Least-effort trajectories lead to emergent crowd behaviors

Dimensionless numbers reveal distinct regimes in the structure and dynamics of pedestrian crowds

In fluid mechanics, dimensionless numbers like the Reynolds number help classify flows. We argue that such a classification is also relevant for crowd flows by putting forward the dimensionless Intrusion and Avoidance numbers, which quantify the intrusions into the pedestrians' personal spaces and the imminency of the collisions that they face, respectively. Using an extensive dataset, we show that these numbers delineate regimes where distinct variables characterize the crowd's arrangement, namely, Euclidean distances at low Avoidance number and times-to-collision at low Intrusion number. On the basis of these findings, a perturbative expansion of the individual pedestrian dynamics is carried out around the noninteracting state, in quite general terms. Simulations confirm that this expansion performs well in its expected regime of applicability.

A Calibrated Force-Based Model for Mixed Traffic Simulation

Virtual traffic benefits a variety of applications, including video games, traffic engineering, autonomous driving, and virtual reality. To date, traffic visualization via different simulation models can reconstruct detailed traffic flows. However, each specific behavior of vehicles is always described by establishing an independent control model. Moreover, mutual interactions between vehicles and other road users are rarely modeled in existing simulators. An all-in-one simulator that considers the complex behaviors of all potential road users in a realistic urban environment is urgently needed. In this work, we propose a novel, extensible, and microscopic method to build heterogeneous traffic simulation using the force-based concept. This force-based approach can accurately replicate the sophisticated behaviors of various road users and their interactions in a simple and unified manner. We calibrate the model parameters using real-world traffic trajectory data. The effectiveness of this approach is demonstrated through many simulation experiments, as well as comparisons to real-world traffic data and popular microscopic simulators for traffic animation.

A least action principle for interceptive walking

The principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

Universal power law governing pedestrian interactions

Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of this interaction, however, has remained an open question. Here, we introduce a novel statistical-mechanical approach to directly measure the interaction energy between pedestrians. This analysis, when applied to a large collection of human motion data, reveals a simple power-law interaction that is based not on the physical separation between pedestrians but on their projected time to a potential future collision, and is therefore fundamentally anticipatory in nature. Remarkably, this simple law is able to describe human interactions across a wide variety of situations, speeds, and densities. We further show, through simulations, that the interaction law we identify is sufficient to reproduce many known crowd phenomena.

Leadership in moving human groups

How is movement of individuals coordinated as a group? This is a fundamental question of social behaviour, encompassing phenomena such as bird flocking, fish schooling, and the innumerable activities in human groups that require people to synchronise their actions. We have developed an experimental paradigm, the HoneyComb computer-based multi-client game, to empirically investigate human movement coordination and leadership. Using economic games as a model, we set monetary incentives to motivate players on a virtual playfield to reach goals via players' movements. We asked whether (I) humans coordinate their movements when information is limited to an individual group member's observation of adjacent group member motion, (II) whether an informed group minority can lead an uninformed group majority to the minority's goal, and if so, (III) how this minority exerts its influence. We showed that in a human group – on the basis of movement alone – a minority can successfully lead a majority. Minorities lead successfully when (a) their members choose similar initial steps towards their goal field and (b) they are among the first in the whole group to make a move. Using our approach, we empirically demonstrate that the rules of swarming behaviour apply to humans. Even complex human behaviour, such as leadership and directed group movement, follow simple rules that are based on visual perception of local movement.

Our article gives empirical evidence of group coordination mechanisms and basic rules of leadership that assist in leading a human group. Using a computer-based multi-client game that blocks explicit signals or other typical human information transfer, we offer a model of human group movement patterns applicable to group scenarios such as emergency, rescue, and sports where inter-individual communication is hindered but the reading of movement is still possible. Results show that even in these communication-restricted situations, movement of an informed minority that is efficient and consistent can effectively pull the majority towards a target goal.

Potential for the dynamics of pedestrians in a socially interacting group

We introduce a simple potential to describe the dynamics of the relative motion of two pedestrians socially interacting in a walking group. We show that the proposed potential, based on basic empirical observations and theoretical considerations, can qualitatively describe the statistical properties of pedestrian behavior. In detail, we show that the two-dimensional probability distribution of the relative distance is determined by the proposed potential through a Boltzmann distribution. After calibrating the parameters of the model on the two-pedestrian group data, we apply the model to three-pedestrian groups, showing that it describes qualitatively and quantitatively well their behavior. In particular, the model predicts that three-pedestrian groups walk in a V-shaped formation and provides accurate values for the position of the three pedestrians. Furthermore, the model correctly predicts the average walking velocity of three-person groups based on the velocity of two-person ones. Possible extensions to larger groups, along with alternative explanations of the social dynamics that may be implied by our model, are discussed at the end of the paper.

A microscopic "social norm" model to obtain realistic macroscopic velocity and density pedestrian distributions

We propose a way to introduce in microscopic pedestrian models a “social norm” in collision avoiding and overtaking, i.e. the tendency, shared by pedestrians belonging to the same culture, to avoid collisions and perform overtaking in a preferred direction. The “social norm” is implemented, regardless of the specific collision avoiding model, as a rotation in the perceived velocity vector of the opponent at the moment of computation of the collision avoiding strategy, and justified as an expectation that the opponent will follow the same “social norm” (for example a tendency to avoid on the left and overtake on the right, as proposed in this work for Japanese pedestrians). By comparing with real world data, we show that the introduction of this norm allows for a better reproduction of macroscopic pedestrian density and velocity patterns.