PROJECT TITLE :

Bearing Rigidity and Almost Global Bearing-Only Formation Stabilization

ABSTRACT:

A elementary problem that the bearing rigidity theory studies is to determine when a framework will be uniquely determined up to a translation and a scaling factor by its inter-neighbor bearings. Whereas several previous works focused on the bearing rigidity of 2-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. During this paper, the proposed bearing rigidity theory is additional applied to the bearing-only formation stabilization problem where the target formation is defined by inter-neighbor bearings and the feedback management uses solely bearing measurements. Nonlinear distributed bearing-solely formation management laws are proposed for the cases with and while not a world orientation. It is proved that the control laws will virtually globally stabilize infinitesimally bearing rigid formations. Numerical simulations are provided to support the analysis.