Nonsmooth Barrier Functions

As multi-agent systems become ubiquitous, guaranteeing safety 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 safety constraints by guaranteeing forward invariance of a set. However, a single barrier function can rarely satisfy all safety aspects of a system, so there remains a need to address the degree to which multiple barrier functions may be composed through Boolean logic. Utilizing max and min operators represents one such method to accomplish Boolean composition for barrier functions. As such, 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. To validate these results, a Boolean compositional barrier function is deployed onto a team of mobile robots.