MIRROR: Reflecting Hidden Symmetries from Offline Robot Interaction Data

Robotic imitation learning has achieved impressive success in learning complex manipulation behaviors from demonstrations. However, many existing robot learning methods do not explicitly account for the physical symmetries of robotic systems, often resulting in asymmetric or inconsistent behaviors under symmetric observations. This limitation is particularly pronounced in dual-arm manipulation, where bilateral symmetry is inherent to both the robot morphology and the structure of many tasks. In this paper, we introduce EquiBim, a symmetry-equivariant policy learning framework for bimanual manipulation that enforces bilateral equivariance between observations and actions during training. Our approach formulates physical symmetry as a group action on both observation and action spaces, and imposes an equivariance constraint on policy predictions under symmetric transformations. The framework is model-agnostic and can be seamlessly integrated into a wide range of imitation learning pipelines with diverse observation modalities and action representations, including point cloud-based and image-based policies, as well as both end-effector-space and joint-space parameterizations. We evaluate EquiBim on RoboTwin, a dual-arm robotic platform with symmetric kinematics, and evaluate it across diverse observation and action configurations in simulation. We further validate the approach on a real-world dual-arm system. Across both simulation and physical experiments, our method consistently improves performance and robustness under distribution shifts. These results suggest that explicitly enforcing physical symmetry provides a simple yet effective inductive bias for bimanual robot learning.

Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in isolation, failing to exploit their combined potential. This paper introduces cross-space symmetry compositions, a framework for learning robot policies that are jointly equivariant to multiple symmetries across configuration and task spaces. Leveraging the differential-geometric structure of the forward kinematics map, we both descend symmetries from configuration to task space and lift symmetries from task to configuration space, enabling their composition within a unified representation space. We validate our framework on simulated and real-world experiments on a dual-arm robot, demonstrating that jointly leveraging multiple symmetries yields improved generalization. Video and source code are available at https://sites.google.com/view/cross-space-symmetries.

Reinforcement learning has enabled impressive locomotion skills on articulated robots, but common policy representations remain only weakly aligned with robot physics. Generic networks ignore kinematic structure, while graph-based policies encode connectivity without specifying how physical quantities transform across symmetric body parts. We introduce a morphological symmetry graph representation for locomotion policy learning and instantiate it in MS-PPO. Starting from the robot's topological graph, our representation augments each observation and action space with the permutation and sign transformations induced by morphological symmetry. This yields a symmetry-equivariant graph actor and a symmetry-invariant graph critic, enforcing the desired policy and value constraints by construction rather than through reward shaping or data augmentation. We evaluate MS-PPO on a variety of locomotion tasks using both Unitree Go2 quadruped and Unitree G1 humanoid, including command tracking, asymmetric joint failures, out-of-distribution command generalization, and zero-shot sim-to-real deployment. Experiments show improved symmetry generalization, robustness, sample efficiency, and model efficiency over topology- and symmetry-aware baselines.