  A fundamental problem that the bearing rigidity theory studies is to
determine when a framework can be uniquely determined up to a translation and a
scaling factor by its inter-neighbor bearings. While many previous works
focused on the bearing rigidity of two-dimensional frameworks, a first
contribution of this paper is to extend these results to arbitrary dimensions.
It is shown that a framework in an arbitrary dimension can be uniquely
determined up to a translation and a scaling factor by the bearings if and only
if the framework is infinitesimally bearing rigid. In this paper, the proposed
bearing rigidity theory is further applied to the bearing-only formation
stabilization problem where the target formation is defined by inter-neighbor
bearings and the feedback control uses only bearing measurements. Nonlinear
distributed bearing-only formation control laws are proposed for the cases with
and without a global orientation. It is proved that the control laws can almost
globally stabilize infinitesimally bearing rigid formations. Numerical
simulations are provided to support the analysis.
