A Differential Game Framework for Multi-Agent Coordination under Signal Temporal Logic Specifications

Master Student : Enrico Dozzi

Supervisor : Gregorio Marchesini

In an increasingly connected world, the growing deployment of networked autonomous agents has intensified the need for scalable methods to manage inter-agent coordination in shared environments. This thesis addresses the problem of multi-agent control synthesis under Signal Temporal Logic (STL) specifications, which provide a formal language to express complex spatial and temporal tasks. However, existing approaches face key limitations: Mixed- Integer Linear Programming (MILP)-based solvers, while expressive, suffer from poor scalability due to the exponential growth in binary variables; Control Barrier Function (CBF)-based methods are computationally efficient but struggle to handle complex STL specifications, especially disjunctions. To overcome these limitations, we propose a novel hybrid Model Predictive Control (MPC) framework that integrates centralized and decentralized decision-making. The centralized MPC layer plans trajectories that satisfy individual STL tasks that do not require coordination. When conflicts arise due to shared tasks, a decentralized layer resolves them through a sequence of STL games, a game-theoretic extension of differential games where agent strategies are coupled by shared STL specifications. Both layers encode STL constraints using time-varying sets defined by CBFs, which guarantee satisfaction of temporal requirements over time. Disjunctive STL conditions are handled efficiently through the intro- duction of a minimal number of binary variables, resulting in significantly improved computational performance. Numerical simulations demonstrate that our hybrid architecture achieves comparable STL satisfaction degree while reducing solver time and binary complexity compared to state-of-the- art MILP-based methods.

</div>