  This paper addresses the problem of bearing-only formation control in
$d~(d\geq 2)$-dimensional space by exploring persistence of excitation (PE) of
the desired bearing reference. By defining a desired formation that is bearing
PE, distributed bearing-only control laws are proposed, which guarantee
exponential stabilization of the desired formation only up to a translation
vector. The key outcome of this approach relies in exploiting the bearing PE to
significantly relax the conditions imposed on the graph topology to ensure
exponential stabilization, when compared to the bearing rigidity conditions,
and to remove the scale ambiguity introduced by bearing vectors. Simulation
results are provided to illustrate the performance of the proposed control
method.
