Control Barrier Functions for Prescribed-time Reach-Avoid-Stay Tasks using Spatiotemporal Tubes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909533828284416 |
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| author | Das, Ratnangshu Bakshi, Pranav Jagtap, Pushpak |
| author_facet | Das, Ratnangshu Bakshi, Pranav Jagtap, Pushpak |
| contents | Prescribed-time reach-avoid-stay (PT-RAS) specifications are crucial in applications requiring precise timing, state constraints, and safety guarantees. While control carrier functions (CBFs) have emerged as a promising approach, providing formal guarantees of safety, constructing CBFs that satisfy PT-RAS specifications remains challenging. In this paper, we present a novel approach using a spatiotemporal tubes (STTs) framework to construct CBFs for PT-RAS tasks. The STT framework allows for the systematic design of CBFs that dynamically manage both spatial and temporal constraints, ensuring the system remains within a safe operational envelope while achieving the desired temporal objectives. The proposed method is validated with two case studies: temporal motion planning of an omnidirectional robot and temporal waypoint navigation of a drone with obstacles, using higher-order CBFs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Control Barrier Functions for Prescribed-time Reach-Avoid-Stay Tasks using Spatiotemporal Tubes Das, Ratnangshu Bakshi, Pranav Jagtap, Pushpak Systems and Control Robotics Prescribed-time reach-avoid-stay (PT-RAS) specifications are crucial in applications requiring precise timing, state constraints, and safety guarantees. While control carrier functions (CBFs) have emerged as a promising approach, providing formal guarantees of safety, constructing CBFs that satisfy PT-RAS specifications remains challenging. In this paper, we present a novel approach using a spatiotemporal tubes (STTs) framework to construct CBFs for PT-RAS tasks. The STT framework allows for the systematic design of CBFs that dynamically manage both spatial and temporal constraints, ensuring the system remains within a safe operational envelope while achieving the desired temporal objectives. The proposed method is validated with two case studies: temporal motion planning of an omnidirectional robot and temporal waypoint navigation of a drone with obstacles, using higher-order CBFs. |
| title | Control Barrier Functions for Prescribed-time Reach-Avoid-Stay Tasks using Spatiotemporal Tubes |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2503.08106 |