arXiv subjects

Gian Carlo Maffettone

Publications and source records attributed to Gian Carlo Maffettone.

13 recordsLinked to original sources

arXiv2026

Leader-Follower Density Control of Multi-Agent Systems with Interacting Followers: Feasibility and Convergence Analysis

We address density control problems for large-scale multi-agent systems in leader-follower settings, where a group of controllable leaders must steer a population of followers toward a desired spatial distribution. Unlike prior work, we explicitly account for follower-follower interactions, capturing realistic behaviors such as flocking and collision avoidance. Within a macroscopic framework based on partial differential equations governing the density dynamics, we derive (i) necessary and sufficient feasibility conditions linking the target distribution to interaction strength, diffusion, and leader mass, and (ii) a feedback control law guaranteeing local stability with an explicit estimate of the basin of attraction. Our analysis reveals sharp feasibility thresholds, phase transitions beyond which no control effort can achieve the desired configuration. Numerical simulations in one- and two-dimensional domains validate the theoretical results at the macroscopic level, and agent-based simulations on finite populations confirm the practical deployability of the proposed framework.

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arXiv2026

Mean-field control barrier functions for stochastic multi-agent systems

Many applications involving multi-agent systems require fulfilling safety constraints. Control barrier functions offer a systematic framework to enforce forward invariance of safety sets. Recent work extended this paradigm to mean-field scenarios, where the number of agents is large enough to make density-space descriptions a reasonable workaround for the curse of dimensionality. However, an open gap in the recent literature concerns the development of mean-field control barrier functions for Fokker-Planck (advection-diffusion) equations. In this work, we address this gap, enabling safe mean-field control of agents with stochastic microscopic dynamics. We provide bounded stability guarantees under safety corrections and corroborate our results through numerical simulations in two representative scenarios, coverage and shepherding control of multi-agent systems.

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arXiv2026

Robust multi-scale leader-follower control of large multi-agent systems

In many multi-agent systems of practical interest, such as traffic networks or crowd evacuation, control actions cannot be exerted on all agents. Instead, controllable leaders must indirectly steer uncontrolled followers through local interactions. Existing results address either leader-follower density control of simple, unperturbed multi-agent systems or robust density control of a single directly actuated population, but not their combination. We bridge this gap by deriving a coupled continuum description for leaders and followers subject to unknown bounded perturbations, and designing a macroscopic feedback law that guarantees global asymptotic convergence of the followers' density to a desired distribution. The coupled stability of the leader-follower system is analyzed via singular perturbation theory, and an explicit lower bound on the leader-to-follower mass ratio required for feasibility is derived. Numerical simulations on heterogeneous biased random walkers validate our theoretical findings.

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arXiv2026

Robust Macroscopic Density Control of Heterogeneous Multi-Agent Systems

Modern applications, such as orchestrating the collective behavior of robotic swarms or traffic flows, require the coordination of large groups of agents evolving in unstructured environments, where disturbances and unmodeled dynamics are unavoidable. In this work, we develop a scalable macroscopic density control framework in which a feedback law is designed directly at the level of an advection--diffusion partial differential equation. We formulate the control problem in the density space and prove global exponential convergence towards the desired behavior in $\mathcal{L}^2$ with guaranteed asymptotic rejection of bounded unknown drift terms, explicitly accounting for heterogeneous agent dynamics, unmodeled behaviors, and environmental perturbations. Our theoretical findings are corroborated by numerical experiments spanning heterogeneous oscillators, traffic systems, and swarm robotics in partially unknown environments.

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arXiv2026

Bio-inspired density control of multi-agent swarms via leader-follower plasticity

The design of control systems for the spatial self-organization of mobile agents is an open challenge across several engineering domains, including swarm robotics and synthetic biology. Here, we propose a bio-inspired leader-follower solution, which is aware of energy constraints of mobile agents and is apt to deal with large swarms. Akin to many natural systems, control objectives are formulated for the entire collective, and leaders and followers are allowed to plastically switch their role in time. We frame a density control problem, modeling the agents' population via a system of nonlinear partial differential equations. This approach allows for a compact description that inherently avoids the curse of dimensionality and improves analytical tractability. We derive analytical guarantees for the existence of desired steady-state solutions and their local stability for one-dimensional and higher-dimensional problems. We numerically validate our control methodology, offering support to the effectiveness, robustness, and versatility of our proposed bio-inspired control strategy.

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arXiv2025

Leader-Follower Density Control of Spatial Dynamics in Large-Scale Multi-Agent Systems

We address the problem of controlling the density of a large ensemble of follower agents by acting on a group of leader agents that interact with them. Using coupled partial integro-differential equations to describe leader and follower density dynamics, we establish feasibility conditions and develop two control architectures ensuring global stability. The first employs feed-forward control on the followers' and a feedback on the leaders' density. The second implements a dual feedback loop through a reference-governor that adapts the leaders' density based on both populations' measurements. Our methods, initially developed in a one-dimensional setting, are extended to multi-dimensional cases, and validated through numerical simulations for representative control applications, both for groups of infinite and finite size.

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arXiv2025

Decentralized Continuification Control of Multi-Agent Systems via Distributed Density Estimation

This paper introduces a novel decentralized implementation of a continuification-based strategy to control the density of large-scale multi-agent systems on the unit circle. While continuification methods effectively address micro-to-macro control problems by reformulating ordinary/stochastic differential equations (ODEs/SDEs) agent-based models into more tractable partial differential equations (PDEs), they traditionally require centralized knowledge of macroscopic state observables. We overcome this limitation by developing a distributed density estimation framework that combines kernel density estimation with PI consensus dynamics. Our approach enables agents to compute local density estimates and derive local control actions using only information from neighboring agents in a communication network. Numerical validations across multiple scenarios - including regulation, tracking, and time-varying communication topologies - confirm the effectiveness of the proposed approach. They also convincingly demonstrate that our decentralized implementation achieves performance comparable to centralized approaches while enhancing reliability and practical applicability.

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arXiv2024

A Continuification-Based Control Solution for Large-Scale Shepherding

In this paper, we address the large-scale shepherding control problem using a continuification-based strategy. We consider a scenario in which a large group of follower agents (targets) must be confined within a designated goal region through indirect interactions with a controllable set of leader agents (herders). Our approach transforms the microscopic agent-based dynamics into a macroscopic continuum model via partial differential equations (PDEs). This formulation enables efficient, scalable control design for the herders' behavior, with guarantees of global convergence. Numerical and experimental validations in a mixed-reality swarm robotics framework demonstrate the method's effectiveness.

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arXiv2024

Mixed Reality Environment and High-Dimensional Continuification Control for Swarm Robotics

Many new methodologies for the control of large-scale multi-agent systems are based on macroscopic representations of the emerging system dynamics, in the form of continuum approximations of large ensembles. These techniques, that are developed in the limit case of an infinite number of agents, are usually validated only through numerical simulations. In this paper, we introduce a mixed reality set-up for testing swarm robotics techniques, focusing on the macroscopic collective motion of robotic swarms. This hybrid apparatus combines both real differential drive robots and virtual agents to create a heterogeneous swarm of tunable size. We also extend continuification-based control methods for swarms to higher dimensions, and assess experimentally their validity in the new platform. Our study demonstrates the effectiveness of the platform for conducting large-scale swarm robotics experiments, and it contributes new theoretical insights into control algorithms exploiting continuification approaches.

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arXiv2024

High-dimensional continuification control of large-scale multi-agent systems under limited sensing and perturbations

This paper investigates the robustness of a novel high-dimensional continuification control method for complex multi-agent systems. We begin by formulating a partial differential equation describing the spatio-temporal density dynamics of swarming agents. A stable control action for the density is then derived and validated under nominal conditions. Subsequently, we discretize this macroscopic strategy into actionable velocity inputs for the system's agents. Our analysis demonstrates the robustness of the approach beyond idealized assumptions of unlimited sensing and absence of perturbations.

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arXiv2023

Continuification control of large-scale multiagent systems under limited sensing and structural perturbations

We investigate the stability and robustness properties of a continuification-based strategy for the control of large-scale multiagent systems. Within continuation-based strategy, one transforms the microscopic, agent-level description of the system dynamics into a macroscopic continuum-level, for which a control action can be synthesized to steer the macroscopic dynamics towards a desired distribution. Such an action is ultimately discretized to obtain a set of deployable control inputs for the agents to achieve the goal. The mathematical proof of convergence toward the desired distribution typically relies on the assumptions that no disturbance is present and that each agent possesses global knowledge of all the others' positions. Here, we analytically and numerically address the possibility of relaxing these assumptions for the case of a one-dimensional system of agents moving in a ring. We offer compelling evidence in favor of the use of a continuification-based strategy when agents only possess a finite sensing capability and spatio-temporal perturbations affect the macroscopic dynamics of the ensemble. We also discuss some preliminary results about the role of an integral action in the macroscopic control solution.

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arXiv2022

Continuification-based control of large multiagent systems in a ring

In this paper, we propose a method to control large-scale multiagent systems swarming in a ring. Specifically, we use a continuification-based approach that transforms the microscopic, agent-level description of the system dynamics into a macroscopic, continuum-level representation, which we employ to synthesize a control action towards a desired distribution of the agents. The continuum-level control action is then discretized at the agent-level in order to practically implement it. To confirm the effectiveness and the robustness of the proposed approach, we complement theoretical derivations with a series of numerical simulations.

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arXiv2022

Distributed control for geometric pattern formation of large-scale multirobot systems

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.

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