  This paper presents a safety-critical approach to the coordination of robots
in dynamic environments. To this end, we leverage control barrier functions
(CBFs) with the forward reachable set to guarantee the safe coordination of the
robots while preserving a desired trajectory via a layered controller. The
top-level planner generates a safety-ensured trajectory for each agent,
accounting for the dynamic constraints in the environment. This planner
leverages high-order CBFs based on the forward reachable set to ensure
safety-critical coordination control, i.e., guarantee the safe coordination of
the robots during locomotion. The middle-level trajectory planner employs
single rigid body (SRB) dynamics to generate optimal ground reaction forces
(GRFs) to track the safety-ensured trajectories from the top-level planner. The
whole-body motions to adhere to the optimal GRFs while ensuring the friction
cone condition at the end of each stance leg are generated from the low-level
controller. The effectiveness of the approach is demonstrated through
simulation and hardware experiments.
