Realistic Stride Length Adaptation in the Optimal Steps Model

Pedestrians move freely in an open space by stepping forward. When the navigational situation becomes difficult, say in a dense crowd, they adjust their stride length and speed. The Optimal Steps Model uses local optimization on a circle around a pedestrian to determine the next position. The target function is a navigational field. Each individual’s stride length, that is, the circle radius depends on his or her speed. This introduces a delay in adaptation, because all speed measurements involve the past. A real person, however, is more likely to react instantaneously. We model this effectively by optimizing on a disk instead of a circle. The radius is chosen in accordance with the pedestrian’s free-flow velocity. A two dimensional continuous optimization problem ensues that we solve efficiently thus maintaining fast computational speed. Our simulations closely match real walking behavior which we demonstrate for navigation around a column in a narrow corridor and behavior at a bottleneck.