{"ID":2893090,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.13888","arxiv_id":"2507.13888","title":"Fixed time convergence guarantees for Higher Order Control Barrier Functions","abstract":"We present a novel method for designing higher-order Control Barrier Functions (CBFs) that guarantee convergence to a safe set within a user-specified finite. Traditional Higher Order CBFs (HOCBFs) ensure asymptotic safety but lack mechanisms for fixed-time convergence, which is critical in time-sensitive and safety-critical applications such as autonomous navigation. In contrast, our approach imposes a structured differential constraint using repeated roots in the characteristic polynomial, enabling closed-form polynomial solutions with exact convergence at a prescribed time. We derive conditions on the barrier function and its derivatives that ensure forward invariance and fixed-time reachability, and we provide an explicit formulation for second-order systems. Our method is evaluated on three robotic systems - a point-mass model, a unicycle, and a bicycle model and benchmarked against existing HOCBF approaches. Results demonstrate that our formulation reliably enforces convergence within the desired time, even when traditional methods fail. This work provides a tractable and robust framework for real-time control with provable finite-time safety guarantees.","short_abstract":"We present a novel method for designing higher-order Control Barrier Functions (CBFs) that guarantee convergence to a safe set within a user-specified finite. Traditional Higher Order CBFs (HOCBFs) ensure asymptotic safety but lack mechanisms for fixed-time convergence, which is critical in time-sensitive and safety-cr...","url_abs":"https://arxiv.org/abs/2507.13888","url_pdf":"https://arxiv.org/pdf/2507.13888v1","authors":"[\"Janani S K\",\"Shishir Kolathaya\"]","published":"2025-07-18T13:05:47Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"cs.RO\"]","methods":"[]","has_code":false}