Eq.Bot: Enhance Robotic Manipulation Learning via Group Equivariant Canonicalization

2025-11-19

AI Summary

Current robotic operating systems lack geometric consistency in multimodal learning, resulting in poor robustness to spatial transformations such as rotation and translation. To address this, we propose Eq.Bot—a model-agnostic normalization framework grounded in SE(2) group equivariance theory and inspired by human spatial cognition. Eq.Bot maps observations into a canonical coordinate space, executes policies therein, and inversely transforms actions back to the original space, thereby guaranteeing strict equivariance under SE(2) transformations. Crucially, it requires no architectural modifications and is compatible with diverse vision-language-action models—including CLIPort and OpenVLA-OFT—whether CNN- or Transformer-based. This design significantly improves spatial reasoning consistency, cross-architecture generalization, and robustness to pose variations. Evaluated across multiple robot manipulation benchmarks, Eq.Bot achieves up to 50.0% relative performance gain, demonstrating its generality and effectiveness.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Computer Vision: Multi-modal Vision
• Natural Language Processing: Safety and Robustness

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Robotic manipulation systems are increasingly deployed across diverse domains. Yet existing multi-modal learning frameworks lack inherent guarantees of geometric consistency, struggling to handle spatial transformations such as rotations and translations. While recent works attempt to introduce equivariance through bespoke architectural modifications, these methods suffer from high implementation complexity, computational cost, and poor portability. Inspired by human cognitive processes in spatial reasoning, we propose Eq.Bot, a universal canonicalization framework grounded in SE(2) group equivariant theory for robotic manipulation learning. Our framework transforms observations into a canonical space, applies an existing policy, and maps the resulting actions back to the original space. As a model-agnostic solution, Eq.Bot aims to endow models with spatial equivariance without requiring architectural modifications. Extensive experiments demonstrate the superiority of Eq.Bot under both CNN-based (e.g., CLIPort) and Transformer-based (e.g., OpenVLA-OFT) architectures over existing methods on various robotic manipulation tasks, where the most significant improvement can reach 50.0%.

Problem

• Robotic manipulation lacks geometric consistency guarantees for spatial transformations
• Existing equivariance methods have high complexity and poor portability
• Need model-agnostic solution to provide spatial equivariance without architecture changes

Innovation

• Canonicalization framework based on SE(2) group equivariance
• Transforms observations to canonical space for policy execution
• Model-agnostic solution enabling spatial equivariance without architecture changes