Contact-rich SE(3)-Equivariant Robot Manipulation Task Learning via Geometric Impedance Control

TL;DR

This paper introduces a geometric impedance control framework leveraging SE(3) invariance and equivariance, enhancing transferability in robot manipulation learning involving environmental interaction, validated through simulations and hardware experiments.

Contribution

It develops a SE(3)-invariant and equivariant control and learning framework using geometric impedance control and neural networks, improving transferability over traditional Cartesian methods.

Findings

Superior transferability demonstrated in simulations

Effective hardware validation on peg-in-hole task

Enhanced robustness to environmental variations

Abstract

This paper presents a differential geometric control approach that leverages SE(3) group invariance and equivariance to increase transferability in learning robot manipulation tasks that involve interaction with the environment. Specifically, we employ a control law and a learning representation framework that remain invariant under arbitrary SE(3) transformations of the manipulation task definition. Furthermore, the control law and learning representation framework are shown to be SE(3) equivariant when represented relative to the spatial frame. The proposed approach is based on utilizing a recently presented geometric impedance control (GIC) combined with a learning variable impedance control framework, where the gain scheduling policy is trained in a supervised learning fashion from expert demonstrations. A geometrically consistent error vector (GCEV) is fed to a neural network to achieve a gain scheduling policy that remains invariant to arbitrary translation and rotations. A comparison of our proposed control and learning framework with a well-known Cartesian space learning impedance control, equipped with a Cartesian error vector-based gain scheduling policy, confirms the significantly superior learning transferability of our proposed approach. A hardware implementation on a peg-in-hole task is conducted to validate the learning transferability and feasibility of the proposed approach.