Learning Stable Vector Fields on Lie Groups
RA-L/ ICRA 2023
Embedded Files
Abstract
Abstract
Learning robot motions from demonstration requires having models that are able to represent vector fields for the full robot pose when the task is defined in operational space. Recent advances in reactive motion generation have shown that it is possible to learn adaptive, reactive, smooth, and stable vector fields. However, these approaches define vector fields on a flat Euclidean manifold, while representing vector fields for orientations require to model 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.
Code Repository
Experiment Videos
Experiment Videos
Robustness evaluation
Robustness evaluation
We present a 11 minutes long video without cuts in which we evaluate the pouring performance. The robot is set an arbitrary configurations and the pot in arbitrary positions. We observe that the robot fails to pour only once in the whole video.
Experiment in 2-Sphere manifold (with audio)
Experiment in 2-Sphere manifold (with audio)
In this video, we visualize the learned vector fields for the 2-Sphere. We also observe the importance of having bounded diffeomorphisms to guarantee global stable dynamics.
Experiment in SE(2) Lie Group (with audio)
Experiment in SE(2) Lie Group (with audio)
In this video, we compare the performance of our SE(2) Stable Vector Field wrt. a naive neural net vector field, a stable vector field modelled in the configuration space and a SE(2) vector field modelled with an unbounded diffeomorphism.
SVF on Mobius Strips
SVF on Mobius Strips
The proposed approach can be easily extended to different manifolds. We add a visualization of stable vector fields on Mobius Strips as an example.
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