  We consider a multi-agent confinement control problem in which a single
leader has a purely repulsive effect on follower agents with double-integrator
dynamics. By decomposing the leader's control inputs into periodic and
aperiodic components, we show that the leader can be driven so as to guarantee
confinement of the followers about a time-dependent trajectory in the plane. We
use tools from averaging theory and an input-to-state stability type argument
to derive conditions on the model parameters that guarantee confinement of the
followers about the trajectory. For the case of a single follower, we show that
if the follower starts at the origin, then the error in trajectory tracking can
be made arbitrarily small depending on the frequency of the periodic control
components and the rate of change of the trajectory. We validate our approach
using simulations and experiments with a small mobile robot.
