Informational Memory Shapes Collective Behavior in Intelligent Swarms

Abstract

We present an experimental and theoretical study of 2-D swarms in which collective behavior emerges from both direct local mechanical coupling between agents and from the exchange and processing of information between agents. Each agent, an air-table drone endowed with internal memory and a binary decision variable, updates its state by integrating a time series of memories of local past collisions. This internal computation transforms the drone swarm into a dynamical information network in which history-dependent feedback drives spontaneous complete spin polarization, pitchfork bifurcated spin collectives, and chaotic switching between collective states. By tuning the depth of memory and the decision algorithm, we uncover a memory-induced phase transition that breaks spin symmetry at the population level. A minimal theoretical model maps these dynamics onto an effective potential landscape sculpted by informational feedback, revealing how temporally correlated computation can replace instantaneous forces as the driver of collective organization, informed by experiments. These results position physically interacting drone swarms as a model system for exploring the physics of informational drone ensembles whose emergent behavior arises from the interplay between physical interaction and information processing.

Figures (4)

• Figure 1: Dynamics of opinion exchange.A. People change their opinions after evaluating opinions from the others. The evaluation depends on a finite memory of recent observations of the peer stored in a queue. B. The state updates with the weighted memory $\Sigma_d=\sum_i w_i q_i$. Observations $q_i\in\{+1,-1\}$ are weighted by $w_i$ depending on their personalities. One common decision is to follow the majority where $w_i$ is constant such that $S=\text{sign}(\Sigma_d)$ picks the larger counts of the spin. Similarly, negative constant weight defines an agent moving against the majority, and higher weights on the more recent events defines an opportunist. Curmudgeons with strong systematic biases have independence of weighted memory. C. A physical agent (spinner) has a microcomputer with gyroscope, accelerometer, and actuates the state of the four blowers. D. A spinner records information of surrounding spinners through mechanical interactions (gray shades) that same spins drop spin upon collision while opposite spins do not spinners. E. A spinner can choose to spin counterclockwise or clockwise by selecting appropriate blowers depending on its internal algorithm. See https://www.dropbox.com/scl/fi/ech59xy6nexs2m2xzrlow/SI1_smartSpinners_c.mp4?rlkey=4ks7wko1lo4v6oxdx0ewqob45&dl=0 for demonstration.
• Figure 2: Memory-induced spontaneous symmetry breaking.A. Probability of states for a collective of pushover with each building its memory of the past $M$ collision inference and following the majority in memory for different $M$. B. When the memory size is small, there is no net polarization. When the size of memory is sufficiently large, the population collapses where one spin dominates the other. See https://www.dropbox.com/scl/fi/00hoxet5xt789koj18ohv/SI2_pushover_c.mp4?rlkey=tfi2tcqqw74h9zx5tbwf2il16&dl=0 for experiment videos. The inset shows the simulation result for large N (=128). See https://www.dropbox.com/scl/fi/468uppenhiqm2em1i1ajj/SI7_simulationBigN_c.mp4?rlkey=qxzq3nsvyvrx7e1lcxjuv95y3&dl=0 for the simulation videos. C. Population over time for spinners with $m$ bits of $+$. When the initial population of $+$ spinners is slightly higher than the $-$ spinners, memory size $M=21$ attracts the population to higher $+$ memory states while $M=5$ erases the initial bias and leads the collective to an even distribution of $+$ and $-$. D. The fraction of $+$ over time for $M=5$ and $M=21$. Here the detection error $\eta=0.3$. E. The fraction of $+$ spinners $n_+=N_+/N$ follows the gradient of an effective potential $V$ which varies from a single well when $M$ is small to a double well when $M$ exceeds a critical value.
• Figure 3: Curmudgeon and contrarian.A. Among pushover spinners with 27-bit memories (above critical), a curmudgeon has a constant opinion which is able to distort the symmetric double-well potential ($V_{\text{no cur.}}$) of the pushovers to a biased double-well ($V_{\text{cur.}}$). An experiment where a group of pushovers with all $-$ bits get directed by a $+$ curmudgeon after the initial diffusion stage. See https://www.dropbox.com/scl/fi/hwpurnhzm82t02a6za2si/SI3_curmudgeon_c.mp4?rlkey=swweg6795i8kwuziapp35l5q6&dl=0 for experiment video. B. A contrarian always acting the opposite to the majority acts like a curmudgeon on a short time scale. Here $M=17$. See https://www.dropbox.com/scl/fi/b14g365dorr8g0krqy7i2/SI4_contrarian_c.mp4?rlkey=sxb7bjo0zoituq4odzi8t0f75&dl=0 for experiment video.
• Figure 4: Weighted memory.A. The weight on the memory $w\propto b^t$ shifts its focus from the past to the recent as the weight bias $b$ increases from $0$. B. The number of $+$ spinner, $N_+$, increases with time after all spinners start with pure $-$ bits. The speed of the process varies among traditionalist, pushover, and opportunist. See https://www.dropbox.com/scl/fi/rwmdfpkitif6zy6stkvct/SI5_timeWeight_c.mp4?rlkey=v3mprpgx6spa0uzwjluknybgo&dl=0 for experiment video. C. Half-lives to reach 50/50 for different bias ($b$) and memory size ($M$) combinations from simulation.