3D Equivariant Visuomotor Policy Learning via Spherical Projection

Equivariant models have recently been shown to improve the data efficiency of diffusion policy by a significant margin. However, prior work that explored this direction focused primarily on point cloud inputs generated by multiple cameras fixed in the workspace. This type of point cloud input is not compatible with the now-common setting where the primary input modality is an eye-in-hand RGB camera like a GoPro. This paper closes this gap by incorporating into the diffusion policy model a process that projects features from the 2D RGB camera image onto a sphere. This enables us to reason about symmetries in SO(3) without explicitly reconstructing a point cloud. We perform extensive experiments in both simulation and the real world that demonstrate that our method consistently outperforms strong baselines in terms of both performance and sample efficiency. Our work is the first SO(3)-equivariant policy learning framework for robotic manipulation that works using only monocular RGB inputs.

A Practical Guide for Incorporating Symmetry in Diffusion Policy

Recently, equivariant neural networks for policy learning have shown promising improvements in sample efficiency and generalization, however, their wide adoption faces substantial barriers due to implementation complexity. Equivariant architectures typically require specialized mathematical formulations and custom network design, posing significant challenges when integrating with modern policy frameworks like diffusion-based models. In this paper, we explore a number of straightforward and practical approaches to incorporate symmetry benefits into diffusion policies without the overhead of full equivariant designs. Specifically, we investigate (i) invariant representations via relative trajectory actions and eye-in-hand perception, (ii) integrating equivariant vision encoders, and (iii) symmetric feature extraction with pretrained encoders using Frame Averaging. We first prove that combining eye-in-hand perception with relative or delta action parameterization yields inherent SE(3)-invariance, thus improving policy generalization. We then perform a systematic experimental study on those design choices for integrating symmetry in diffusion policies, and conclude that an invariant representation with equivariant feature extraction significantly improves the policy performance. Our method achieves performance on par with or exceeding fully equivariant architectures while greatly simplifying implementation.

Hierarchical Equivariant Policy via Frame Transf

Recent advances in hierarchical policy learning highlight the advantages of decomposing systems into high-level and low-level agents, enabling efficient long-horizon reasoning and precise fine-grained control. However, the interface between these hierarchy levels remains underexplored, and existing hierarchical methods often ignore domain symmetry, resulting in the need for extensive demonstrations to achieve robust performance. To address these issues, we propose Hierarchical Equivariant Policy (HEP), a novel hierarchical policy framework. We propose a frame transfer interface for hierarchical policy learning, which uses the high-level agent's output as a coordinate frame for the low-level agent, providing a strong inductive bias while retaining flexibility. Additionally, we integrate domain symmetries into both levels and theoretically demonstrate the system's overall equivariance. HEP achieves state-of-the-art performance in complex robotic manipulation tasks, demonstrating significant improvements in both simulation and real-world settings.

Coarse-to-Fine 3D Keyframe Transporter

Recent advances in Keyframe Imitation Learning (IL) have enabled learning-based agents to solve a diverse range of manipulation tasks. However, most approaches ignore the rich symmetries in the problem setting and, as a consequence, are sample-inefficient. This work identifies and utilizes the bi-equivariant symmetry within Keyframe IL to design a policy that generalizes to transformations of both the workspace and the objects grasped by the gripper. We make two main contributions: First, we analyze the bi-equivariance properties of the keyframe action scheme and propose a Keyframe Transporter derived from the Transporter Networks, which evaluates actions using cross-correlation between the features of the grasped object and the features of the scene. Second, we propose a computationally efficient coarse-to-fine SE(3) action evaluation scheme for reasoning the intertwined translation and rotation action. The resulting method outperforms strong Keyframe IL baselines by an average of >10% on a wide range of simulation tasks, and by an average of 55% in 4 physical experiments.

Baichuan-Omni-1.5 Technical Report

We introduce Baichuan-Omni-1.5, an omni-modal model that not only has omni-modal understanding capabilities but also provides end-to-end audio generation capabilities. To achieve fluent and high-quality interaction across modalities without compromising the capabilities of any modality, we prioritized optimizing three key aspects. First, we establish a comprehensive data cleaning and synthesis pipeline for multimodal data, obtaining about 500B high-quality data (text, audio, and vision). Second, an audio-tokenizer (Baichuan-Audio-Tokenizer) has been designed to capture both semantic and acoustic information from audio, enabling seamless integration and enhanced compatibility with MLLM. Lastly, we designed a multi-stage training strategy that progressively integrates multimodal alignment and multitask fine-tuning, ensuring effective synergy across all modalities. Baichuan-Omni-1.5 leads contemporary models (including GPT4o-mini and MiniCPM-o 2.6) in terms of comprehensive omni-modal capabilities. Notably, it achieves results comparable to leading models such as Qwen2-VL-72B across various multimodal medical benchmarks.

Equivariant Reinforcement Learning under Partial Observability

Incorporating inductive biases is a promising approach for tackling challenging robot learning domains with sample-efficient solutions. This paper identifies partially observable domains where symmetries can be a useful inductive bias for efficient learning. Specifically, by encoding the equivariance regarding specific group symmetries into the neural networks, our actor-critic reinforcement learning agents can reuse solutions in the past for related scenarios. Consequently, our equivariant agents outperform non-equivariant approaches significantly in terms of sample efficiency and final performance, demonstrated through experiments on a range of robotic tasks in simulation and real hardware.

OrbitGrasp: $SE(3)$-Equivariant Grasp Learning

While grasp detection is an important part of any robotic manipulation pipeline, reliable and accurate grasp detection in $SE(3)$ remains a research challenge. Many robotics applications in unstructured environments such as the home or warehouse would benefit a lot from better grasp performance. This paper proposes a novel framework for detecting $SE(3)$ grasp poses based on point cloud input. Our main contribution is to propose an $SE(3)$-equivariant model that maps each point in the cloud to a continuous grasp quality function over the 2-sphere $S^2$ using a spherical harmonic basis. Compared with reasoning about a finite set of samples, this formulation improves the accuracy and efficiency of our model when a large number of samples would otherwise be needed. In order to accomplish this, we propose a novel variation on EquiFormerV2 that leverages a UNet-style backbone to enlarge the number of points the model can handle. Our resulting method, which we name $\textit{OrbitGrasp}$, significantly outperforms baselines in both simulation and physical experiments.

Equivariant Diffusion Policy

Recent work has shown diffusion models are an effective approach to learning the multimodal distributions arising from demonstration data in behavior cloning. However, a drawback of this approach is the need to learn a denoising function, which is significantly more complex than learning an explicit policy. In this work, we propose Equivariant Diffusion Policy, a novel diffusion policy learning method that leverages domain symmetries to obtain better sample efficiency and generalization in the denoising function. We theoretically analyze the $\mathrm{SO}(2)$ symmetry of full 6-DoF control and characterize when a diffusion model is $\mathrm{SO}(2)$-equivariant. We furthermore evaluate the method empirically on a set of 12 simulation tasks in MimicGen, and show that it obtains a success rate that is, on average, 21.9% higher than the baseline Diffusion Policy. We also evaluate the method on a real-world system to show that effective policies can be learned with relatively few training samples, whereas the baseline Diffusion Policy cannot.

Open-vocabulary Pick and Place via Patch-level Semantic Maps

Controlling robots through natural language instructions in open-vocabulary scenarios is pivotal for enhancing human-robot collaboration and complex robot behavior synthesis. However, achieving this capability poses significant challenges due to the need for a system that can generalize from limited data to a wide range of tasks and environments. Existing methods rely on large, costly datasets and struggle with generalization. This paper introduces Grounded Equivariant Manipulation (GEM), a novel approach that leverages the generative capabilities of pre-trained vision-language models and geometric symmetries to facilitate few-shot and zero-shot learning for open-vocabulary robot manipulation tasks. Our experiments demonstrate GEM's high sample efficiency and superior generalization across diverse pick-and-place tasks in both simulation and real-world experiments, showcasing its ability to adapt to novel instructions and unseen objects with minimal data requirements. GEM advances a significant step forward in the domain of language-conditioned robot control, bridging the gap between semantic understanding and action generation in robotic systems.

Equivariant Offline Reinforcement Learning

Sample efficiency is critical when applying learning-based methods to robotic manipulation due to the high cost of collecting expert demonstrations and the challenges of on-robot policy learning through online Reinforcement Learning (RL). Offline RL addresses this issue by enabling policy learning from an offline dataset collected using any behavioral policy, regardless of its quality. However, recent advancements in offline RL have predominantly focused on learning from large datasets. Given that many robotic manipulation tasks can be formulated as rotation-symmetric problems, we investigate the use of $SO(2)$-equivariant neural networks for offline RL with a limited number of demonstrations. Our experimental results show that equivariant versions of Conservative Q-Learning (CQL) and Implicit Q-Learning (IQL) outperform their non-equivariant counterparts. We provide empirical evidence demonstrating how equivariance improves offline learning algorithms in the low-data regime.