# A Unified Dissertation on Bearing Rigidity Theory

## TL;DR

This paper provides a comprehensive framework for bearing rigidity theory, establishing fundamental definitions, reviewing existing literature, and identifying a necessary and sufficient condition for system rigidity across various metric spaces.

## Contribution

It introduces a unified framework for bearing rigidity theory and derives a metric-independent condition for system rigidity.

## Key findings

- Complete overview of bearing rigidity literature
- Unified framework for definitions and results
- Necessary and sufficient rigidity condition

## Abstract

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.