Multirobot Adversarial Resilience Using Control Barrier Functions
Matthew Cavorsi, Lorenzo Sabattini, Stephanie Gil
Abstract
In this article, we develop an algorithm for resilient path planning, where a team of robots must navigate in a resilient formation such that they achieve <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F$</tex-math></inline-formula> -resilience, meaning they can coordinate in the presence of up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F$</tex-math></inline-formula> adversaries. Resilient formations are those having high connectivity often achieved by driving robots close together. Unfortunately, the objective of maintaining resilience can often times conflict with achieving collision and obstacle avoidance. We seek to provide safe navigation while maintaining resilience by employing a local controller that uses control barrier functions (CBFs). CBF-based formulations are amenable to satisfying multiple objectives, but can be prone to deadlock if any of the objectives conflict with each other. Furthermore, it is difficult to know a priori where this may occur in a given environment. To this end, we 1) characterize when the environment will force a tradeoff between safe navigation and resilience, and 2) develop an algorithm that derives a new representation of the environment in which areas where resilience cannot be provably guaranteed are blocked off. This algorithm can be used to plan a path through an environment that always provably admits a resilient formation. If the algorithm cannot find such a path, an alternative CBF is proposed where resilience can be treated as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">soft constraint</i> . For this case, a nested form of the CBF is executed and a critical gain is derived that provably prioritizes navigation over resilience while resilience is not attainable. Finally, in addition to simulation results, we run hardware experiments with six GoPiGo differential-drive robots that achieve <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F$</tex-math></inline-formula> -resilient consensus while navigating through a cluttered environment, to showcase the applicability of our methods in the presence of adversaries.