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Collision avoidance in pedestrian dynamics

There is a lot of experimental evidence that collision avoidance is among the main driving principles in pedestrian dynamics: individuals actively anticipate the future to predict a possible collision time and adjust their velocity accordingly, see [1]. At the same time they show no intention to change their direction when walking close to each other in the same direction. In this paper we propose an optimal control model based upon a simple two-player pursuer evader game. We shall use Bellman's approach to study the embedded multi-player game for collision avoidance and discuss related theoretical as well as numerical aspects.