  Microrobotics has the potential to revolutionize many applications including
targeted material delivery, assembly, and surgery. The same properties that
promise breakthrough solutions---small size and large populations---present
unique challenges for controlling motion.
  Robotic manipulation usually assumes intelligent agents, not particle systems
manipulated by a global signal. To identify the key parameters for particle
manipulation, we used a collection of online games where players steer swarms
of up to 500 particles to complete manipulation challenges. We recorded
statistics from over ten thousand players. Inspired by techniques where human
operators performed well, we investigate controllers that use only the mean and
variance of the swarm. We prove the mean position is controllable and provide
conditions under which variance is controllable. We next derive automatic
controllers for these and a hysteresis-based switching control to regulate the
first two moments of the particle distribution. Finally, we employ these
controllers as primitives for an object manipulation task and implement all
controllers on 100 kilobots controlled by the direction of a global light
source.
