  This paper proposes a distributed controller synthesis framework for safe
navigation of multi-agent systems. We leverage control barrier functions to
formulate collision avoidance with obstacles and teammates as constraints on
the control input for a state-dependent network optimization problem that
encodes team formation and the navigation task. Our algorithmic solution is
valid for general nonlinear control dynamics and optimization problems. The
resulting controller is distributed, satisfies the safety constraints at all
times, and is asymptotically optimal. We illustrate its performance in a team
of differential-drive robots in a variety of complex environments, both in
simulation and in hardware.
