  We present a method for controlling a swarm using its spectral decomposition
-- that is, by describing the set of trajectories of a swarm in terms of a
spatial distribution throughout the operational domain -- guaranteeing scale
invariance with respect to the number of agents both for computation and for
the operator tasked with controlling the swarm. We use ergodic control,
decentralized across the network, for implementation. In the DARPA OFFSET
program field setting, we test this interface design for the operator using the
STOMP interface -- the same interface used by Raytheon BBN throughout the
duration of the OFFSET program. In these tests, we demonstrate that our
approach is scale-invariant -- the user specification does not depend on the
number of agents; it is persistent -- the specification remains active until
the user specifies a new command; and it is real-time -- the user can interact
with and interrupt the swarm at any time. Moreover, we show that the
spectral/ergodic specification of swarm behavior degrades gracefully as the
number of agents goes down, enabling the operator to maintain the same approach
as agents become disabled or are added to the network. We demonstrate the
scale-invariance and dynamic response of our system in a field relevant
simulator on a variety of tactical scenarios with up to 50 agents. We also
demonstrate the dynamic response of our system in the field with a smaller team
of agents. Lastly, we make the code for our system available.
