Spatiotemporal Tubes based Control of Unknown Multi-Agent Systems for Temporal Reach-Avoid-Stay Tasks

The paper focuses on designing a controller for unknown dynamical multi-agent systems to achieve temporal reach-avoid-stay tasks for each agent while preventing inter-agent collisions. The main objective is to generate a spatiotemporal tube (STT) for each agent and thereby devise a closed-form, approximation-free, and decentralized control strategy that ensures the system trajectory reaches the target within a specific time while avoiding time-varying unsafe sets and collisions with other agents. In order to achieve this, the requirements of STTs are formulated as a robust optimization problem (ROP) and solved using a sampling-based scenario optimization problem (SOP) to address the issue of infeasibility caused by the infinite number of constraints in ROP. The STTs are generated by solving the SOP, and the corresponding closed-form control is designed to fulfill the specified task. Finally, the effectiveness of our approach is demonstrated through two case studies, one involving omnidirectional robots and the other involving multiple drones modelled as Euler-Lagrange systems.