Abstract
Title: Multi Agents Systems and Max-Plus Algebra Theoretical Frameworks for a Robot-Fish Shoal Modelling and Control The MAXFISH project explores innovative methodologies and implementation strategies for controlling and coordinating a shoal of autonomous underwater robots inspired by the swimming capabilities of fish. This interdisciplinary research combines robotic engineering, control theory, and applied mathematics, with the specific aim to enhance the performance and efficiency of underwater patrolling, inspection, and monitoring operations. Project Objectives MAXFISH is structured around three main scientific objectives: 1. Modelling and development of biomimetic fish robots The goal is to design and mathematically model autonomous underwater vehicles (AUVs) with hybrid propulsion systems (caudal fin and propellers). These robots will replicate fish-like movements to achieve energy-efficient and maneuverable behavior. The modelling approach will use Lie groups, specifically SO(3), to capture the nonlinear dynamics of the fish-robots more accurately than traditional models such as Fossen’s. 2. Design of distributed control and cooperative perception for multi-agent systems (MAS) MAXFISH aims to develop coordination strategies for a team of underwater robots with limited sensing, actuation, and communication capabilities. These strategies will allow decentralized area coverage, cooperative navigation, anomaly detection, and state estimation even in the presence of communication constraints typical of the underwater environment. 3. Application of Max-Plus algebra for scheduling periodic multi-robot patrolling tasks The project introduces a novel use of Max-Plus algebra to optimize the allocation and sequencing of patrol tasks across a heterogeneous robotic team. This framework is particularly suited to repetitive missions in predefined areas such as submerged archaeological sites, coral reefs, or critical marine infrastructure, where agents must visit different points of interest with varying durations and requirements. Expected Results The MAXFISH project will produce the following key results: • A comprehensive theoretical framework for modelling single and multi-agent robotic systems using advanced mathematical tools such as Lie groups and Max-Plus algebra. • The development and validation of two low-cost fish robots and one high-performance prototype, equipped with sensors and actuators suitable for different operational scenarios. • A suite of simulation tools, digital twins, and control algorithms for robot behavior and team coordination, to be released as Open Educational Resources (OER). • Real-world test cases validating navigation, guidance, control, and cooperative strategies in underwater environments. • An xIL implementation infrastructure (HIL, SIL, MIL) enabling accurate simulation and hardware-in-the-loop testing. • A robust dissemination plan including scientific publications, conference participation, stakeholder engagement, and final demonstrations with end-users (e.g., marine biologists, archaeologists). Scientific and Technological Innovation From a scientific standpoint, MAXFISH contributes to the field of marine robotics by addressing critical open problems in MAS coordination under real-world constraints such as communication latency, heterogeneous agent capabilities, and sensor limitations. The innovative use of Max-Plus algebra for mission scheduling in underwater MAS is a novel application not previously explored in the literature. The adoption of bio-inspired design enhances the maneuverability and energy efficiency of underwater robots, offering operational advantages in confined or sensitive environments. The digital twin environment, developed with Unity, ROS, and MATLAB, allows for rapid prototyping and testing, supporting reproducibility and technology transfer. Implementation Strategy MAXFISH is organized into five integrated Work Packages (WPs): • WP1 – Management and Dissemination: coordination and stakeholder engagement. • WP2 – Robot Design and Modelling: development of fish-robot prototypes and digital twins. • WP3 – Multi-Robot Coordination: design of area coverage, cooperative navigation, and distributed estimation algorithms. • WP4 – Max-Plus Algebra Framework: formalization and control synthesis for periodic patrolling tasks. • WP5 – Verification and Validation: integration of hardware and software components, final acceptance testing, and demo preparation. The project will involve engineering spin-offs for the hardware development, promoting technology transfer and entrepreneurship. Hardware components will remain proprietary to encourage further exploitation by the spin-offs, while the methodological infrastructure will be openly shared to benefit the scientific community. Societal and Economic Impact MAXFISH targets application areas with strong societal and economic relevance, including: • Underwater environmental monitoring (e.g., pollution detection, marine ecosystem preservation) • Surveillance of critical underwater infrastructure (e.g., oil & gas facilities, aquaculture farms) • Support for underwater archaeology (e.g., repeated inspections of submerged cultural heritage sites) The robotic shoal paradigm provides a scalable, redundant, and cost-effective alternative to traditional AUV missions. By enabling multi-robot collaboration, MAXFISH reduces mission costs and increases operational resilience. The project aligns with the Sustainable Development Goals (SDGs), particularly those related to Life Below Water (SDG 14) and Industry, Innovation, and Infrastructure (SDG 9). Its outcomes will support EU and national priorities in marine technology, blue economy, and environmental protection. Results The project “MAXFISH: Multi-agent systems and Max-Plus algebra theoretical frameworks for robot-fish shoal modelling and control” aimed to develop multi-agent systems and to exploit the mathematical framework of max-plus algebra for modelling and controlling shoals of fish robots used in surveillance, patrolling, and reconnaissance operations in confined marine areas. The project developed along two main lines: an implementation-oriented line and a methodological line. The implementation framework used standard tools for the architecture and design of engineering models, such as MATLAB/Simulink, Python/MicroPython, ROS2, MQTT, and Gazebo or Unity, to create complete digital twins of the robots. From the methodological point of view, MAXFISH improved existing strategies for the navigation, guidance, and control of multi-agent robotic systems by focusing on the following aspect, which was the priority for the Bologna unit. For shoals of robots involved in patrolling and reconnaissance, the focus was on modelling them not according to the time scale, but according to the tasks to be performed. In many real situations, different robots, each with specific sensing and actuation capabilities, have to inspect points of interest according to a predefined strategy, in which each agent performs a sequence of specific tasks. In this case, the formalization based on max-plus algebra proved useful for optimizing the synchronization of these robots. The research activity focused on the study and development of solutions for the modelling and control of such shoals of fish robots, with particular attention to their use in inspection and repetitive tasks. In this context, the usual time-based approach to the modelling and control of team dynamics was reconsidered in favor of a task-oriented approach. Max-plus algebra provided the mathematical tools needed to formalize and solve the problem addressed within this methodological perspective. The work concerned the formalization, within the framework of max-plus algebra, of the mathematical model of the behavior of a shoal of fish robots and of the related tasks. In parallel with the modelling activity, the synchronization problem for the shoal of fish robots was formalized, together with the solvability conditions and the algorithmic procedures for constructing the solution. The ScicosLab software package was used for algorithm development and simulation-based validation of the results. ScicosLab includes the “Max-Plus Algebra Toolbox”, which is useful for implementing the main operations of this algebra. Max-plus algebra is defined on the set ℝmax, consisting of the real numbers together with −∞, and its main operations are maximum and addition. It also includes further specific operators, whose implementation is more complex. By solving the synchronization problem, it was possible to control the behavior and performance of the shoal of fish robots, ensuring that each patrol cycle was completed within a predefined time. The problem of reconnaissance was approached by resorting to a switching max-plus linear system, which took into account the different configurations of the robots during the various exploration steps. The formalization of the synchronization problem was then extended to the more general case of max-plus linear dynamical systems subject to polytopic parametric uncertainties. This extension reflected what occurs in applications and tests with real devices, where time values are not constant but may vary within an interval of uncertainty, typically due to environmental factors, such as sea currents, water salinity, and temperature. A progressive approach was adopted: first, a system with uncertainty limited to the dynamics matrix was considered, and then the problem formalization was extended to include uncertainties also in the input and output distribution matrices, thus allowing broader applicability to real contexts. The transferability of the theoretical results to different application contexts, such as the sharing of infrastructure and/or equipment among different groups of users, was also explored.
Dettagli del progetto
Responsabile scientifico: Elena Zattoni
Strutture Unibo coinvolte:
Dipartimento di Ingegneria dell'Energia Elettrica e dell'Informazione "Guglielmo Marconi"
Coordinatore:
Università degli Studi di Cassino e del Lazio Meridionale(Italy)
Contributo totale Unibo: Euro (EUR) 39.200,00
Durata del progetto in mesi: 24
Data di inizio
28/09/2023
Data di fine:
28/02/2026
