Robust Adaptive Time-Varying Control Barrier Function with Application to Robotic Surface Treatment

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.