  Collective motions emerging from the interaction of autonomous mobile
individuals play a key role in many phenomena, from the growth of bacterial
colonies to the coordination of robotic swarms. For these collective behaviours
to take hold, the individuals must be able to emit, sense and react to signals.
When dealing with simple organisms and robots, these signals are necessarily
very elementary, e.g. a cell might signal its presence by releasing chemicals
and a robot by shining light. An additional challenge arises because the motion
of the individuals is often noisy, e.g. the orientation of cells can be altered
by Brownian motion and that of robots by an uneven terrain. Therefore, the
emphasis is on achieving complex and tunable behaviors from simple autonomous
agents communicating with each other in robust ways. Here, we show that the
delay between sensing and reacting to a signal can determine the individual and
collective long-term behavior of autonomous agents whose motion is
intrinsically noisy. We experimentally demonstrate that the collective
behaviour of a group of phototactic robots capable of emitting a radially
decaying light field can be tuned from segregation to aggregation and
clustering by controlling the delay with which they change their propulsion
speed in response to the light intensity they measure. We track this transition
to the underlying dynamics of this system, in particular, to the ratio between
the robots' sensorial delay time and the characteristic time of the robots'
random reorientation. Supported by numerics, we discuss how the same mechanism
can be applied to control active agents, e.g. airborne drones, moving in a
three-dimensional space.
