Neural Network-based Control for Multi-Agent Systems from Spatio-Temporal Specifications

We propose a framework for solving control synthesis problems for multi-agent networked systems required to satisfy spatio-temporal specifications. We use Spatio-Temporal Reach and Escape Logic (STREL) as a specification language. For this logic, we define smooth quantitative semantics, which captures the degree of satisfaction of a formula by a multi-agent team. We use the novel quantitative semantics to map control synthesis problems with STREL specifications to optimization problems and propose a combination of heuristic and gradient-based methods to solve such problems. As this method might not meet the requirements of a real-time implementation, we develop a machine learning technique that uses the results of the off-line optimizations to train a neural network that gives the control inputs at current states. We illustrate the effectiveness of the proposed framework by applying it to a model of a robotic team required to satisfy a spatial-temporal specification under communication constraints.Comment: 8 pages. Submitted to the CDC 202

Signal Temporal Logic Task Decomposition via Convex Optimization

In this paper we focus on the problem of decomposing a global Signal Temporal Logic formula (STL) assigned to a multi-agent system to local STL tasks when the team of agents is a-priori decomposed to disjoint sub-teams. The predicate functions associated to the local tasks are parameterized as hypercubes depending on the states of the agents in a given sub-team. The parameters of the functions are, then, found as part of the solution of a convex program that aims implicitly at maximizing the volume of the zero level-set of the corresponding predicate function. Two alternative definitions of the local STL tasks are proposed and the satisfaction of the global STL formula is proven when the conjunction of the local STL tasks is satisfied.Comment: 6 pages, 6 figure

Learning Spatio-Temporal Specifications for Dynamical Systems

Learning dynamical systems properties from data provides important insights that help us understand such systems and mitigate undesired outcomes. In this work, we propose a framework for learning spatio-temporal (ST) properties as formal logic specifications from data. We introduce SVM-STL, an extension of Signal Signal Temporal Logic (STL), capable of specifying spatial and temporal properties of a wide range of dynamical systems that exhibit time-varying spatial patterns. Our framework utilizes machine learning techniques to learn SVM-STL specifications from system executions given by sequences of spatial patterns. We present methods to deal with both labeled and unlabeled data. In addition, given system requirements in the form of SVM-STL specifications, we provide an approach for parameter synthesis to find parameters that maximize the satisfaction of such specifications. Our learning framework and parameter synthesis approach are showcased in an example of a reaction-diffusion system.Comment: 12 pages, submitted to L4DC 202

Sampling-based Synthesis of Controllers for Multiple Agents under Signal Temporal Logic Specifications

openL’ampia applicazione dei robot nelle industrie e nella società ha portato alla necessità di prescrivere complessi compiti di alto livello ad agenti autonomi. Signal Temporal Logic (STL) è una logica temporale che consente di esprimere requisiti spazio-temporali e quantificare il livello di soddisfazione delle preferenze. Quando si pianifica considerando specifiche STL, la sfida principale è generare traiettorie che soddisfino le formule logiche e seguire le traiettorie così ottenute. Il progetto propone una soluzione per il problema di pianificazione del movimento di multipli agenti autonomi, soggetti a specifiche STL accoppiate. Partendo da uno scenario in cui sono coinvolti solo due agenti, un algoritmo basato sul campionamento, Coupled STL_RRT*, è progettato. L’approccio proposto, basato su RRT*, costruisce in modo distribuito due alberi nel dominio del tempo e dello stato accoppiati. Per ogni sistema dinamico, data una posizione iniziale, la strategia sviluppata trova la traiettoria probabilisticamente ottimale in termini di una funzione di costo che dipende dagli input di controllo richiesti. Prima di aggiungere nuovi stati all’albero corrispondente, l’algoritmo controlla se la formula logica non viene violata, assicurando quindi che la traiettoria finale, variabile nel tempo, soddisfi le specifiche spazio-temporali. La dinamica dell’agente autonomo è presa direttamente in considerazione e il concetto di raggiungibilità viene sfruttato per ottenere traiettorie ammissibili rispetto ai vincoli dinamici. L’algoritmo è quindi simulato, considerando un ambiente con ostacoli statici e diversi requisiti STL, specificati dall’utente. L’approccio viene poi esteso al caso di sistemi multi-agente con più di tre agenti. Come nel caso precedente, l’algoritmo costruisce un albero spazio-temporale per ciascun agente, assicurando che la traiettoria finale soddisfi i requisiti STL. La soluzione proposta è poi verificata in scenari simulati, considerando sistemi con 4 o 6 agenti.The wide application of robots in industries and society has brought the need to prescribe complex high-level tasks to autonomous agents. Signal Temporal Logic (STL) is a temporal logic that allows to express desired spatio-temporal requirements, while quantifying the satisfaction of the preferences. When planning under STL specifications, the main challenge is to generate trajectories that satisfy the logical formulas and to track those trajectories. The project proposes a solution for the motion planning problem of multiple autonomous agents, subject to coupled STL specifications. Starting from a scenario where only two agents are involved, a sampling-based algorithm, Coupled STL_RRT*, is designed. The proposed RRT*-based approach builds two trees in the coupled time and state domain in a distributed manner. For each dynamical system, given an initial position, the developed strategy finds a probabilistic optimal trajectory in terms of a cost function that depends on the required control inputs. Before adding new states to the corresponding tree, the algorithm checks if the logical formula is not violated, hence ensuring that the final time-varying trajectory satisfies the spatio-temporal specifications. The dynamics of the autonomous agent is directly taken into account and reachability is exploited to obtain a trajectory that is feasible with respect to the dynamic constraints. The algorithm is then simulated, considering an environment with static obstacles and different STL requirements, specified by the user. The approach is then extended to the case of multi-agent systems with more than three agents. As in the previous case, the algorithm builds a spatiotemporal tree for each agent, ensuring that the final trajectory satisfies the STL requirements. The proposed solution is then verified in simulated scenarios, considering 4-agents and 6-agents systems

Control Strategies for COVID-19 Epidemic with Vaccination, Shield Immunity and Quarantine: A Metric Temporal Logic Approach

Ever since the outbreak of the COVID-19 epidemic, various public health control strategies have been proposed and tested against the coronavirus SARS-CoV-2. We study three specific COVID-19 epidemic control models: the susceptible, exposed, infectious, recovered (SEIR) model with vaccination control; the SEIR model with shield immunity control; and the susceptible, un-quarantined infected, quarantined infected, confirmed infected (SUQC) model with quarantine control. We express the control requirement in metric temporal logic (MTL) formulas (a type of formal specification languages) which can specify the expected control outcomes such as "the deaths from the infection should never exceed one thousand per day within the next three months" or "the population immune from the disease should eventually exceed 200 thousand within the next 100 to 120 days". We then develop methods for synthesizing control strategies with MTL specifications. To the best of our knowledge, this is the first paper to systematically synthesize control strategies based on the COVID-19 epidemic models with formal specifications. We provide simulation results in three different case studies: vaccination control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; shield immunity control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; and quarantine control for the COVID-19 epidemic with model parameters estimated from data in Wuhan, China. The results show that the proposed synthesis approach can generate control inputs such that the time-varying numbers of individuals in each category (e.g., infectious, immune) satisfy the MTL specifications. The results also show that early intervention is essential in mitigating the spread of COVID-19, and more control effort is needed for more stringent MTL specifications