Visual imitation learning has achieved remarkable progress in robotic manipulation, yet generalization to unseen objects, scene layouts, and camera viewpoints remains a key challenge. Recent advances address this by using 3D point clouds, which provide geometry-aware, appearance-invariant representations, and by incorporating equivariance into policy architectures to exploit spatial symmetries. However, existing equivariant approaches often lack interpretability and rigor due to unstructured integration of equivariant components. We introduce canonical policy, a principled framework for 3D equivariant imitation learning that unifies 3D point cloud observations under a canonical representation. We first establish a theory of 3D canonical representations, enabling equivariant observation-to-action mappings by grouping both seen and novel point clouds to a canonical representation. We then propose a flexible policy learning pipeline that leverages geometric symmetries from canonical representation and the expressiveness of modern generative models. We validate canonical policy on 12 diverse simulated tasks and 4 real-world manipulation tasks across 16 configurations, involving variations in object color, shape, camera viewpoint, and robot platform. Compared to state-of-the-art imitation learning policies, canonical policy achieves an average improvement of 18.0% in simulation and 39.7% in real-world experiments, demonstrating superior generalization capability and sample efficiency.

Accurate perception of the surrounding environment stands as a primary objective for robots. Through tactile interaction, vision-based tactile sensors provide the capability to capture high-resolution and multi-modal surface information of objects, thereby facilitating robots in achieving more dexterous manipulations. However, the prevailing GelSight sensors entail intricate calibration procedures, posing challenges in their application on curved surfaces and requiring the maintenance of stable lighting conditions throughout experimentation. Additionally, constrained by shape and structure, current vision-based tactile sensors are predominantly applied to measurements within a limited area. In this study, we design a novel cylindrical vision-based tactile sensor that enables continuous and swift perception of large-scale object surfaces through rolling. To tackle the challenges posed by laborious calibration processes, we propose a self-supervised photometric stereo method based on deep learning, which eliminates pre-calibration requirements and enables the derivation of surface normals from a single image without relying on stable lighting conditions. Finally, we perform surface reconstruction from normal and point cloud registration on the multiple frames of images obtained by rolling the cylindrical sensor, resulting in large surface reconstruction. We compare our method with the representative lookup table method in the GelSight sensors. The results show that the proposed method enhances both reconstruction accuracy and robustness, thereby demonstrating the potential of the proposed sensor in large-scale surface reconstruction. Codes and mechanical structures are available at: https://github.com/ZhangZhiyuanZhang/GelRoller