  This paper presents a robust estimator-based safety-critical controller for
formation control of non-holonomic mobile robots in communication-limited
environments. The proposed decentralized framework integrates a robust state
estimator with a formation tracking control law that guarantees inter-agent
collision avoidance using control barrier functions. String stability is
incorporated into the control design to maintain stability against noise from
predecessors in leader-follower formations. Rigorous stability analysis using
Lyapunov functions ensures the stability of estimation errors and the
convergence of the formation to desired configurations. The effectiveness and
robustness of the proposed approach are validated through numerical simulations
of various maneuvers and realistic Gazebo experiments involving formations in a
warehouse environment. The results demonstrate the controller's ability to
maintain safety, achieve precise formation control, and mitigate disturbances
in scenarios without inter-robot communication.
