High Order Tuners for Adaptive Safety of Robotic Systems

TL;DR

This paper introduces high-order tuners to improve adaptive safety in robotic systems, reducing conservativeness and decoupling adaptation gains from initial conditions for better safety guarantees.

Contribution

It extends high-order tuners to adaptive safety frameworks, enabling less conservative conditions and improved safety performance in nonlinear robotic systems.

Findings

High-order tuners decouple adaptation gains from initial conditions.

Simulations demonstrate improved safety performance.

Extension to linear-in-parameters robotic systems.

Abstract

The combination of control barrier functions (CBFs) and adaptive control -- a framework referred to as adaptive safety -- has proven to be a powerful paradigm for safety-critical control of nonlinear systems with parametric uncertainties. Yet the theoretical conditions for forward invariance within this framework are often quite conservative, and may require using large adaptation gains to achieve acceptable performance, an approach that is traditionally discouraged in adaptive control. This paper mitigates these issues via high-order tuners, a recent class of higher-order adaptation laws that leverages different adaptation gains at different orders of differentiation. We illustrate that these high-order tuners decouple adaptation gain conditions from those placed on the initial conditions of the system required for set invariance. We extend these results to robotic systems whose linear-in-the-parameters structure proves particularly useful for adaptive control. The efficacy of our results are illustrated via simulations.