Set invariance techniques such as control barrier functions (CBFs) can be used to enforce time-varying constraints such as keeping a safe distance from dynamic objects. However, existing methods for enforcing time-varying constraints often overlook model uncertainties. To address this issue, this paper proposes a CBFs-based robust adaptive controller design endowing time-varying constraints while considering parametric uncertainty and additive disturbances. To this end, we first leverage Robust adaptive Control Barrier Functions (RaCBFs) to handle model uncertainty, along with the concept of Input-to-State Safety (ISSf) to ensure robustness towards input disturbances. Furthermore, to alleviate the inherent conservatism in robustness, we also incorporate a set membership identification scheme. We demonstrate the proposed method on robotic surface treatment that requires time-varying force bounds to ensure uniform quality, in numerical simulation and real robotic setup, showing that the quality is formally guaranteed within an acceptable range.

翻译：控制屏障函数（CBFs）等集合不变性技术可用于强制执行时变约束，例如与动态物体保持安全距离。然而，现有强制执行时变约束的方法往往忽略模型不确定性。为解决此问题，本文提出一种基于CBFs的鲁棒自适应控制器设计，在考虑参数不确定性和加性扰动的同时赋予时变约束能力。为此，我们首先利用鲁棒自适应控制屏障函数（RaCBFs）处理模型不确定性，并结合输入到状态安全（ISSf）概念确保对输入扰动的鲁棒性。此外，为减轻鲁棒性固有的保守性，我们还引入了集合成员辨识方案。我们在机器人表面处理任务中验证了所提方法——该任务需要时变力约束以确保均匀质量，通过数值仿真和真实机器人实验表明，质量可在可接受范围内得到形式化保证。