Control Barrier Functions for Prescribed-time Reach-Avoid-Stay Tasks using Spatiotemporal Tubes

Abstract: 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.