Hybrid Rigidity Theory: A Unifying Mathematical Framework for Heterogeneous Multi-Agent Systems with Mixed Measurements

Rigidity theory has emerged as a cornerstone for addressing coordination problems in multi-agent systems (MASs), particularly when absolute positioning is unavailable or lacks the precision required for the task, necessitating a strict reliance on relative inter-agent measurements. Current methodologies rely on distinct rigidity paradigms tailored to specific sensor capabilities, such as distance, displacement, and bearing measurements. Driven by the need to model complex real-world scenarios, recent research has shifted toward heterogeneous MASs, characterized by agents with distinct dynamics evolving on different manifolds. However, although the framework proposed by Michieletto et al. successfully addresses heterogeneous configurations based exclusively on bearing measurements, the literature still lacks a systematic methodology for handling MASs defined by mixed measurement topologies. To bridge this gap, this thesis introduces Hybrid Rigidity Theory: a unifying mathematical framework designed to accommodate multi-agent systems featuring both heterogeneous dynamics and mixed sensing modalities. By seamlessly integrating different measurement paradigms, the proposed theory provides a rigorous foundation for the distributed coordination and control of fully heterogeneous MASs. Furthermore, the theoretical framework is validated through a comprehensive set of case studies. Notably, these case studies demonstrate the broad effectiveness of the proposed approach across a variety of scenarios, including successful applications to complex settings where agents are subject to submanifold-constrained dynamics.