Adaptive pedestrian dynamics based on geodesics

Here, we report on a new approach for adaptive path finding in microscopic simulations of pedestrian dynamics. The approach extends a widely used concept based on scalar navigation fields-the so-called floor field method. Adopting a continuum perspective, navigation fields used in our approach correspond to the shortest distances to the pedestrian's targets with respect to arbitrary metrics, e. g. metrics depending on the local terrain. If the metric correlates inversely with the expected speed, these distances could be interpreted as expected travel times. Following this approach, it is guaranteed that virtual pedestrians navigate along the steepest descent of the navigation field and thus follow geodesics. Using the Eikonal equation, i.e. a continuum model, navigation fields can be determined with respect to arbitrary metrics in an efficient manner. The fast marching method used in this work offers a fast method to solve the Eikonal equation (complexity N log N, where N is degree of freedom). Increasing computational efforts with respect to classical approaches only mildly, the consideration of locally varying metrics allows a realistic adaptive movement behavior like the avoidance of certain terrains. The method is outlined using a simple cellular automaton approach. Extensions to other microscopic models, e.g. cellular automata approaches or social force models, are possible.