High Order Tuners for Adaptive Safety of Robotic Systems
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.