Natural discretization of pedestrian movement in continuous space

Is there a way to describe pedestrian movement with simple rules, as in a cellular automaton, but without being restricted to a cellular grid? Inspired by the natural stepwise movement of humans, we develop a model that uses local discretization on a circle around virtual pedestrians. This allows for movement in arbitrary directions, only limited by the chosen optimization algorithm and numerical resolution. The radii of the circles correspond to the step lengths of pedestrians and thus are model parameters, which must be derived from empirical observation. Therefore, we conducted a controlled experiment, collected empirical data for step lengths in relation with different speeds, and used the findings in our model. We complement the model with a simple calibration algorithm that allows reproducing known density-velocity relations, which constitutes a proof of concept. Further validation of the model is achieved by reenacting an evacuation scenario from experimental research. The simulated egress times match the values reported for the experiment very well. A new normalized measure for space occupancy serves to visualize the results.