Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3D

Many complex robotic manipulation tasks can be decomposed as a sequence of pick and place actions. Training a robotic agent to learn this sequence over many different starting conditions typically requires many iterations or demonstrations, especially in 3D environments. In this work, we propose Fourier Transporter (\ours{}) which leverages the two-fold $\SE(d)\times\SE(d)$ symmetry in the pick-place problem to achieve much higher sample efficiency. \ours{} is an open-loop behavior cloning method trained using expert demonstrations to predict pick-place actions on new environments. \ours{} is constrained to incorporate symmetries of the pick and place actions independently. Our method utilizes a fiber space Fourier transformation that allows for memory-efficient construction. We test our proposed network on the RLbench benchmark and achieve state-of-the-art results across various tasks.