Stochastic Control Barrier Functions under State Estimation: From Euclidean Space to Lie Groups
Ruoyu Lin, Magnus Egerstedt
TL;DR
The paper addresses safety for stochastic systems when the true state is not fully observable and the state evolves on manifolds. It introduces SEA-SCBF, a state-estimation-aware control barrier framework that yields a provable bound on finite-time safety probability by leveraging martingale concentration, while incorporating both process and measurement noise. In linear settings, it delivers closed-form expressions and a CBF-QP, and it extends to Lie groups SE(2) and SE(3) using Lie-algebra tools and Taylor approximations to enable online safety-filtering. Experiments on SE(2) and SE(3) demonstrate improved, uncertainty-adaptive safety and planning performance compared with baseline methods, highlighting practical impact for geometry-aware, safety-critical robotics under uncertainty.
Abstract
Ensuring safety for autonomous systems under uncertainty remains challenging, particularly when safety of the true state is required despite the true state not being fully known. Control barrier functions (CBFs) have become widely adopted as safety filters. However, standard CBF formulations do not explicitly account for state estimation uncertainty and its propagation, especially for stochastic systems evolving on manifolds. In this paper, we propose a safety-critical control framework with a provable bound on the finite-time safety probability for stochastic systems under noisy state information. The proposed framework explicitly incorporates the uncertainty arising from both process and measurement noise, and synthesizes controllers that adapt to the level of uncertainty. The framework admits closed-form solutions in linear settings, and experimental results demonstrate its effectiveness on systems whose state spaces range from Euclidean space to Lie groups.