  Formation control of autonomous agents can be seen as a physical system of
individuals interacting with local potentials, and whose evolution can be
described by a Lagrangian function. In this paper, we construct and implement
forced variational integrators for the formation control of autonomous agents
modeled by double integrators. In particular, we provide an accurate numerical
integrator with a lower computational cost than traditional solutions. We find
error estimations for the rate of the energy dissipated along with the agents'
motion to achieve desired formations. Consequently, this permits to provide
sufficient conditions on the simulation's time step for the convergence of
discrete formation control systems such as the consensus problem in discrete
systems. We present practical applications such as the rapid estimation of
regions of attraction to desired shapes in distance-based formation control.
