EquiForm: Noise-Robust SE(3)-Equivariant Policy Learning from 3D Point Clouds

TL;DR

EquiForm addresses the sensitivity of point-cloud policies to noise and viewpoint changes by integrating a geometric denoising module with a contrastive, SE(3)-equivariant representation learning objective. The method canonicalizes observations into a shared frame while enforcing feature stability under both rigid transformations and noise, yielding robust generalization across diverse tasks. Evaluations across 16 simulated and 4 real-world tasks show substantial improvements in noise robustness and spatial generalization over state-of-the-art point-cloud imitation methods. This work advances practical deployment of SE(3)-equivariant policies by explicitly modeling and mitigating sensing imperfections in 3D robotic manipulation.

Abstract

Visual imitation learning with 3D point clouds has advanced robotic manipulation by providing geometry-aware, appearance-invariant observations. However, point cloud-based policies remain highly sensitive to sensor noise, pose perturbations, and occlusion-induced artifacts, which distort geometric structure and break the equivariance assumptions required for robust generalization. Existing equivariant approaches primarily encode symmetry constraints into neural architectures, but do not explicitly correct noise-induced geometric deviations or enforce equivariant consistency in learned representations. We introduce EquiForm, a noise-robust SE(3)-equivariant policy learning framework for point cloud-based manipulation. EquiForm formalizes how noise-induced geometric distortions lead to equivariance deviations in observation-to-action mappings, and introduces a geometric denoising module to restore consistent 3D structure under noisy or incomplete observations. In addition, we propose a contrastive equivariant alignment objective that enforces representation consistency under both rigid transformations and noise perturbations. Built upon these components, EquiForm forms a flexible policy learning pipeline that integrates noise-robust geometric reasoning with modern generative models. We evaluate EquiForm on 16 simulated tasks and 4 real-world manipulation tasks across diverse objects and scene layouts. Compared to state-of-the-art point cloud imitation learning methods, EquiForm achieves an average improvement of 17.2% in simulation and 28.1% in real-world experiments, demonstrating strong noise robustness and spatial generalization.

Figures (21)

• Figure 1: Real-world robotic manipulation with point cloud observations. Image observations are shown in the top row, and the corresponding point cloud observations are shown in the bottom row.
• Figure 2: Comparison of non-equivariant, fragile equivariant, and robust equivariant policies under noisy point cloud observations. Robust equivariance produces consistent behaviors across task progressions, while non-equivariant or fragile equivariant policies suffer from misalignment or instability.
• Figure 3: A rigid transformation of the scene observation induces a corresponding transformation of the expert action.
• Figure 4: Illustration of the canonicalization process. Within each column, observations differ only by $\mathrm{SE}(3)$ transformations and thus share the same canonical form. Across columns, $\mathrm{SE}(3)$-noncoincident observations cannot be aligned and retain distinct canonical representations.
• Figure 5: Clean observations related by an $\mathrm{SE}(3)$ transformation canonicalize to the same frame, whereas noise corrupts this relationship: noisy observations become $\mathrm{SE}(3)$-noncoincident and yield inconsistent canonical forms.

Theorems & Definitions (6)

• Proposition 1
• proof
• Proposition 2
• proof
• Proposition 3
• proof