Integrating Symmetry into Differentiable Planning with Steerable Convolutions

TL;DR

This paper demonstrates how incorporating symmetry via steerable convolutions into differentiable planning algorithms enhances data efficiency and generalization across various navigation and manipulation tasks.

Contribution

It extends Value Iteration Networks with steerable convolutions to explicitly incorporate symmetry, improving planning performance and generalization.

Findings

Symmetric planning algorithms outperform non-equivariant methods in training efficiency.

Steerable convolutions effectively encode symmetry, leading to better generalization.

Experiments show significant improvements across multiple tasks.

Abstract

We study how group symmetry helps improve data efficiency and generalization for end-to-end differentiable planning algorithms when symmetry appears in decision-making tasks. Motivated by equivariant convolution networks, we treat the path planning problem as \textit{signals} over grids. We show that value iteration in this case is a linear equivariant operator, which is a (steerable) convolution. This extends Value Iteration Networks (VINs) on using convolutional networks for path planning with additional rotation and reflection symmetry. Our implementation is based on VINs and uses steerable convolution networks to incorporate symmetry. The experiments are performed on four tasks: 2D navigation, visual navigation, and 2 degrees of freedom (2DOFs) configuration space and workspace manipulation. Our symmetric planning algorithms improve training efficiency and generalization by large margins compared to non-equivariant counterparts, VIN and GPPN.