  This work studies a robot-assisted crowd evacuation problem where we control
a small group of robots to guide a large human crowd to safe locations. The
challenge lies in how to model human-robot interactions and design robot
controls to indirectly control a human population that significantly outnumbers
the robots. To address the challenge, we treat the crowd as a continuum and
formulate the evacuation objective as driving the crowd density to target
locations. We propose a novel mean-field model which consists of a family of
microscopic equations that explicitly model how human motions are locally
guided by the robots and an associated macroscopic equation that describes how
the crowd density is controlled by the navigation velocity fields generated by
all robots. Then, we design density feedback controllers for the robots to
dynamically adjust their states such that the generated navigation velocity
fields drive the crowd density to a target density. Stability guarantees of the
proposed controllers are proven. Agent-based simulations are included to
evaluate the proposed evacuation algorithms.
