Information Control Barrier Functions: Preventing Localization Failures in Mobile Systems Through Control

TL;DR

This paper introduces a control barrier function-based framework to ensure the well-conditioned nature of localization algorithms in mobile systems, preventing failures by maintaining positive Hessian eigenvalues for safe state estimation.

Contribution

It presents a novel, general control barrier function approach to guarantee localization safety without relying on specific measurement types or system constraints.

Findings

Successfully prevents localization failures in range-only and heading-only measurement scenarios.

Ensures the Hessian matrix remains positive definite for stable localization.

Provides a general framework applicable to various measurement types.

Abstract

This paper develops a new framework for preventing localization failures in mobile systems that must estimate their state using measurements. Safety is guaranteed by imposing the nonlinear least squares optimization solved in modern localization algorithms remains well-conditioned. Specifically, the eigenvalues of the Hessian matrix are made to be always positive via two methods that leverage control barrier functions to achieve safe set invariance. The proposed method is not constrained to any specific measurement or system type, offering a very general solution to the safe mobility with localization problem. The efficacy of the approach is demonstrated on a system being provided range-only and heading-only measurements for localization.