Perception-Limited Smooth Safety Filtering

TL;DR

This paper introduces perception-aware smooth safety filters for nonlinear control systems with limited sensing, enabling safer and smoother control actions compared to traditional methods.

Contribution

It proposes two novel perception-aware safety filtering approaches that ensure smooth, Lipschitz-safe control under sensing limitations, with theoretical guarantees and practical validation.

Findings

Enables higher-order tracking control for drones and ground robots.

Provides smoother and more robust safety behaviors than classical CBF filters.

Guarantees forward invariance and uniqueness of the closed-loop system.

Abstract

This paper develops a smooth safety-filtering framework for nonlinear control-affine systems under limited perception. Classical Control Barrier Function (CBF) filters assume global availability of the safety function - its value and gradient must be known everywhere - an assumption incompatible with sensing-limited settings, and the resulting filters often exhibit nonsmooth switching when constraints activate. We propose two complementary perception-aware safety filters applicable to general control-invariant safety sets. The first introduces a smooth perception gate that modulates barrier constraints based on sensing range, yielding a closed-form Lipschitz-safe controller with forward-invariance guarantees. The second replaces the hard CBF constraint with a differentiable penalty term, leading to a smooth unconstrained optimization-based safety filter consistent with CBF principles. For both designs, we establish existence, uniqueness, and forward invariance of the closed-loop trajectories. Numerical results demonstrate that the proposed smooth filters enable the synthesis of higher-order tracking controllers for systems such as drones and second-order ground robots, offering substantially smoother and more robust safety-critical behaviors than classical CBF-based filters.