Emergent Field-Driven Robot Swarm States

We present an ecology-inspired form of active matter consisting of a robot swarm. Each robot moves over a planar dynamic resource environment represented by a large light-emitting diode array in search of maximum light intensity; the robots deplete (dim) locally by their presence the local light intensity and seek maximum light intensity. Their movement is directed along the steepest local light intensity gradient; we call this emergent symmetry breaking motion “field drive.” We show there emerge dynamic and spatial transitions similar to gas, crystalline, liquid, glass, and jammed states as a function of robot density, resource consumption rates, and resource recovery rates. Paradoxically the nongas states emerge from smooth, flat resource landscapes, not rough ones, and each state can directly move to a glassy state if the resource recovery rate is slow enough, at any robot density.

Figure 1

Robots and the interactive LED light board environment. (a) Each robot has one microcontroller. A robot base, of diameter of 65 mm, has four RGB sensors for detection of light color from the LED light board. The movement of each robot is controlled by two independent pulse-width modulated gear motors. (b) The four RGB sensors are used to codetect gradient vectors from the underneath resource landscape. (c) The LED light board of dimension $4.0\times 4.0{\mathrm{m}}^2$ and 2.5 mm pitch supplies complex and dynamic environment for the robot communities. (d) The rules and parameters that control landscape resource and agents consumption property.

Figure 2

Robotic field-drive emergent motion. (a1),(a2) Each robot consumes (dims) the light in a Gaussian circle around its position. (a3) Fluctuations give rise to transient intensity gradients which spontaneously give rise to a random velocity direction (a4). (b) Self-drive of a robot over an initially smooth resource field. (c) Each robot has a different response to light gradients determined by variations in the motor and drive train quality. Histogram of robot velocity distributions for all robots when moving alone in a flat landscape, ordered by their average kinetic energy, and some typical trajectories.

Figure 3

The basic robot spatial distribution and the resource landscape field dynamic as the light environment radius shrinks. Column (a1)–(e1) outlines how field drive results in robot different localized states, and column (a2)–(e2) shows snapshots of robot positions in five different phases. Column (a3)–(e3) shows the spatial Fourier transformation of the robot positions in column (a2)–(e2).

Figure 4

(a) Demonstration for ${\psi }_6$ calculation. (b) Demonstration for ${\chi }_4$ calculation. (c) An example of characteristic time ${\tau }^{*}$ evaluated from the peak position of ${\chi }_4(\tau ,a)$.

Figure 5

(a) ${\psi }_6$ as a function of robot density and resource recovery rate $1/{\tau }_R$. (b) Robot kinetic energy density ${\overrightarrow{v}}_j^2$ as a function of robot density for a fixed resource recovery time of ${\tau }_R=5$ time steps. (c) ${\tau }_{*}$ as a function of robot density and resource recovery rate $1/{\tau }_R$.