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Abstraction-based formal synthesis with a symbolic control barrier function is useful for obtaining a finite-state safe controller for an infinite system with sporadic disturbances. In the case of multiple mobile robots sharing a common workspace, a controller ensuring arrival to destinations without any collisions is obtained with the symbolic control barrier function, despite the existence of unpredictable sporadic packet dropouts among robots. In the existing method, a local abstracted model of each robot is constructed, they are composed to obtain an abstracted model of the entire system, and unsafe transitions in it are eliminated with a symbolic control barrier function. However, a considerable computation time is required when the number of robots is large. To solve this problem, a shield called an alternating simulation-based shield (AS-Shield) was introduced into abstraction-based formal synthesis. As well as the existing method, a local abstracted model for each robot was constructed. Instead of the composition, a local controller was constructed for each robot, and a safe controller for the robot was obtained by attaching an AS-Shield. Because a composition to obtain the entire system is not necessary, the control inputs are computable, even though the number of robots is large. To confirm the validity of the proposed method, it was implemented using a robot simulator. |
