How navigation according to a distance function improves pedestrian motion in ODE-based models

We present a new ODE-based model for pedestrian motion where a superposition of gradients of distance functions directly changes the direction of the velocity vector: the Gradient Navigation Model (GNM). The approach differs fundamentally from force based models where the accelerative term is affected by forces and in turn changes the velocity. In the GNM, model induced oscillations are avoided completely since no actual forces are present. The use of fast and accurate high order numerical integrators is possible through smooth derivatives in the equations of motion. As a consequence, almost no overlapping of pedestrians occurs. Empirically known phenomena are well reproduced. The parameter calibration is performed by theoretical arguments based on empirically validated assumptions rather than numerical tests. The Gradient Navigation Model is compared quantitatively and qualitatively to Helbing’s Social Force Model.