Boolean Composability of Constraints and Control Synthesis for Multi-Robot Systems via Nonsmooth Control Barrier Functions

Abstract

From mobile sensor networks to autonomous transportation systems, multi-agent solutions have been proposed to accomplish a variety of tasks. However, these systems typically require satisfaction of multiple constraints, such as safety or connectivity maintenance, while completing their primary objectives. Barrier functions represent one method to enforce such constraints via forward set invariance, and this work extends recent results on Boolean composition of nonsmooth barrier functions by explicitly addressing controlled systems, resulting in nonsmooth control barrier functions. The presented results permit a discontinuous controller, which is particularly amenable to control synthesis, and this paper develops an almost-active gradient for Boolean compositions of nonsmooth control barrier functions, which, when included as a constraint to a quadratic program, yields a valid controller. To verify these theoretical findings, the experimental results encode a series of constraints and synthesize a controller for a leader-follow team of mobile robots in real time.