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

Andrea Giusti

TL;DR

The thesis addresses the challenge of modelling, analyzing, and controlling spatial behaviours in large-scale LS-MAS across biology and robotics. It advances a distributed, displacement-based control law for geometric pattern formation enabling self-organization into triangular or square lattices, and provides a formal convergence analysis showing local asymptotic stability of rigid lattices under attracting/repulsive interactions. In parallel, it develops a data-driven stochastic model of microorganism motion with light-responsive dynamics, validated through open-loop experiments on Euglena and other species using the DOME platform, and complemented by the SwarmSim simulation framework and Robotarium validation. The work integrates formal control theory, numerical simulations, and experimental platforms to deliver both methodological insights and practical tools for multi-scale LS-MAS control with broad applicability in synthetic biology and swarm robotics.

Abstract

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.

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

TL;DR

The thesis addresses the challenge of modelling, analyzing, and controlling spatial behaviours in large-scale LS-MAS across biology and robotics. It advances a distributed, displacement-based control law for geometric pattern formation enabling self-organization into triangular or square lattices, and provides a formal convergence analysis showing local asymptotic stability of rigid lattices under attracting/repulsive interactions. In parallel, it develops a data-driven stochastic model of microorganism motion with light-responsive dynamics, validated through open-loop experiments on Euglena and other species using the DOME platform, and complemented by the SwarmSim simulation framework and Robotarium validation. The work integrates formal control theory, numerical simulations, and experimental platforms to deliver both methodological insights and practical tools for multi-scale LS-MAS control with broad applicability in synthetic biology and swarm robotics.

Abstract

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.
Paper Structure (94 sections, 4 theorems, 49 equations, 49 figures, 10 tables, 1 algorithm)

This paper contains 94 sections, 4 theorems, 49 equations, 49 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation
  3. Open challenges
  4. Main contributions
  5. Thesis outline
  6. Background
  7. Emergent behaviours
  8. Modelling & Analysis
  9. Control algorithms
  10. Hierarchic classification of control algorithms
  11. High level control layer.
  12. Middle level control layer.
  13. Low level control layer.
  14. Distributed and centralized implementations
  15. Discussion
  16. ...and 79 more sections

Key Result

Theorem 3.1

A $d$-dimensional framework with $N\geq d$ vertices and rigidity matrix $\mathbf{M}$ is infinitesimally rigid if and only if $\mathrm{rank}(\mathbf{M})=dN-d(d+1)/2$.

Figures (49)

  • Figure 1: Schematic comparison between classic systems and LS-MAS.
  • Figure 2: Hierarchy of control algorithms for LS-MAS. The higher the layer the more abstract is the system representation and the lower the required execution frequency.
  • Figure 3: Examples of lattices in 2D (a-b) and 3D (c) spaces.
  • Figure 4: $(L,R)$-lattice formations: triangular ($L=6$) (a) and square ($L=4$) (b). Red dots are agents in the adjacency set ($\mathcal{A}_i$) of the generic agent $i$ depicted as a black dot.
  • Figure 5: Schematic diagram of two agents, $i$ and $j$, showing the key variables describing the agents' position and their geometrical relationship.
  • ...and 44 more figures

Theorems & Definitions (27)

  • Definition 3.1: Equilibrium set
  • Definition 3.2: Local asymptotic stability Kuznetsov2004
  • Definition 3.3: Incidence matrix
  • Definition 3.4: Framework Mesbahi2010
  • Definition 3.5: Congruent frameworks Jackson2007
  • Definition 3.6: Rigidity matrix Jackson2007
  • Definition 3.7: Infinitesimal rigidity Mesbahi2010
  • Definition 3.8: Rigidity Jackson2007
  • Theorem 3.1: Hendrickson1992
  • Definition 3.9: Interaction set
  • ...and 17 more