Criticality in swarm robots

Research summary

One paper, summarised for reference. Exploring the criticality hypothesis using programmable swarm robots with Vicsek-like interactions — Xiaokang Lei, Yalun Xiang, Mengyuan Duan & Xingguang Peng, J. R. Soc. Interface (2023) 20, 20230176. doi:10.1098/rsif.2023.0176.

The question

Many different factors can drive a collective through the order–disorder transition — but does every such transition confer the functional benefit the criticality hypothesis promises? Using a real programmable swarm (up to 50 SwarmBang robots) with Vicsek-like interactions, subject to time-varying stimuli and a predator, this paper asks which inducer of criticality actually maximizes collective response, and to what extent other behavioural factors modulate it — questions hard to answer in animals (you can’t fine-tune their interaction rules) or in idealized simulations (which omit real-world physics).

The model

Each robot follows short-range repulsion, long-range attraction, and alignment with neighbours, then blends its own heading, the social heading (weighted by a social level $\alpha_{\text{soc}}$), and motion noise $\eta_m$; polarization $\psi=|\tfrac1N\sum_i \mathbf r_i|$ is the order parameter. Five programmable factors split into alignment factors (alignment weight $w_{\text{ali}}$, scale $D_{\text{ali}}$) and non-alignment factors ($\eta_m$, $\alpha_{\text{soc}}$, action cycle $\tau$). An “informed robot” tracks an external signal (attractive: periodic 120° turns; repulsive: a faster predator robot), imposing a local stimulus the rest of the swarm must respond to.

Result 1 — many factors induce the transition

Noise, alignment weight, alignment scale, and social level all drive an order–disorder transition. Noise gives an (empirically) continuous/second-order transition; alignment weight and scale give discontinuous/first-order transitions with bistability near the critical points. Critical slowing down appears near all of them, and nearest-neighbour distance (safety) peaks just above the alignment transition.

Result 2 — only alignment-induced criticality maximizes response

To an attractive stimulus, the group responsiveness $R$ varies non-monotonically with alignment, peaking at a critical $w_{\text{ali}}\approx25$, $D_{\text{ali}}\approx40$ (with minimal turning time and maximal spacing there) — clean support for the criticality hypothesis. But for the non-alignment factors, $R$ falls monotonically with noise and with decreasing social level: the noise-induced order–disorder transition gives no functional gain. The transition’s source matters — phenomenology (being “at the edge”) does not by itself confer the benefit.

Result 3 — non-alignment factors sharpen the alignment benefit

Increasing noise (or lowering the social level, or lengthening the action cycle) makes the peak of $R$ versus alignment more pronounced (steeper fall-off away from the critical alignment). So noise, while unable to create the benefit, highlights alignment-induced criticality — implying real (noisy) groups may show the advantage more clearly than noise-free toy models. The effect also strengthens with group size (invisible at $N=10$, clear by $N=30$–$50$).

Predator-evasion re-validation

Under a pursuing predator, the first-capture time, polarization, and spacing all peak near the critical alignment ($w_{\text{ali}}\approx25$): longest survival, most synchronized escape, lowest collision risk. Escape information (the informed robot’s manoeuvre) propagates most efficiently near the critical point, with naive robots rapidly “copying” it.

The upshot

The functional advantage the criticality hypothesis predicts is real and physically demonstrable, but specific to alignment (velocity/directional coupling), not to noise or other non-alignment factors — and moderate, not strong, alignment is best. The authors suggest treating alignment strength/scale as adjustable parameters in models, and float the social level and action cycle — how agents allocate attention and how often they act — as candidate internal self-tuning (SOC) knobs by which real groups might hold themselves near criticality.

References

Lei et al. (2023), J. R. Soc. Interface 20, 20230176 · Vicsek et al. (1995), Phys. Rev. Lett. 75, 1226 · Mora & Bialek (2011), J. Stat. Phys. 144, 268 · Muñoz (2018), Rev. Mod. Phys. 90, 031001 · Klamser & Romanczuk (2021), PLoS Comput. Biol. 17, e1008832 · Calovi et al. (2015), J. R. Soc. Interface 12, 20141362 · Kinouchi & Copelli (2006), Nat. Phys. 2, 348 · Poel et al. (2022), Sci. Adv. 8, eabm6385.