Topology-based analysis and optimization for agent fleet behavior

<ns3:p>We introduce novel topological methods for analyzing the behaviors and navigation of an agent fleet. Our goal is to understand and enhance the evolution of agent fleet behaviors to minimize unintended behaviors, such as collisions and deadlocks. Understanding the dynamics of the agent fleet enables us to predict safer and more efficient routes for their deployment. To achieve this, we propose employing geometric-topological approaches such as graph-based techniques, Vietoris-Rips filtrations, persistent homology, matching diagrams, and persistent entropy. These methods leverage the geometric and topological structure of the data, allowing us to capture spatial and relational patterns in agent fleet behaviors and configurations. Unlike classical approaches, which often rely on predefined features or statistical assumptions, geometric-topological-based techniques offer an interpretable framework that highlights qualitative differences in the dynamics of the agent fleet. The added interpretability and the ability to capture intrinsic spatial structures make these techniques particularly suitable for characterizing different agent fleet behaviors and ensuring safe and efficient simulation runs. This work is part of the European Project “REliable & eXplainable Swarm Intelligence for People with Reduced mObility - REXASIPRO”.</ns3:p>