Modelling and Control of Spatial Behaviours in Multi-Agent Systems with Applications to Biology and Robotics

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.