Hybrid Diffusion Policies with Projective Geometric Algebra for Efficient Robot Manipulation Learning

TL;DR

This paper introduces a novel hybrid diffusion policy for robot manipulation that embeds geometric inductive biases using Projective Geometric Algebra, significantly enhancing training efficiency and task performance in both simulated and real-world environments.

Contribution

It proposes hPGA-DP, a hybrid diffusion policy leveraging PGA for better spatial reasoning, and demonstrates improved efficiency and effectiveness over existing methods.

Findings

Faster convergence compared to standard diffusion policies

Improved task performance in simulated and real environments

Effective reasoning about spatial structures using PGA

Abstract

Diffusion policies are a powerful paradigm for robot learning, but their training is often inefficient. A key reason is that networks must relearn fundamental spatial concepts, such as translations and rotations, from scratch for every new task. To alleviate this redundancy, we propose embedding geometric inductive biases directly into the network architecture using Projective Geometric Algebra (PGA). PGA provides a unified algebraic framework for representing geometric primitives and transformations, allowing neural networks to reason about spatial structure more effectively. In this paper, we introduce hPGA-DP, a novel hybrid diffusion policy that capitalizes on these benefits. Our architecture leverages the Projective Geometric Algebra Transformer (P-GATr) as a state encoder and action decoder, while employing established U-Net or Transformer-based modules for the core denoising process. Through extensive experiments and ablation studies in both simulated and real-world environments, we demonstrate that hPGA-DP significantly improves task performance and training efficiency. Notably, our hybrid approach achieves substantially faster convergence compared to both standard diffusion policies and architectures that rely solely on P-GATr. The project website is available at: https://apollo-lab-yale.github.io/26-ICRA-hPGA-website/.