Emergent functional dynamics of link-bots

Abstract

Synthetic active collectives, composed of many nonliving individuals capable of cooperative changes in group shape and dynamics, hold promise for practical applications and for the elucidation of guiding principles of natural collectives. However, the design of collective robotic systems that operate effectively without intelligence or complex control at either the individual or group level is challenging. We investigate how simple steric interaction constraints between active individuals produce a versatile active system with promising functionality. Here we introduce the link-bot: a V-shape-based, single-stranded chain composed of active bots whose dynamics are defined by its geometric link constraints, allowing it to possess scale- and processing-free programmable collective behaviors. A variety of emergent properties arise from this dynamic system, including locomotion, navigation, transportation, and competitive or cooperative interactions. Through the control of a few link parameters, link-bots show rich usefulness by performing a variety of divergent tasks, including traversing or obstructing narrow spaces, passing by or enclosing objects, and propelling loads in both forward and backward directions. The reconfigurable nature of the link-bot suggests that our approach may significantly contribute to the development of programmable soft robotic systems with minimal information and materials at any scale.

Figures (6)

• Figure 1: The structure and dynamics of a single bot and link-bot in experiments.(A) A single bot consists of (i) a cylindrical body on tilted legs and topped with a crest. The (ii) trajectory, (iii) speed profile, and (iv) diffusion plot of a single bot show characteristic active Brownian motion. (B) To construct a link-bot, rigid links connect $N$ bots together in a symmetric V-shape. The links have (i) length $L$, notch angle $\theta$, and spread angle $\alpha$, with two center links connecting the center bot at the V vertex and side links connecting all other bots that make up the side chains. In the neutral V-shape configuration (ii), all bot crests are aligned in the direction of motion. The link constraints allow two main modes of link-bot movement: breathing (shown by the green arrow) in which the central V angle opens and closes, and flapping (blue arrows) where the side chains bend inwards and outwards. (iii) Regardless of the initial configuration, the self-propelled link-bot relaxes into its neutral configuration (seen in the inset schematic) determined by the link properties. (C) Link-bots exhibit three gaits at a boundary, controlled by the link angles: translation (unidirectional motion, shown in blue), oscillation (changing directions by flipping along the wall, shown in green), and stationary (pushing against the wall without significant movement, shown in red). (ii) The changes in velocity for the three gaits. (iii) Phase diagram showing how the gaits change based on $\theta_\mathrm{c}$ and $\alpha_\mathrm{s}$.
• Figure 2: Link-bot structure and dynamics in the computational model.(A) The (i) trajectory, (ii) speed, and (iii) MSD of a single bot over 20 s is pictured, showing active Brownian motion matching that of the experiments. (B) Each self-propelled bot within a link-bot is modeled with translational and rotational constraints caused by the center and side links. This results in a noisy relaxation to the neutral configuration, where the bots form a V with all crests aligned, when the link-bot moves forward in space, regardless of the initial configuration. (C) (i) As in the experiments, the modeled link-bots exhibit three gaits at a wall: translation, oscillation, and stationary. (ii) The gaits are distinctive in their velocity patterns and (iii) show the same dependencies on $\theta_\mathrm{c}$ and $\alpha_\mathrm{s}$ at $\theta_\mathrm{s}=60^\circ$ as seen in experiments.
• Figure 3: Link-bots possess programmable locomotion in a variety of environments.(A) The trajectories of two identical link-bots through a wall with a gap of $b=3d$, showing that the alignment (yellow) or misalignment (blue) of the center bot with the gap plays an important role in determining whether the link-bot will pass through or remain stuck at the wall. (B) A link-bot traveling along a narrow channel with width $x=2d$. The speed and direction of the link-bot motion is controlled by the link angles. (C) Upon encountering two walls with a spacing of $z=4d$, link-bots with different side link angles either pass through the maze of walls (blue) or remain trapped at a wall (yellow). (D) The link angles of a link-bot control the distance it will travel along a curved surface. An obstacle with three curvatures ($r_1/d = 3.5, r_2/d = 2.8, r_3/d = 2$) can thus be used to sort link-bots of different properties. Shown here are link-bots with $\theta_\mathrm{c} = 20^\circ$, $\alpha_\mathrm{s} = 15^\circ$ (blue), $\theta_\mathrm{c} = 40^\circ$, $\alpha_\mathrm{s} = 30^\circ$ (yellow), and $\theta_\mathrm{c} = 20^\circ$, $\alpha_\mathrm{s} = 45^\circ$ with the left-most side link at 0 s inverted (purple).
• Figure 4: Link-bots perform selective transportation and dynamic social interactions. (A) By adjusting the link angles and number of bots within a link-bot, its transport behaviors can be controlled. Snapshots show the following behaviors of the simulated link-bot when it encounters a passive mobile object: pushing the object forwards, pulling the object backwards, passing without carrying the object, and wrapping/rotating around the object staying relatively stationary. The link-bot trajectory is shown in green, the object trajectory is brown. The last snapshot in each panel with a black background shows the analogous experimental results at the final time point, with the link-bot trajectory shown in red and the object trajectory in blue. In all cases the diameter of the object is $d_{\mathrm{obj}}=2.67d$. (B) Two interacting experimental link-bots, one with $N=15$, $\theta_\mathrm{c}=90^\circ$, $\alpha_\mathrm{s}=75^\circ$ (colored gray, with the center bot shown in yellow) and another with $N=7$, $\theta_\mathrm{c}=20^\circ$, $\alpha_\mathrm{s}=15^\circ$ (colored pink), show competitive and cooperative actions in traversing a wall with a gap. In both cases, the longer link-bot initially blocks a gap of $2.67d$ in the wall. (i) In the competitive situation, a link-bot approaching from the same side of the wall encounters the blocking link-bot and gets stuck so that neither link-bot is able to move. (ii) In the cooperative case, the blocking link-bot is moved by the smaller link-bot which approaches from the other side of the wall. This motion allows both link-bots to traverse the gap and pass through the wall in opposite directions.
• Figure 5: Schematic representation of the angles and vectors in the link-bot model. (A) Position and velocity vector of a single bot. Schematics of a partial link-bot showing the translational forces, $\mathbf{F}^{\mathrm{notch}}$, due to the links for (B) bots connected by center links and (C) bots connected by side links. Pictured here is a side chain to the left of the center bot, which is flapping outward. For the case where the side chain flaps inward, the results are mirrored. For both the center and side links, $\mathbf{F}^{\mathrm{notch}} > 0$ only when $\gamma_{i} > \gamma_{\mathrm{max}}$. The notches constrain bot rotation for (D) the center bot and (E) the side bots. In the neutral configuration (shown in the middle) the bots possess maximum rotational freedom, shown by a shaded orange region. When the bots are in their fully extended breathing and flapping modes (shown for both directions on either side) the bots have no rotational freedom.