  In this paper we consider multi-agent navigation with collision avoidance
using Control Barrier Functions (CBF). In the case of non-communicating agents,
we consider trade-offs between level of safety guarantee and liveness - the
ability to reach destination in short time without large detours or gridlock.
We compare several CBF-based driving policies against the benchmark established
by the Centralized controller that requires communication. One of the policies
(CCS2) being compared is new and straddles the space between policies with only
local control available and a more complex Predictor-Corrector for Collision
Avoidance (PCCA) policy that adjusts local copies of everyone's control actions
based on observed behavior. The paper establishes feasibility for the
Centralized, PCCA and CCS2 policies. Monte Carlo simulations show that
decentralized, host-only control policies lack liveness compared to the ones
that use all the control inputs in calculations and that the PCCA policy
performs equally well as the Centralized, even though it is decentralized.
