  Self-navigation in non-coordinating crowded environments is formidably
challenging within multi-agent systems consisting of non-holonomic robots
operating through local sensing. Our primary objective is the development of a
novel, rapid, sensor-driven, self-navigation controller that directly computes
control commands to enable safe maneuvering while coexisting with other agents.
We propose an input-constrained feedback controller meticulously crafted for
non-holonomic mobile robots and the characterization of associated invariant
sets. The invariant sets are the key to maintaining stability and safety amidst
the non-cooperating agents. We then propose a planning strategy that
strategically guides the generation of invariant sets toward the agent's
intended target. This enables the agents to directly compute theoretically safe
control inputs without explicitly requiring pre-planned paths/trajectories to
reliably navigate through crowded multi-agent environments. The practicality of
our technique is demonstrated through hardware experiments, and the ability to
parallelize computations to shorten computational durations for synthesizing
safe control commands. The proposed approach finds potential applications in
crowded multi-agent scenarios that require rapid control computations based on
perceived safety bounds during run-time.
