Ensuring safety of learning-enabled robotic manipulation across diverse embodiments and tasks still requires significant manual engineering. Existing approaches typically rely on heuristically designed fallback controllers or complex forward invariance assessments. These methods are often too conservative for task success, too computationally expensive for real-time execution, too heuristic to provide useful safety guarantees, or too engineering-heavy to transfer between setups. In this paper, we propose a universal safeguarding approach, X-Safe, which reasons directly in the robot's configuration space to provide formal probabilistic guarantees for collision avoidance. By operating in the configuration space, our method transfers across embodiments while relying solely on an object-based, quasi-static scene representation and a forward kinematics model of the robotic manipulator. Thus, X-Safe provides useful formal safety guarantees without requiring additional data, or engineering effort for different embodiments or scenes. We demonstrate X-Safe for diverse embodiments and policies, both in simulation and on hardware. We observe less degradation in task performance compared to state-of-the-art safeguarding, no collisions on hardware experiments, and empirically corroborate our formal guarantees.

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