Bridging the gap: From cellular automata to differential equation models for pedestrian dynamics

Cellular automata (CA) and ordinary differential equation (ODE) models compete for dominance in microscopic pedestrian dynamics. There are two major differences: movement in a CA is restricted to a grid and navigation is achieved by moving directly in the desired direction. Force based ODE models operate in continuous space and navigation is computed indirectly through the acceleration vector. We present the Optimal Steps Model and the Gradient Navigation Model, which produce trajectories similar to each other. Both are grid-free and free of oscillations, leading to the conclusion that the two major differences are also the two major weaknesses of the older models.