Research ArticleCOLLECTIVE BEHAVIOR

A robot made of robots: Emergent transport and control of a smarticle ensemble

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Science Robotics  18 Sep 2019:
Vol. 4, Issue 34, eaax4316
DOI: 10.1126/scirobotics.aax4316
  • Fig. 1 Stochastic robotic collectives.

    Future robots may be composed of components whose delineation is neither clear nor deterministic, yet are capable of self-propulsion via the expression of ensemble-level behaviors leading to collective locomotion. In such a robot, groups of largely generic agents may be able to achieve complex goals, as routinely observed in biological collectives.

  • Fig. 2 Smarticle robot dynamics.

    (A) Top view schematic w = 5.3 cm and l = 4.9 cm. (B) Clockwise (CW) square gait, with key configurations enumerated. (C) Drift of a single smarticle on a flat surface, executing a square gait over 38τ. (D) Tracked trajectory of a smarticle within an ensemble of other self-deforming smarticles; color gradient (blue to red) represents passage of time 47τ, with τ = 1.6s.

  • Fig. 3 Smarticle cloud dynamics.

    (A) Snapshot of experimental trial, with the dashed line indicating the boundary of the convex hull area AC. The cloud’s CoM trajectory is illustrated in red, beginning at the black dot and ending at the red dot. Experiment ran for 113τ. (B) Center link trajectory of geometrically repulsive (top) and attractive interactions (bottom). (C) Evolution of φ averaged over 20 trials (black, with gray shaded region representing a single standard deviation); four individual trials are shown in blue, red, green, and brown lines. (D) 〈V2〉 averaged over 20 cloud trials. Raw data are in black; the blue line is moving mean with a window size of 1τ. Red line and area surrounding it represent mean value and single standard deviation of 〈V2〉 noise of an experiment lasting 10τ with seven moving, but non-interacting, smarticles. Here, gait period τ = 1.6 s.

  • Fig. 4 Collective confined diffusion.

    (A) Supersmarticle top view; ring inner radius is 9.6 cm. The four gray spheres were used to track the motion of the ring. (B) Granular temperature of five active smarticles confined in a ring; black line is raw data over 10 trials, and blue is a moving window mean with a window size of 1τ. (C) Trajectories, from an experiment, of a smarticle inside the ring (purple), and the ring’s center of geometry (blue). (D) Experimental tracks of ring trajectory for 50 trials; mring = 68 g. The black circle represents the size and initial position of the ring. (E) MSD averaged over 50 and 80 trials, for the active and inactive systems, respectively, all lasting 75τ. The inset shows the average change of γ for active (black) and inactive (blue) systems. The oscillation seen in both the MSD and γ is related to the gait period τ (where τ = 1.6 s).

  • Fig. 5 Biasing supersmarticle transport.

    (A) Supersmarticle schematic, with the inactive smarticle in red. (B) Supersmarticle trajectory frame transformation from laboratory to inactive smarticle frame. (C) Supersmarticle trajectories rotated into the laboratory frame, where axes are now the perpendicular and parallel components to the frame of the inactive particle.

  • Fig. 6 Statistical model of supersmarticle transport.

    (A) Schematic of the theoretical collision model. (B) Three regions with distinct collision types for the theory as described in the text. (C) Theoretical (red) and experimental (black and blue) data for velocity versus mass ratio M, showing mean and standard deviation. The blue data point is offset in M for visibility and represents an experiment where the inactive particle was endogenously chosen by light (see text) for 40 trials. (D) Distributions of drift speed probabilities for M regimes.

  • Fig. 7 Endogenous supersmarticle phototaxis.

    (A) Trajectory from an experiment of a self-directed (endogenously forced) photophilic supersmarticle tracking a static light source (movie S6). Inset: Schematic showing how a smarticle in the straight configuration can occlude light from smarticle behind it. (B) Map depicting when and which smarticles endogenously inactivate. (C) Lorenz plots detailing general equality of smarticle inactivity over a 25-min endogenous trial consisting of five separate excursions in different directions (see movie S6). Over the complete trial, we found G = 0.21, as shown in the bolded line. The unbolded lines are the Lorenz curves for the five separate excursions, where we found G = [0.28, 0.4, 0.42, 0.34, 0.49].

  • Fig. 8 Comparison between observed and numerically generated behavioral patterns.

    (A) Model shown is a graphical representation of a single inactive smarticle switching sequence observed in a phototactic experiment (such as Fig. 7A). We extracted graphical models using the DSS algorithm from the same experiment with and without candidate control information, shown in (C) and (B), respectively. (D) Simulated supersmarticle trajectories predict that the ensemble is capable of movement anywhere in the plane while receiving exogenous feedback from an external controller. (E) Experimental trajectory of a photophilic supersmarticle in which the system was exogenously steered through a maze by an experimenter (movie S7), validating the simulation’s predictions. The trajectory evolves in time from blue to red, and the black circles represent the initial and final ring configurations.

Supplementary Materials

  • robotics.sciencemag.org/cgi/content/full/4/34/eaax4316/DC1

    Text

    Fig. S1. Unrotated center of mass trajectory of the smarticle cloud.

    Fig. S2. Unrotated trajectories of the supersmarticle.

    Fig. S3. Theoretical and experimental data for the perpendicular component of the supersmarticle drift speed.

    Table S1. List of all six different types of collisions in the theoretical model.

    Table S2. List of all parameters used in the theoretical model.

    Algorithm S1. Dynamical system segmentation.

    Movie S1. Individual smarticle performing square gait.

    Movie S2. Smarticle cloud: Seven active smarticles.

    Movie S3. Supersmarticle: M = 0.51, five active smarticles.

    Movie S4. Supersmarticle: M = 0.51, one inactive, four active smarticles.

    Movie S5. Supersmarticle: M = 3.6, one inactive, four active smarticles.

    Movie S6. Supersmarticle: M = 3.6, endogenous phototaxing.

    Movie S7. Supersmarticle: M = 3.6, exogenous phototaxing.

  • Supplementary Materials

    The PDF file includes:

    • Text
    • Fig. S1. Unrotated center of mass trajectory of the smarticle cloud.
    • Fig. S2. Unrotated trajectories of the supersmarticle.
    • Fig. S3. Theoretical and experimental data for the perpendicular component of the supersmarticle drift speed.
    • Table S1. List of all six different types of collisions in the theoretical model.
    • Table S2. List of all parameters used in the theoretical model.
    • Algorithm S1. Dynamical system segmentation.

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Individual smarticle performing square gait.
    • Movie S2 (.mp4 format). Smarticle cloud: Seven active smarticles.
    • Movie S3 (.mp4 format). Supersmarticle: M = 0.51, five active smarticles.
    • Movie S4 (.mp4 format). Supersmarticle: M = 0.51, one inactive, four active smarticles.
    • Movie S5 (.mp4 format). Supersmarticle: M = 3.6, one inactive, four active smarticles.
    • Movie S6 (.mp4 format). Supersmarticle: M = 3.6, endogenous phototaxing.
    • Movie S7 (.mp4 format). Supersmarticle: M = 3.6, exogenous phototaxing.

    Files in this Data Supplement:

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