A Unified Dissertation on Bearing Rigidity Theory

This work focuses on bearing rigidity theory, namely, the branch of knowledge investigating the structural properties necessary for multielement systems to preserve the interunit bearings under deformations. The contributions of this work are two-fold. The first one consists in the development of a general framework for the statement of the principal definitions and properties of bearing rigidity. We show that this approach encompasses results existing in the literature, and provides a systematic approach for studying bearing rigidity on any differential manifold inSE(3)ⁿ, wherenis the number of agents. The second contribution is the derivation of a general form of the rigidity matrix, a central construct in the study of rigidity theory. We provide a necessary and sufficient condition for the infinitesimal rigidity of a bearing framework as a property of the rank of the rigidity matrix. Finally, we present two examples of multiagent systems not encountered in the literature and we study their rigidity properties using the developed methods.