Symmetries Here and There, Combined Everywhere: Cross-space Symmetry Compositions in Robotics

In robot learning, scaling training datasets across diverse embodiments and environments has become a dominant paradigm for learning generalizable robot policies. These policies are commonly trained via behavior cloning to imitate actions from pre-collected demonstrations. However, since robot actions are tied to the dynamics of the data collection robot, different robots may require different actions to achieve the same motion. This discrepancy hinders both policy training and deployment across diverse robots. To address this, we propose using Cartesian state delta as a universal action representation across robots, and introduce State Prediction and Adaptive Command Execution (SPACE) framework. SPACE handles robot dynamics variation at three levels: across different embodiments, across hardware units of the same embodiment, and within a single robot during operation. It consists of two components: (i) a Cartesian state delta policy that predicts geometric end-effector displacement, and (ii) Action Adapter, which converts the predicted Cartesian state delta into robot-specific control commands. Experiments show that SPACE substantially outperforms policies that directly predict control commands when learning from data collected across different embodiments and across hardware units of the same embodiment. SPACE also remains robust under dynamics shifts at deployment, including changes in control frequency, object weight, and controller gains. The project page is available at http://haeone.site/space-website/.

Deep reinforcement policy learning directly in physical robots (on-robot learning) remains bottlenecked by slow wall-clock training times. We present SymmGrid, a trajectory level augmentation framework inspired by parallelized symmetries that super-scales group transformations to significantly accelerate on-robot learning in both egocentric and exocentric visual setups. We model a Markov Decision Process (MDP) under a symmetry tree, in which state-action pairs have admissible parallelized invariant transformations that yield a geometric grid structure. The state is modelled with ego- or exocentric images and proprioception information. The latter require special treatment, in the form of homographies, to warp visual scenes in line with their corresponding spatial transformations. These parallelized transformations produce a large set of unique symmetric equivalences that populate the replay buffer with diverse and consistent experiences that speed up learning and improve performance. We present extensive training and evaluations performed directly on real robot manipulation contact tasks including peg-insertions, cable routing, and object relocations. Relative to SOTA, SymmGrid achieved wall-clock training convergence speed-ups of 1.37-2.17x, evaluation success rate improvements of 1.09x-1.27x, fastest training convergence times of 16.6, 10.9, and 79.3 minutes respectively. For trajectory wide assessments, we used normalized area under the curve (nAUC) ratios. SymmGrid achieved improvements of up to 2.59x. These results confirm that simple branch symmetries can have an outsized result due to super-scaling and bring us closer to sub-10 minute on-robot learning training in manipulation tasks suitable for arms and humanoids. The project page is available at symmgrid-robot.github.io

Mobile manipulation requires coordinated control of high-dimensional, bimanual robots. Imitation learning methods have been broadly used to solve these robotic tasks, yet typically ignore the bilateral morphological symmetry inherent in such systems. We argue that morphological symmetry is an underexplored but crucial inductive bias for learning in bimanual mobile manipulation: knowing how to solve a task in one configuration directly determines how to solve its mirrored counterpart. In this paper, we formalize this symmetry prior and show that it constrains optimal bimanual policies to be ambidextrous and equivariant under reflections across the robot's sagittal plane. We introduce a $\mathbb{C}_2$-equivariant flow matching policy that enforces reflective symmetry either via a regularized training loss or an equivariant velocity network. Across planar and 6-DoF mobile manipulation tasks, symmetry-informed policies consistently improve sample efficiency and achieve zero-shot generalization to mirrored configurations absent from the training distribution. We further validate this zero-shot generalization capability on a real-world manipulation task with a TIAGo++ robot. Together, our findings establish morphological symmetry as an effective, generalizable, and scalable inductive bias for ambidextrous generative policy learning.