Realistic Stride Length Adaptation in the Optimal Steps Model
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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.
KeywordsOptimal Steps Model Stride Length Navigational Situation Free Flow Velocity Crowd Density
This work was funded by the German Federal Ministry of Education and Research through the project MEPKA on mathematical characteristics of pedestrian stream models (grant number 17PNT028).
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