The growing availability of data on pedestrian movement allows for increasingly sophisticated models of people's goals, preferences, and perception of their environment. Such models are important not only in traffic engineering ("How do we structure the foyer in this building to avoid a stampede in case of evacuation?") but also in improving our ability to detect emerging threats in urban settings. Any dramatic change in the usual "patterns of life" might provide a clue about the evolving conditions ("Why did this group of pedestrians take such an unusual path to their target? Why is there suddenly a crowd at this intersection?"), while the analysis of data aggregated over a longer horizon can be also useful in improving our monitoring and modeling ("Which parts of the city are generally perceived as more dangerous? Where should we deploy our limited observation resources?").
This project focuses on two specific applications: (a) civilians in dangerous environments planning their paths to minimize threat exposure, and (b) adversaries aware of the existing monitoring measures planning their paths to evade the observation. In both contexts, the PIs propose models and numerical methods for (1) path planning based on one's beliefs about the environment and (2) adversarial/robust path planning, with the environment possibly changing in response to people's routing choices. The threat avoidance under selfish/independent decision making will be also treated in the framework of "mean field games". The proposed approach draws on methods from game theory, convex optimization, optimal control, and multi-objective dynamic programming. The information patterns built into this model make it possible to leverage the efficiency of fast numerical algorithms already developed for a broad range of deterministic optimal control applications. This project continues earlier work on causal/non-iterative numerical methods and distributed optimal control.
