A Unified Dissertation on Bearing Rigidity Theory
For researchers in multi-agent systems, this work offers a foundational unification of bearing rigidity theory, though it is primarily theoretical and incremental in nature.
This dissertation unifies bearing rigidity theory across metric spaces, providing a general framework and a necessary and sufficient condition for rigidity that is independent of the metric space.
This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original contributions are twofold. The first one consists in the definition of a general framework for the statement of the principal definitions and results that are then particularized by evaluating the most studied metric spaces, providing a complete overview of the existing literature about the bearing rigidity theory. The second one rests on the determination of a necessary and sufficient condition guaranteeing the rigidity properties of a given multi-element system, independently of its metric space.