Reciprocal-Compensated Control Barrier Functions for Dynamic Environments with Unknown Derivatives

Guaranteeing safety of a control system is challenging under dynamic environments. Although environmental control barrier functions (ECBFs) have been recently proposed to handle this scenario, they typically require high-order derivatives of environmental information for safe controller synthesis. This letter proposes a new class of ECBFs, termed reciprocal-compensated ECBFs (rECBFs) to strictly guarantee safety under dynamic environments whose high-order derivatives are not available for controller design. A high-order extension of rECBFs is further proposed for constraints with arbitrary relative degree. A case study on adaptive cruise control illustrates the efficacy of the proposed approach.