  This paper presents the analysis on the influence of distance mismatches on
the standard gradient-based rigid formation control for second-order agents. It
is shown that, similar to the first-order case as recently discussed in the
literature, these mismatches introduce two undesired group behaviors: a
distorted final shape and a steady-state motion of the group formation. We show
that such undesired behaviors can be eliminated by combining the standard
formation control law with distributed estimators. Finally, we show how the
mismatches can be effectively employed as design parameters in order to control
a combined translational and rotational motion of the formation.
