  As multi-agent systems proliferate, there is increasing demand for
coordination protocols that protect agents' sensitive information while
allowing them to collaborate. To help address this need, this paper presents a
differentially private formation control framework. Agents' state trajectories
are protected using differential privacy, which is a statistical notion of
privacy that protects data by adding noise to it. We provide a private
formation control implementation and analyze the impact of privacy upon the
system. Specifically, we quantify tradeoffs between privacy level, system
performance, and connectedness of the network's communication topology. These
tradeoffs are used to develop guidelines for calibrating privacy in terms of
control theoretic quantities, such as steady-state error, without requiring
in-depth knowledge of differential privacy. Additional guidelines are also
developed for treating privacy levels and network topologies as design
parameters to tune the network's performance. Simulation results illustrate
these tradeoffs and show that strict privacy is inherently compatible with
strong system performance.
