Contact-Rich <i>SE(3)</i>-Equivariant Robot Manipulation Task Learning via Geometric Impedance Control
Joohwan Seo, Nikhil Potu Surya Prakash, Xiang Zhang, Changhao Wang, Jongeun Choi, Masayoshi Tomizuka, Roberto Horowitz
Abstract
This letter presents a differential geometric control approach that leverages <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SE(3)</i> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SE(3)</i> transformations of the manipulation task definition. Furthermore, the control law and learning representation framework are shown to be <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SE(3)</i> 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.