Large-Scale Multi-Agent Systems (LS-MAS) consist of several autonomous components, interacting in a non-trivial way, so that the emerging behaviour of the ensemble depends on the individual dynamics of the components and their reciprocal interactions. These models can describe a rich variety of natural systems, as well as artificial ones, characterised by unparalleled scalability, robustness, and flexibility. Indeed, a crucial objective is devising efficient strategies to model and control the spatial behaviours of LS-MAS to achieve specific goals. However, the inherent complexity of these systems and the wide spectrum of their emerging behaviours pose significant challenges. The overarching goal of this thesis is, therefore, to advance methods for modelling, analyzing and controlling the spatial behaviours of LS-MAS, with applications to cellular populations and swarm robotics. The thesis begins with an overview of the existing Literature, and is then organized into two distinct parts. In the context of swarm robotics, Part I deals with distributed control algorithms to spatially organize agents on geometric patterns. The contribution is twofold, encompassing both the development of original control algorithms, and providing a novel formal analysis, which allows to guarantee the emergence of specific geometric patterns. In Part II, looking at the spatial behaviours of biological agents, experiments are carried out to study the movement of microorganisms and their response to light stimuli. This allows the derivation and parametrization of mathematical models that capture these behaviours, and pave the way for the development of innovative approaches for the spatial control of microorganisms. The results presented in the thesis were developed by leveraging formal analytical tools, simulations, and experiments, using innovative platforms and original computational frameworks.

Geometric pattern formation is crucial in many tasks involving large-scale multi-agent systems. Examples include mobile agents performing surveillance, swarm of drones or robots, or smart transportation systems. Currently, most control strategies proposed to achieve pattern formation in network systems either show good performance but require expensive sensors and communication devices, or have lesser sensor requirements but behave more poorly. Also, they often require certain prescribed structural interconnections between the agents (e.g., regular lattices, all-to-all networks etc). In this paper, we provide a distributed displacement-based control law that allows large group of agents to achieve triangular and square lattices, with low sensor requirements and without needing communication between the agents. Also, a simple, yet powerful, adaptation law is proposed to automatically tune the control gains in order to reduce the design effort, while improving robustness and flexibility. We show the validity and robustness of our approach via numerical simulations and experiments, comparing it with other approaches from the existing literature.