Bearing Rigidity and Almost Global Bearing-Only Formation Stabilization

• Published in: IEEE transactions on automatic control Vol. 61; no. 5; pp. 1255 - 1268
• Main Authors: Shiyu Zhao, Zelazo, Daniel
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aerospace electronics; almost global input-to-state stability; attitude synchronization; Azimuth; Bearing rigidity; formation control; Null space; Position measurement; Shape; Symmetric matrices; Synchronization; bearing rigidity; attitude synchronization; Almost global input-to-state stability; formation control
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2015.2459191

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.