Robust Estimator-Based Safety Verification: A Vector Norm Approach

TL;DR

This paper introduces a new vector norm-based barrier function and estimator approach for safety verification of uncertain SISO systems, enabling safety guarantees without full state measurement and demonstrated via human-exoskeleton simulation.

Contribution

It proposes a novel barrier function and estimator synthesis method using convex optimization for safety verification under uncertainty.

Findings

Measurable upper bound on safety barrier without full state info

Exponential decay of estimator error from initial safety assumption

Successful simulation on human-exoskeleton interaction

Abstract

In this paper, we consider the problem of verifying safety constraint satisfaction for single-input single-output systems with uncertain transfer function coefficients. We propose a new type of barrier function based on a vector norm. This type of barrier function has a measurable upper bound without full state availability. An identifier-based estimator allows an exact bound for the uncertainty-based component of the barrier function estimate. Assuming that the system is safe initially allows an exponentially decreasing bound on the error due to the estimator transient. Barrier function and estimator synthesis is proposed as two convex sub-problems, exploiting linear matrix inequalities. The barrier function controller combination is then used to construct a safety backup controller. And we demonstrate the system in a simulation of a 1 degree-of-freedom human-exoskeleton interaction.