How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraints

TL;DR

This paper introduces LatentCBF, a method for smooth safety filtering in high-dimensional visuomotor control that overcomes incompatibilities in existing latent-space reachability approaches, improving safety and task success.

Contribution

The paper identifies fundamental issues with current latent-space reachability value functions and proposes LatentCBF, a novel approach with gradient penalties and mixed data training for smooth, effective safety filtering.

Findings

LatentCBF enables smooth safety filtering in high-dimensional control.

It doubles task completion rate compared to prior switching methods.

Experiments validate improved safety and performance on benchmarks and hardware.

Abstract

Latent safety filters extend Hamilton-Jacobi (HJ) reachability to operate on latent state representations and dynamics learned directly from high-dimensional observations, enabling safe visuomotor control under hard-to-model constraints. However, existing methods implement "least-restrictive" filtering that discretely switch between nominal and safety policies, potentially undermining the task performance that makes modern visuomotor policies valuable. While reachability value functions can, in principle, be adapted to be control barrier functions (CBFs) for smooth optimization-based filtering, we theoretically and empirically show that current latent-space learning methods produce fundamentally incompatible value functions. We identify two sources of incompatibility: First, in HJ reachability, failures are encoded via a "margin function" in latent space, whose sign indicates whether or not a latent is in the constraint set. However, representing the margin function as a classifier yields saturated value functions that exhibit discontinuous jumps. We prove that the value function's Lipschitz constant scales linearly with the margin function's Lipschitz constant, revealing that smooth CBFs require smooth margins. Second, reinforcement learning (RL) approximations trained solely on safety policy data yield inaccurate value estimates for nominal policy actions, precisely where CBF filtering needs them. We propose the LatentCBF, which addresses both challenges through gradient penalties that lead to smooth margin functions without additional labeling, and a value-training procedure that mixes data from both nominal and safety policy distributions. Experiments on simulated benchmarks and hardware with a vision-based manipulation policy demonstrate that LatentCBF enables smooth safety filtering while doubling the task-completion rate over prior switching methods.