Nonsmooth Barrier Functions with Applications to Multi-Robot Systems

As multi-agent systems become ubiquitous, the ability to satisfy multiple system-level constraints in these systems grows increasingly important. In applications ranging from automated cruise control to safety in robot swarms, barrier functions have emerged as a tool to provably meet such constraints by guaranteeing forward invariance of a set. However, satisfying multiple constraints typically implies formulating multiple barrier functions, bringing up the need to address the degree to which multiple barrier functions may be composed through Boolean logic. The use of max and min operators, which yields nonsmooth functions, represents one such method to accomplish Boolean composition. The main contribution of this work extends previously established concepts for barrier functions to a class of nonsmooth barrier functions that operate on systems described by differential inclusions. We validate our results by deploying a Boolean compositional nonsmooth barrier function onto a team of mobile robots.