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

Prescribed-time reach-avoid-stay (PT-RAS) specifications are critical in applications that involve guiding a system to reach a desired state within a specified time, avoiding unsafe regions, and respecting state constraints [1]. PT-RAS tasks also serve as fundamental building blocks in the design of complex specifications [2, 3] for autonomous systems involving temporal and spatial constraints. Effective design control strategies ensuring PT-RAS task is crucial in applications like robotics, autonomous vehicles, and aerospace to ensure reliability and safety with precise timing. Several control techniques have been proposed in the literature to address these specifications, including model predictive control (MPC) [4] and potential field methods [5, 6]. While these approaches can handle time-bound tasks and obstacle avoidance, they often suffer from difficulty in ensuring safety guarantees over the entire mission duration. These limitations highlight the need for more efficient and reliable methods that can provide formal safety guarantees. Symbolic control techniques [7] have emerged as powerful tools for specifying and solving complex tasks. However, these techniques typically rely on state space abstraction, which can lead to increased computational complexity.