CrossSafe: Towards Cross-Embodiment Latent Safety Filters

Cross-embodiment learning has shown that a single model, such as a vision-language-action (VLA) model, can learn state representations and manipulation skills that can be applied across heterogeneous robots to accomplish various tasks. We hypothesize that the same holds for safety enforcement. The reasoning required to satisfy a safety constraint, such as detecting an obstacle, recognizing that it should be avoided, and selecting a safe abstract action, is largely shared across robots. What differs across embodiments is how the abstract safe action is realized: morphology, kinematics, and dynamics determine which actions are safe and feasible. Consequently, the same action can be safe for one robot and unsafe for another. This is especially important for generalist manipulation policies that operate in a common end-effector action space without explicitly capturing how safety depends on the robot's morphology and kinematics. We propose embodiment-conditioned safety filtering, in which a Hamilton-Jacobi reachability-based value function and its corresponding safety-maximizing policy are shared across robots. Using a morphology-aware latent representation of the robot and its environment, we perform Hamilton-Jacobi reachability analysis directly in latent space so that the learned safety concepts can generalize across embodiments while remaining explicitly conditioned on each robot's morphology and kinematics. We evaluate our approach across five bimanual robot embodiments and five manipulation tasks with whole-body collision-avoidance constraints. Our results show that a single policy, jointly trained across five manipulation tasks and four embodiments, exhibits zero-shot generalization to a held-out embodiment, reducing the nominal policy's collision rate. They also show that training using more embodiments improves generalization.