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

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