Safe Control using Learned Safety Filters and Adaptive Conformal Inference

We augment the Slotine--Li adaptive controller for Euler--Lagrange systems with three learned components: a structured-quadratic Lyapunov function $V_ψ$ whose positive-definiteness follows from a Cholesky parameterization, a residual Soft Actor--Critic policy that adds bounded torque corrections to the analytic baseline, and a physics-informed neural network that estimates unmodeled dynamics. A closed-form safety filter, derived from the single affine constraint $\dot V_ψ+ αV_ψ\le 0$, projects every policy output onto the safe set without requiring an online QP solver. We prove: global feasibility of the filter under a drift-decay condition on the control-degeneracy set; exponential stability under exact shielding, with a robust extension whose margin depends on the PINN approximation error; almost-sure convergence of the three-timescale policy--certificate--multiplier updates to a KKT point; and a PAC generalization bound for the certificate over compacts. On a 2-DOF manipulator with nonlinear friction and variable payload, the learned certificate accounts for most of the empirical gain: tracking error drops by 41% on nominal friction and 24% on aggressive friction at the centroid of the training distribution. A 7-DOF scalability study on a Franka Emika Panda confirms clean convergence of the full pipeline at industrial scale, identifies the conditions under which gains over exact model-based baselines should and should not be expected, and documents a warm-start pathology of the learned certificate that has practical implications for deployment.

Autonomous robots that interact with people must make safe and efficient decisions under human-induced uncertainty, such as their preferences, goals, competency, and willingness to cooperate. Safety filters are a popular approach for ensuring safety in interactive robotics, since their modular design separates safety from performance, allowing robots to operate safely around people with minimal impact on task efficiency. While traditional safety filters typically operate only in the physical space, neglecting the robot's ability to learn and adapt online, the recently proposed belief-space safety filter (BeliefSF) reasons about robot safety in closed-loop with runtime inference that actively reduces the robot's uncertainty online, thereby reducing conservativeness in filtering. However, providing formal safety guarantees for robots deploying BeliefSF remains a significant challenge due to errors in runtime inference and neural approximation of safety filters required to handle the high dimensionality of belief spaces. In this paper, we propose an algorithmic approach to certify high-probability safety of BeliefSF using conformal prediction, while explicitly accounting for the reliability of the robot's runtime inference module. Our method leverages the structure of belief-space safety filtering by focusing verification on a region where inference is expected to be reliable. It preserves the simplicity and sample complexity of standard conformal prediction, yet can certify a substantially less conservative safety filter. Through a simulated human-vehicle interaction benchmark, we show that our approach verifies a significantly more permissive belief-space safety filter than a standard conformal prediction baseline.

Reinforcement learning (RL), while powerful and expressive, can often prioritize performance at the expense of safety. Yet safety violations can lead to catastrophic outcomes in real-world deployments. Control Barrier Functions (CBFs) offer a principled method to enforce dynamic safety -- traditionally deployed online via safety filters. While the result is safe behavior, the fact that the RL policy does not have knowledge of the CBF can lead to conservative behaviors. This paper proposes CBF-RL, a framework for generating safe behaviors with RL by enforcing CBFs in training. CBF-RL has two key attributes: (1) minimally modifying a nominal RL policy to encode safety constraints via a CBF term, (2) and safety filtering of the policy rollouts in training. Theoretically, we prove that continuous-time safety filters can be deployed via closed-form expressions on discrete-time roll-outs. Practically, we demonstrate that CBF-RL internalizes the safety constraints in the learned policy -- both enforcing safer actions and biasing towards safer rewards -- enabling safe deployment without the need for an online safety filter. We validate our framework through ablation studies on navigation tasks and on the Unitree G1 humanoid robot, where CBF-RL enables safer exploration, faster convergence, and robust performance under uncertainty, enabling the humanoid robot to avoid obstacles and climb stairs safely in real-world settings without a runtime safety filter.