR

This paper introduces a novel vector field model capable of learning stable, smooth, and reactive robot motions on non-Euclidean manifolds like Lie Groups, extending previous Euclidean-based approaches.

Contribution

The paper presents a new vector field model that guarantees stability and smoothness for robot pose learning on Lie Groups such as SE(2) and SE(3).

Findings

Successfully learned stable vector fields for robot poses in SE(2) and SE(3).

Demonstrated effectiveness in both simulated and real robotic tasks.

Extended reactive motion generation to non-Euclidean manifolds.

Abstract

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.