Research ArticleCOLLECTIVE BEHAVIOR

From collections of independent, mindless robots to flexible, mobile, and directional superstructures

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Science Robotics  21 Jul 2021:
Vol. 6, Issue 56, eabd0272
DOI: 10.1126/scirobotics.abd0272
  • Fig. 1 Paper at a glance.

    The experiments use centimeter-sized robots enclosed in scaffolds For flexible scaffolds, the self-organization of the robots gives rise to a polar ordering of the individual robots and mobility of the structure. These superstructures can then go through constrictions, drag loads, move around obstacles, and carry out simple tasks such as cleaning an arena. Rudimentary control over the individual robots can lead to control over the self-organization and the mobility of the superstructure.

  • Fig. 2 Robot-filled scaffolds in straight channels.

    (A) Photographs of superstructures in straight channels of different widths H of 39 and 19 cm. Here, the diameter of the scaffold is D = 39 cm and the number of robots is N = 20 and N = 25 in the upper and lower images, respectively. The thickness e of the scaffold wall is 100 μm. (B) Trajectories of superstructures of D = 39 cm in channels of H = 39 cm with e = 100 μm for N = 15 and N = 30. (C) Angular momentum of the robot assembly L(t), normalized by RVB, where R = D/2 and VB is the mean velocity of the individual robots, and velocity of the superstructure normalized by VB versus number of robots, for H = 39 cm, D = 39 cm, and e = 100 μm. The embedded images show the state of organization of the robots with swirling motion at low N and high polar order near the boundary (the arrow indicates the total polarization P) at high N. For intermediate values of N, the state of organization is disordered with the appearance of small intermittent clusters. (D) Phase diagram for superstructures with scaffolds of thickness e = 100 μm. Number of robots above which no swirling motion is observed versus superstructure perimeter normalized by the length of a robot l. Below the indicated value of N, the robots undergo swirling motion along the boundary of the scaffold, whereas above this value, surface clusters pointing perpendicularly to the boundary start to form. The dashed line indicates full coverage of the circumference of the scaffold with robots parallel to its boundary. The band around the data points indicates the range of intermediate values of N values for which the state of organization is ill defined.

  • Fig. 3 Properties of superstructure mobility.

    Velocity VX versus polar order PX along the channel from experiments (A) for a number of robots N = 30, diameter D = 39 cm, and thickness e = 100 μm and simulations (B) for a number of robots N = 25 and diameter D = 39 cm. Insets, cross-correlation function C(VX, PX) of velocity and polar order. (C) Average rate of change of polar order <dPX/dt> versus polar order <PX>. The slope gives the correlation time τc. (D) Autocorrelation function C(PX, PX) of the polar order PX and an exponential fit. Both (C) and (D) are for the same conditions as (A) and (B).

  • Fig. 4 Transition across a constriction, a two-state geometry.

    (A and B) Photographs of a superstructure in a channel with two compartments separated by a constriction [(A) experiments and (B) simulations]. Note that the robots form a cluster that rotates and explores the superstructure walls to find the constriction entrance. Diameter D = 39 cm, length of the constriction L = 14 cm, thickness of the scaffold walls e = 100 μm (for experiments), number of robots N = 25, and width of the constriction H = 19 cm. (C and D) Superstructure center of mass versus time as it passes through the constriction. The shaded region represents the constriction (length L = 14 cm and width H = 19 cm), and the green dashed lines are the position of the center of mass of the superstructure when its walls touch the constriction. (E) Survival probability functions S(τ) of waiting times. (F) Mean waiting times <τ)> versus length of constriction L. (G) PDFs of waiting times τ. In (E) to (G), the solid lines are the results from the resolution of our model based on Eqs. 3 and 4.

  • Fig. 5 Superstructure trajectories and forces at play in the presence of a constriction.

    (A to D) Results from experiments. (E to H) Results from simulations. (A and E) Superstructure trajectories in velocity VX versus position x representation. (B and F) Map of mean polar order <PX> in the direction of motion in the same representation. (C and G) Mean of the difference <VX/μ − PX> between velocity and polar order. (D and H) Mean of the difference <dPX/dtPXc> in PX versus x representation. D = 39 cm, L = 14 cm, H = 19 cm, and N = 25. For experiments, e = 100 μm.The scale of the color maps, where red indicates high positive values and blue indicates high negative values, is displayed on the right.

  • Fig. 6 Guiding superstructures.

    (A) Photograph of the multichamber linear channel. From left to right, L = 30, 20, 10 , and 2 cm at fixed H = 15 cm, e = 100 μm, and D = 25 cm for N = 21. (B) Position of the superstructure in the multichamber channel in chamber number versus transition number representation for the same values of L as (A) but for N = 13, D = 23 cm, and H = 13 cm. Only a small sample is represented; the full time series is shown in fig. S8. (C) Transition probabilities from compartment k to k + 1 (green triangles) and from k to k − 1 (red triangles). (D) Transition probabilities from compartment 1 to k in k − 1 successive steps (green circles) and from compartment 5 to k in 5 − k successive steps (red circles). These are the probabilities to undergo directed paths from one end of the channel to the other. The red and green dashed lines with triangles are calculated using the independent probabilities of transition shown in (C).

  • Fig. 7 Pulling a load.

    Robot-filled scaffolds pull a load (circle with four immobile robots) through an obstacle course The obstacles are highlighted by black circles. D = 30 cm and N = 19.

  • Fig. 8 Cleaning an arena and light control.

    (A) Cleaning an arena: A robot-filled scaffold pushes empty circles out of the arena and into its open corners. In less than 40 s, two such circles have been evacuated. The diameter of the scaffold is 30 cm and is filled with 20 robots. (B) Light-controlled superstructure: When light is off, the robots are in the swirling state (in the counterclockwise direction) and the superstructure has little or no mobility. As the light is turned on (at 10 s), the robots acquire circular trajectories in the clockwise direction, triggering collisions and clustering in less than 2 s (at 12 s) leading to mobility of the superstructure; its crossing a constriction between two obstacles is highlighted in blue. D = 39 cm and N = 18.

  • Movie 1. Overview of the superstructure resulting from the self-organization of a collection of mobile simple robots.

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