Improving flocking behaviors in street networks with vision

TL;DR

The paper addresses decentralized flocking on street networks using only local information by introducing a vision-based extension to alignment and attraction rules. Walkers evaluate multiple branches within a vision depth $d_n$ and $d_j$ for node counts and net flux, respectively, and use a weighted combination $w_B(d_n,d_j,t)$ to decide moves. The key contributions are (i) demonstrating that vision prevents intersections from causing group splits and (ii) identifying an optimal tactic with $d_n=6$ and $d_j=2$ that yields groups up to 10× larger and more robust to breakups, compared to prior work. The findings illuminate how simple, local-perception rules can drive large, resilient collective behavior in urban settings with potential applications to protests and pedestrian dynamics, while maintaining tractable, decentralized computation that relies on local information and network structure.

Abstract

We improve a flocking model on street networks introduced in a previous paper. We expand the field of vision of walkers, making the model more realistic. Under such conditions, we obtain groups of walkers whose gathering times and robustness to break ups are better than previous results. We explain such improvements because the alignment rule with vision guaranties walkers do not split into divergent directions at intersections anymore, and because the attraction rule with vision gathers distant groups. This paves the way to a better understanding of events where walkers have collective decentralized goals, like protests.

Figures (6)

• Figure 1: A piece of the discretized street network around Place de la Nation in Paris.
• Figure 2: Walker on node $u$ with $d = 2$ has access to the information on the sequences of links and nodes highlighted by arrows, as they are the $d$ first nodes and links of the branches in $\mathcal{B}(u)$.
• Figure 3: Evolution of the last step gathering score for the alignment and attraction rules with different vision depths.
• Figure 4: Heatmap of gathering scores for every tactic with combinations of vision depths $d_n$ and $d_j$ from $0$ to $10$.
• Figure 5: Evolution of gathering score for some relevant tactics with different vision depths.

Theorems & Definitions (4)

• Definition 3.1: Gathering score
• Definition 4.1: Vision depth
• Definition 4.2: Branch
• Definition 4.3: Tactic