skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Relative rate of expansion controls speed in one-dimensional pedestrian following
Patterns of crowd behavior are believed to result from local interactions between pedestrians. Many studies have investigated the local rules of interaction, such as steering, avoiding, and alignment, but how pedestrians control their walking speed when following another remains unsettled. Most pedestrian models assume the physical speed and distance of others as input. The present study compares such “omniscient” models with “visual” models based on optical variables.We experimentally tested eight speed control models from the pedestrian- and car-following literature. Walking participants were asked to follow a leader (a moving pole) in a virtual environment, while the leader’s speed was perturbed during the trial. In Experiment 1, the leader’s initial distance was varied. Each model was fit to the data and compared. The results showed that visual models based on optical expansion (θ˙) had the smallest root mean square error in speed across conditions, whereas other models exhibited increased error at longer distances. In Experiment 2, the leader’s size (pole diameter) was varied. A model based on the relative rate of expansion (θ˙/θ) performed better than the expansion rate model (θ˙), because it is less sensitive to leader size. Together, the results imply that pedestrians directly control their walking speed in one-dimensional following using relative rate of expansion, rather than the distal speed and distance of the leader.  more » « less
Award ID(s):
1849446
PAR ID:
10514716
Author(s) / Creator(s):
;
Publisher / Repository:
Association for Research in Vision and Ophthalmology
Date Published:
Journal Name:
Journal of Vision
Volume:
23
Issue:
10
ISSN:
1534-7362
Page Range / eLocation ID:
3
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Collective motion in human crowds emerges from local interactions between individual pedestrians. Previously, we found that an individual in a crowd aligns their velocity vector with a weighted average of their neighbors’ velocities, where the weight decays with distance (Rio, Dachner, & Warren, PRSB, 2018; Warren, CDPS, 2018). Here, we explain this “alignment rule” based solely on visual information. When following behind a neighbor, the follower controls speed by canceling the neighbor’s optical expansion (Bai & Warren, VSS, 2018) and heading by canceling the neighbor’s angular velocity. When walking beside a neighbor, these relations reverse: Speed is controlled by canceling angular velocity and heading by canceling optical expansion. These two variables trade off as sinusoidal functions of eccentricity (Dachner & Warren, VSS, 2018). We use this visual model to simulate the trajectories of participants walking in virtual (12 neighbors) and real (20 neighbors) crowds. The model accounts for the data with root mean square errors (.04–.05 m/s, 1.5°–2.0°) the distance decay as a consequence of comparable to those of our previous velocity-alignment model. Moreover, the model explains Euclid’s law of perspective, without an explicit distance term. The visual model thus provides a better explanation of collective motion. 
    more » « less
  2. Patterns of collective motion in bird flocks, fish schools and human crowds are believed to emerge from local interactions between individuals. Most ‘flocking' models attribute these local interactions to hypothetical rules or metaphorical forces and assume an omniscient third-person view of the positions and velocities of all individuals in space. We develop a visual model of collective motion in human crowds based on the visual coupling that governs pedestrian interactions from a first-person embedded viewpoint. Specifically, humans control their walking speed and direction by cancelling the average angular velocity and optical expansion/contraction of their neighbours, weighted by visibility (1 − occlusion). We test the model by simulating data from experiments with virtual crowds and real human ‘swarms'. The visual model outperforms our previous omniscient model and explains basic properties of interaction: ‘repulsion' forces reduce to cancelling optical expansion, ‘attraction' forces to cancelling optical contraction and ‘alignment' to cancelling the combination of expansion/contraction and angular velocity. Moreover, the neighbourhood of interaction follows from Euclid's Law of perspective and the geometry of occlusion. We conclude that the local interactions underlying human flocking are a natural consequence of the laws of optics. Similar perceptual principles may apply to collective motion in other species. 
    more » « less
  3. Abstract Accurate control of a humanoid robot's global position (i.e., its three-dimensional (3D) position in the world) is critical to the reliable execution of high-risk tasks such as avoiding collision with pedestrians in a crowded environment. This paper introduces a time-based nonlinear control approach that achieves accurate global-position tracking (GPT) for multi-domain bipedal walking. Deriving a tracking controller for bipedal robots is challenging due to the highly complex robot dynamics that are time-varying and hybrid, especially for multi-domain walking that involves multiple phases/domains of full actuation, over actuation, and underactuation. To tackle this challenge, we introduce a continuous-phase GPT control law for multi-domain walking, which provably ensures the exponential convergence of the entire error state within the full and over actuation domains and that of the directly regulated error state within the underactuation domain. We then construct sufficient multiple-Lyapunov stability conditions for the hybrid multi-domain tracking error system under the proposed GPT control law. We illustrate the proposed controller design through both three-domain walking with all motors activated and two-domain gait with inactive ankle motors. Simulations of a ROBOTIS OP3 bipedal humanoid robot demonstrate the satisfactory accuracy and convergence rate of the proposed control approach under two different cases of multi-domain walking as well as various walking speed and desired paths. 
    more » « less
  4. For transportation hubs, leveraging pedestrian flows for commercial activities presents an effective strategy for funding maintenance and infrastructure improvements. However, this introduces new challenges, as consumer behaviors can disrupt pedestrian flow and efficiency. To optimize both retail potential and pedestrian efficiency, careful strategic planning in store layout and facility dimensions was done by expert judgement due to the complexity in pedestrian dynamics in the retail areas of transportation hubs. This paper introduces an attention-based movement model to simulate these dynamics. By simulating retail potential of an area through the duration of visual attention it receives, and pedestrian efficiency via speed loss in pedestrian walking behaviors, the study further explores how design features can influence the retail potential and pedestrian efficiency in a bi-directional corridor inside a transportation hub. 
    more » « less
  5. null (Ed.)
    The safety of distracted pedestrians presents a significant public health challenge in the United States and worldwide. An estimated 6,704 American pedestrians died and over 200,000 pedestrians were injured in traffic crashes in 2018, according to the Centers for Disease Control and Prevention (CDC). This number is increasing annually and many researchers posit that distraction by smartphones is a primary reason for the increasing number of pedestrian injuries and deaths. One strategy to prevent pedestrian injuries and death is to use intrusive interruptions that warn distracted pedestrians directly on their smartphones. To this end, we developed StreetBit, a Bluetooth beacon-based mobile application that alerts distracted pedestrians with a visual and/or audio interruption when they are distracted by their smartphones and are approaching a potentially-dangerous traffic intersection. In this paper, we present the background, architecture, and operations of the StreetBit Application. 
    more » « less