Building granular structures with elasto-active systems

Abstract

Natural active systems routinely reshape and reorganize their environments through sustained local interactions. Examples of decentralized collective construction are common in nature, e.g., many insects achieve large-scale constructions through indirect communication. While synthetic realizations of self-organization exist, they typically rely on rigid agents that require some kind of sensors and direct programming to achieve their function. Understanding how soft, deformable active matter navigates and remodels crowded landscapes remains an open challenge. Here we show that connecting rigid microbots to elastic beams yields elasto-active structures that can restructure and adapt to heterogeneous surroundings. We investigate the dynamics of these agents in environments with varying granular densities, rationalizing how they can aggregate or carve the medium through gentle interactions. At low density, the system compacts dispersed obstacles into clusters, a process modeled by a modified Smoluchowski coagulation theory. At high density, our agents carve voids whose size is predicted by a force-limited argument. These results establish a framework for understanding how activity, elasticity, and deformability can influence active navigation and environmental reconfiguration in granular media.

Figures (5)

• Figure 1: Elasto-active structure interacts with passive granular medium (a) Experimental snapshot showing the details of the elasto-active structure and the cylindrical particles. The structure consists of two active microbots connected via an elastic beam. The gray cylindrical particles are 3D printed, and the red stickers are used for tracking purposes. (b) At low solid fraction (density), the elasto-active structure pushes obstacles into clusters. At a high solid fraction (density), the structure carves a void within the medium.
• Figure 2: Coagulation dynamics in low-packed medium (a) Snapshots of the experiment with a density of obstacles $\phi \simeq 0.1$ and with a bucklebot with parameter$F\ell^2/B \simeq 380$. The dark blue circles denote isolated obstacles, and the green boundaries denote formed clusters. (b) The number of elements $N(t)$ (single obstacles and clusters) is plotted against time. The shaded area denotes the standard deviation within three trials. The dashed red line is the initial slope when taking the limit $n(t)\simeq n_0$ (See SI Eqn. \ref{['soln_coagulation1']}). The solid red line is the theory combining coagulation and fragmentation dynamics. (c) Plot of the coagulation timescale $\tau$ versus the effective gap parameter $\sqrt{A/N_0}-2r$. The markers are color-coded by area, while different shapes correspond to different types of obstacles. Error bars denote the standard deviation within 3 trials. Inset: definition of the effective gap parameter. (d) Rescaled time $\tau V\ell' /A$ versus rescaled gap. The markers are color-coded by the rescaled forces of the bucklebots. The black line is a linear fit of $y=kx$ with $k=1.93\pm0.06$, where the shaded band indicates the 95% confidence interval of the fit. Inset: a sketch of the bucklebot showing its equilibrium width $\ell'$ and velocity $V$.
• Figure 3: Fragmentation dynamics (a) Consecutive snapshots showing a bucklebot fragments a cluster into two separate clusters, highlighted by the red boundaries. (b) The number of coagulation(green) and fragmentation(red) events plotted against time. Each shaded area denotes the standard deviation within five trials. The slope of the fragmentation line gives the global fragmentation rate $r_f$. (c) Rescaled final element concentration $n_\infty/n_0$ versus the evolution parameter $K_1n_0/K_2$. The markers are color-coded by the rescaled forces of the bucklebots. The black line represents the prediction from the theory. The inset shows the value of the fragmentation time $1/r_f$ across all experiments. The black dashed line represents the mean.
• Figure 4: Bucklebot navigates in a densely-packed medium (a) Snapshots of the experiments with densigy $\phi \simeq 0.6$, carved by a bucklebot with rescaled force $F\ell^2/B \simeq 380$. The obstacles are color-coded by the number of contacts they share with their neighbors. (b) Histograms showing the obstacle distance to the boundary $R$ rescaled by their diameter $2r$. They are color-coded by the number of contacting neighbors (same code as (a)). The inset zooms on the area highlighted in (a), defining the Euclidean distance from the obstacle center to the boundary $R$. (c) We show the void area $A_v$ versus the density $\phi$. The two lines represent two predictions from our geometric model (blue, square lattice; red, hexagonal lattice). Insets: sketch of the corresponding lattices.
• Figure 5: Carving and writing in a densely-packed medium (a) Snapshots of the evolution of the space with $\phi \simeq 0.6$ where a few obstacles (red) are pre-removed and the bucklebot with $F\ell^2/B \simeq 380$ is then sent in. (b) The penetration length $L_p$ is plotted against time for cases with (red) and without (green) pre-removed obstacles. Each shaded area denotes the standard deviation within three trials. (c) Representative trajectories of the bucklebot carving in dense media. Multiple trajectories can be assembled to form the letters "P" and "U".