Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper)

Exploiting the efficiency and stability of Position-Based Dynamics (PBD), we introduce a novel crowd simulation method that runs at interactive rates for hundreds of thousands of agents. Our method enables the detailed modeling of per-agent behavior in a Lagrangian formulation. We model short-range and long-range collision avoidance to simulate both sparse and dense crowds. On the particles representing agents, we formulate a set of positional constraints that can be readily integrated into a standard PBD solver. We augment the tentative particle motions with planning velocities to determine the preferred velocities of agents, and project the positions onto the constraint manifold to eliminate colliding configurations. The local short-range interaction is represented with collision and frictional contact between agents, as in the discrete simulation of granular materials. We incorporate a cohesion model for modeling collective behaviors and propose a new constraint for dealing with potential future collisions. Our new method is suitable for use in interactive games.Comment: 9 page

Two-way multi-lane traffic model for pedestrians in corridors

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian density cannot exceed a maximal density corresponding to contact between pedestrians. In a first step, we propose a singularly perturbed pressure relation which models the fact that the pedestrian velocity is considerably reduced, if not blocked, at congestion. In a second step, we carry over the singular limit into the model and show that abrupt transitions between compressible flow (in the uncongested regions) to incompressible flow (in congested regions) occur. We also investigate the hyperbolicity of the two-way models and show that they can lose their hyperbolicity in some cases. We study a diffusive correction of these models and discuss the characteristic time and length scales of the instability

Modeling of Complex Large-Scale Flow Phenomena

Flows at large scales are capable of unmatched complexity. At large spatial scales, they can exhibit phenomena like waves, tornadoes, and a screaming concert audience; at high densities, they can create shockwaves, and can cause stampedes. Though strides have been made in simulating flows like fluids and crowds, extending these algorithms with scale poses challenges in ensuring accuracy while maintaining computational efficiency. In this dissertation, I present novel techniques to simulate large-scale flows using coupled Eulerian-Lagrangian models that employ a combination of discretized grids and dynamic particle-based representations. I demonstrate how such models can efficiently simulate flows at large-scales, while maintaining fine-scale features. In fluid simulation, a long-standing problem has been the simulation of large-scale scenes without compromising fine-scale features. Though approximate multi-scale models exist, accurate simulation of large-scale fluid flow has remained constrained by memory and computational limits of current generation PCs. I propose a hybrid domain-decomposition model that, by coupling Lagrangian vortex-based methods with Eulerian velocity-based methods, reduces memory requirements and improves performance on parallel architectures. The resulting technique can efficiently simulate scenes significantly larger than those possible with either model alone. The motion of crowds is another class of flows that exhibits novel complexities with increasing scale. Navigation of crowds in virtual worlds is traditionally guided by a static global planner, combined with dynamic local collision avoidance. However, such models cannot capture long-range crowd interactions commonly observed in pedestrians. This discrepancy can cause sharp changes in agent trajectories, and sub-optimal navigation. I present a technique to add long-range vision to virtual crowds by performing collision avoidance at multiple spatial and temporal scales for both Eulerian and Lagrangian crowd navigation models, and a novel technique to blend both approaches in order to obtain collision-free velocities efficiently. The resulting simulated crowds show better correspondence with real-world pedestrians in both qualitative and quantitative metrics, while adding a minimal computational overhead. Another aspect of real-world crowds missing from virtual agents is their behavior at high densities. Crowds at such scales can often exhibit chaotic behavior commonly known as emph{crowd turbulence}; this phenomenon has the potential to cause mishaps leading to loss of life. I propose modeling inter-personal stress in dense crowds using an Eulerian model, coupled with a physically-based Lagrangian agent-based model to simulate crowd turbulence. I demonstrate how such a hybrid model can create virtual crowds whose trajectories show visual and quantifiable similarities to turbulent crowds in the real world. The techniques proposed in this thesis demonstrate that hybrid Eulerian-Lagrangian modeling presents a versatile approach for modeling large-scale flows, such as fluids and crowds, efficiently on current generation PCs.Doctor of Philosoph

Continuum modeling of crowd turbulence

With the growth in world population, the density of crowds in public places has been increasing steadily, leading to a higher incidence of crowd disasters at high densities. Recent research suggests that emergent chaotic behavior at high densities-known collectively as crowd turbulence-is to blame. Thus, a deeper understanding of crowd turbulence is needed to facilitate efforts to prevent and plan for chaotic conditions in high-density crowds. However, it has been noted that existing algorithms modeling collision avoidance cannot faithfully simulate crowd turbulence. We hypothesize that simulation of crowd turbulence requires modeling of both collision avoidance and frictional forces arising from pedestrian interactions. Accordingly, we propose a model for turbulent crowd simulation, which incorporates a model for interpersonal stress and acceleration constraints similar to real-world pedestrians. Our simulated results demonstrate a close correspondence with observed metrics for crowd turbulence as measured in known crowd disasters

Pedestrian flows in bounded domains with obstacles

In this paper we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Radon positive measures generated by a push-forward recursive relation. We assume that two fundamental aspects of pedestrian behavior rule the dynamics of the system: On the one hand, the will to reach specific targets, which determines the main direction of motion of the walkers; on the other hand, the tendency to avoid crowding, which introduces interactions among the individuals. The resulting model is able to reproduce several experimental evidences of pedestrian flows pointed out in the specialized literature, being at the same time much easier to handle, from both the analytical and the numerical point of view, than other models relying on nonlinear hyperbolic conservation laws. This makes it suitable to address two-dimensional applications of practical interest, chiefly the motion of pedestrians in complex domains scattered with obstacles.Comment: 25 pages, 9 figure