Time-Varying Robust Sampled-Data High-Order Control Barrier Functions With Variable Sampling

Safety-critical robots increasingly operate in dynamic environments where safety specifications evolve over time (e.g., moving obstacles) and control inputs are applied digitally via zero-order-hold at a fixed, often conservative update rate. These challenges are addressed within a unified robust sampled-data high-order control barrier function (HOCBF) framework. The sampled-data doubly robust HOCBF condition is extended to time-varying safe sets by incorporating barrier time derivatives and a tightening term that certifies inter-sample safety under explicit time variation. A reachability-certified variable holding-time policy is then introduced, selecting the next update interval online via a scalar feasibility test of the safety-filtered input, allowing longer holds away from constraint activation and shorter updates near constraint-active regions. Validation on a unicycle with a moving circular keep-out set and on a QBot digital twin shows that the time-varying treatment restores safety where a time-invariant baseline fails, while the variable holding-time policy reduces conservatism and unnecessary updates while maintaining forward invariance.