This study focuses on synthesizing controllers for unknown dynamics control-affine nonlinear systems, aiming to satisfy reach-avoid-stay (RAS) specifications within prescribed-time. The main objective is to derive a closed-form control law, incorporating a novel notion of spatiotemporal tubes, to guarantee that the system trajectories reach a designated target set while avoiding an unsafe set and adhering to state constraints. The efficacy of this approach is demonstrated through simulation.

Multi-robot exploration is a complex problem that involves multiple robots working in a shared unknown environment. In such scenarios, the safety of the robots is of paramount importance alongside the completion of the exploration task. In this paper, we propose a modular exploration framework that (i) identifies safe frontier targets for multiple robots while taking into account the system dynamics of each robot to ensure collision avoidance with previously unknown obstacles and (ii) ensures that the robots reach their exploration targets while avoiding any obstacles discovered and each other. We employ a scalable approach to generate symbolic controllers for the multi-robot system, utilizing distance functions. We also provide formal guarantees on the safety of the exploration targets and the completion of each exploration run, with the robots avoiding collisions with each other and the obstacles. We test our approach on simulation experiments and a real-world implementation to validate it.