Safe Adaptive Control With Vanishing Conservativeness for Robotic Systems With Unknown Dynamics via Barrier Functions

Adaptive controllers offer powerful tools for controlling nonlinear systems with parametric uncertainties, yet ensuring safety, particularly during the initial learning phase, remains a significant challenge. Conventional safety approaches often rely on filtering the control output using Control Barrier Functions (CBFs), which may fail to prevent unsafe behavior when parameter estimates are poor and can lead to reckless or overly conservative actions. This paper introduces a novel framework that directly integrates safety constraints into the parameter adaptation process itself. We propose enforcing safety by modulating the parameter update law through a minimally invasive perturbation, calculated via a real-time Quadratic Program (QP). This QP incorporates constraints derived from both a Robust Adaptive Control Lyapunov Function (RaCLF), ensuring system stability, and a CBF, guaranteeing forward invariance of a safe set. Critically, the CBF constraint leverages a formally derived, time-varying upper bound on the parameter estimation error, mitigating conservativeness as the system learns. We provide formal proofs for the stability of the closed-loop system and the validity of the safety constraint. The efficacy and practicality of the proposed safe parameter update strategy are demonstrated across diverse platforms, including numerical simulations of a mass-damper system and a mobile robot, high-fidelity simulation of a UR10 manipulator, and hardware experiments on a quadrupedal robot navigating amidst obstacles.