Barrier Function-based Collaborative Control of Multiple Robots under Signal Temporal Logic Tasks

Motivated by the recent interest in cyber-physical and autonomous robotic systems, we study the problem of dynamically coupled multi-agent systems under a set of signal temporal logic tasks. In particular, the satisfaction of each of these signal temporal logic tasks depends on the behavior of a distinct set of agents. Instead of abstracting the agent dynamics and the temporal logic tasks into a discrete domain and solving the problem therein or using optimization-based methods, we derive collaborative feedback control laws. These control laws are based on a decentralized control barrier function condition that results in discontinuous control laws, as opposed to a centralized condition resembling the single-agent case. The benefits of our approach are inherent robustness properties typically present in feedback control as well as satisfaction guarantees for continuous-time multi-agent systems. More specifically, time-varying control barrier functions are used that account for the semantics of the signal temporal logic tasks at hand. For a certain fragment of signal temporal logic tasks, we further propose a systematic way to construct such control barrier functions. Finally, we show the efficacy and robustness of our framework in an experiment including a group of three omnidirectional robots.