As learning-based methods for legged robots rapidly grow in popularity, it is important that we can provide safety assurances efficiently across different controllers and environments. Existing works either rely ona prioriknowledge of the environment and safety constraints to ensure system safety or provide assurances for a specific locomotion policy. To address these limitations, we propose an observation-conditioned reachability-based (OCR) safety-filter framework. Our key idea is to use an OCR value network (OCR-VN) that predicts the optimal control-theoretic safety value function for new failure regions and dynamic uncertainty during deployment time. Specifically, the OCR-VN facilitates rapid safety adaptation through two key components: a LiDAR-based input that allows the dynamic construction of safe regions in light of new obstacles and a disturbance estimation module that accounts for dynamics uncertainty in the wild. The predicted safety value function is used to construct an adaptive safety filter that overrides the nominal quadruped controller when necessary to maintain safety. Through simulation studies and hardware experiments on a Unitree Go1 quadruped in agile planar navigation tasks, we demonstrate that the proposed framework can automatically safeguard a wide range of hierarchical quadruped controllers, adapts to novel environments, and is robust to unmodeled dynamicswithout a priori access to the controllers or environments- hence, “One Filter to Deploy Them All”. The experiment videos can be found on the project website here:https://sia-lab-git.github.io/One_Filter_to_Deploy_Them_All.

Providing formal safety and performance guarantees for autonomous systems is becoming increasingly important. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for providing these guarantees, since it can handle general nonlinear system dynamics, bounded adversarial system disturbances, and state and input constraints. However, it involves solving a PDE, whose computational and memory complexity scales exponentially with respect to the state dimensionality, making its direct use on large-scale systems intractable. A recently proposed method called DeepReach overcomes this challenge by leveraging a sinusoidal neural PDE solver for high-dimensional reachability problems, whose computational requirements scale with the complexity of the underlying reachable tube rather than the state space dimension. Unfortunately, neural networks can make errors and thus the computed solution may not be safe, which falls short of achieving our overarching goal to provide formal safety assurances. In this work, we propose a method to compute an error bound for the DeepReach solution. This error bound can then be used for reachable tube correction, resulting in a safe approximation of the true reachable tube. We also propose a scenario-based optimization approach to compute a probabilistic bound on this error correction for general nonlinear dynamical systems. We demonstrate the efficacy of the proposed approach in obtaining probabilistically safe reachable tubes for high-dimensional rocket-landing and multi-vehicle collision-avoidance problems.