| Summary: | We live in a populous world. Furthermore, as social animals, we participate in activities which draw us together into shared spaces -- office buildings, city sidewalks, parks, events (e.g., religious, sporting, or political), etc. Models that can predict how crowds of humans behave in such settings would be valuable in allowing us to analyze the designs for novel environments and anticipate issues with space utility and safety. They would also better enable robots to safely work in a common environment with humans. Furthermore, credible simulation of crowds of humans would allow us to populate virtual worlds, helping to increase the immersive properties of virtual reality or entertainment applications. We propose a new model for pedestrian crowd simulation: Pedestrian Velocity Obstacles (PedVO). PedVO is based on Optimal Reciprocal Collision Avoidance (ORCA), a local navigation algorithm for computing optimal feasible velocities which simultaneously avoid collisions while still allowing the agents to progress toward their individual goals. PedVO extends ORCA by introducing new models of pedestrian behavior and relationships in conjunction with a modified geometric optimization planning technique to efficiently simulate agents with improved human-like behaviors. PedVO introduces asymmetric relationships between agents through two complementary techniques: Composite Agents and Right of Way. The former exploits the underlying collision avoidance mechanism to encode abstract factors and the latter modifies the optimization algorithm's constraint definition to enforce asymmetric coordination. PedVO further changes the optimization algorithm to more fully encode the agent's knowledge of its environment, allowing the agent to make more intelligent decisions, leading to a better utilization of space and improved flow. PedVO incorporates a new model, which works in conjunction with the local planning algorithm, to introduce a ubiquitous density-sensitive behavior observed in human crowds -- the so-called ``fundamental diagram.'' We also provide a physically-plausible, interactive model for simulating walking motion to support the computed agent trajectories. We evaluate these techniques by simulating various scenarios, such as pedestrian experiments and a challenging real-world scenario: simulating the performance of the Tawaf, an aspect of the Muslim Hajj.
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