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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.13888 |
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| _version_ | 1866911063757291520 |
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| author | K, Janani S Kolathaya, Shishir |
| author_facet | K, Janani S Kolathaya, Shishir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13888 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed time convergence guarantees for Higher Order Control Barrier Functions K, Janani S Kolathaya, Shishir Systems and Control Robotics 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. |
| title | Fixed time convergence guarantees for Higher Order Control Barrier Functions |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2507.13888 |