Single file motion of robot swarms

TL;DR

The present work demonstrates the suitability of robot swarms to model complex behaviors in many particle systems, with a transition from free flow to congested traffic as the density of the system increases.

Abstract

We present experimental results on the single file motion of a group of robots interacting with each other through position sensors. We successfully replicate the fundamental diagram typical of these systems, with a transition from free flow to congested traffic as the density of the system increases. In the latter scenario we also observe the characteristic stop-and-go waves. The unique advantages of this novel system, such as experimental stability and repeatability, allow for extended experimental runs, facilitating a comprehensive statistical analysis of the global dynamics. Above a certain density, we observe a divergence of the average jam duration and the average number of robots involved in it. This discovery enables us to precisely identify another transition: from congested intermittent flow (for intermediate densities) to a totally congested scenario for high densities. Beyond this finding, the present work demonstrates the suitability of robot swarms to model complex behaviors in many particle systems.

Figures (4)

• Figure 1: (a) Photograph of a robot. Green circles mark the infrared proximity sensors. (b) Snapshot of 18 robots on the circular lane; a jam of five robots can be seen at approximately 11 o’clock. (c) Single-robot speed over a 20-second interval in an experiment with $N=20$ robots and $V_{max}=69$ cm/s.
• Figure 2: (a) Average flow rate versus the number of robots in the system (N) for two different robot speeds ($V_{max}=28$ cm/s and $V_{max}=69$ cm/s, as indicated in the legend of d). Solid lines are results of numerical simulations. (b) Average speed $\langle v \rangle$ as a function of the number of robots $N$. (c) Rescaled speed (i.e., the average speed divided by robot speed $V_{max}$), as a function of $N$. (d) Order parameter $t$ as a function of N. (e) Log-lin survival function of the time lapse that an individual robot is running $t_r$, for scenarios with $V_{max}=69$ cm/s and different $N$ (as indicated in the legend above panel (f)). (f) Survival function of the time lapse that an individual robot is stopped $t_s$ in log-log scale. The solid line has a slope of $-1$, hence corresponding to a power-law exponent of $-2$.
• Figure 3: (a-c) Spatiotemporal diagrams depicting six seconds of experimental results with $V_{max}=69$ cm/s and $N$=10, 20, and 30 robots, respectively. Speeds are color-coded as shown in the color bar. (d) Survival function of the jam length ($l$) for $V_{max}=69$ cm/s and different numbers of robots ($N$), as indicated in the legend. Note the logarithmic scale. (e) Survival function in logarithmic scale for the jam duration $d$. Solid lines serve as guides to the eye, illustrating an exponent of $-1$ which to power law tails with an exponent of $-2$ in the probability density. (f) Average jam duration $\langle d \rangle$ as a function of $N$. The point corresponding to $N=24$ represents the average of the registered data; remark, however, that this value does not accurately reflect convergence of the first moment, as $\langle d \rangle$ grows unboundedly with the measuring time. This is indicated with the dashed line.
• Figure 4: (a) Survival function for jam duration in simulations ($d_S$) for different number of agents ($N_S$). The solid line serves as a guide to the eye, illustrating an exponent of -1 in the survival, corresponding to power laws with an exponent of -2. Note the logarithmic scale. (b) Average jam duration $\langle d_S \rangle$ as a function of $N_S$. The top axis indicates the number of agents ($N_E$) corresponding to systems with equal density and the size of the experimental scenario.