Microstructural view of burrowing with a bioinspired digging robot

RoboClam is a burrowing technology inspired by Ensis directus, the Atlantic razor clam. Atlantic razor clams should only be strong enough to dig a few centimeters into the soil, yet they burrow to over 70 cm. The animal uses a clever trick to achieve this: by contracting its body, it agitates and locally fluidizes the soil, reducing the drag and energetic cost of burrowing. RoboClam technology, which is based on the digging mechanics of razor clams, may be valuable for subsea applications that could benefit from efficient burrowing, such as anchoring, mine detonation, and cable laying. We directly visualize the movement of soil grains during the contraction of RoboClam, using a novel index-matching technique along with particle tracking. We show that the size of the failure zone around contracting RoboClam can be theoretically predicted from the substrate and pore fluid properties, provided that the timescale of contraction is sufficiently large. We also show that the nonaffine motions of the grains are a small fraction of the motion within the fluidized zone, affirming the relevance of a continuum model for this system, even though the grain size is comparable to the size of RoboClam.

Figure 1

(a–f) Ensis directus digging cycle kinematics and energetics. White arrows indicate valve movements. Red silhouette denotes valve geometry in expanded state, before contraction. (a) Extension of foot at initiation of digging cycle. (b) Valve uplift. (c) Valve contraction, which pushes blood into the foot, expanding it to serve as a terminal anchor. (d) Retraction of foot and downwards pull on the valves. (e) Valve expansion, reset for next digging cycle. (f) Energetic cost to reach burrow depth for E. directus (red circles) and a blunt body of the same size and shape (blue squares) as the animal pushed into static soil.

Figure 2

The experimental setup. (a) The immersion fluid is fluorescent and index-matched to the granular material. A red laser sheet fluorescently excites a slice within the sample and so the camera captures that slice only. The slice recorded is the plane of motion of the end effector. Images are captured at 150 fps as the end effector is contracting. (b) A top view of the end effector's motion, illustrating the plane the camera is capturing. (c) A portion of an image taken. Due to the fluorescent dye within the fluid, the fluid is bright red within the images, and the grains are dark. Images are subjected to particle identification and tracking algorithms, which yield measurements of individual grain trajectories.

Figure 3

(a) An actual sample image (inverted) from an experiment. The blue arrows indicate the contraction motion of the end effector, also shown. The yellow box illustrates the area used for data analysis, to the right of the contracting end effector. (b) Particle tracks for this same experiment. Particles are identified and tracks are made by connecting particles between frames. The overlaid points are particle positions for a full contraction cycle, and the color indicates the relative time in the cycle. A streak of red-to-blue represents a unique particle track.

Figure 4

Details of the model. (a) Mohr's circles of stress states for equilibrium (a) and active failure (b). (b) Cylindrical model of soil failure around the contracting end effector. As RoboClam contracts it reduces the pressure acting between its body and the soil, $p_i$, below that of the equilibrium lateral soil pressure, $p_0$. This stress imbalance induces a localized failure zone around the animal. $R_0$ is RoboClam's expanded size, and $R_f$ is the size of the failure zone. (c) Predicted size of the failure zone around the end effector, using the full range of possible values for $K_0\in [0.31,1.0]$ and $K_a\in [0.19,0.52]$. The dashed yellow oval corresponds to the expectation for our experimental system.

Figure 5

Contour plots of the substrate's local speed for different contraction times, after the contraction. In all images the end effector is to the left of the image and is not shown. The shortest contraction times are on the left, and specifically: (a) $t_{\text{in}}=0.053$ s, (b) $t_{\text{in}}=0.153$ s, (c) $t_{\text{in}}=0.247$ s, (d) $t_{\text{in}}=0.295$ s, and (e) $t_{\text{in}}=0.378$ s. The color scale is the same in all plots, and scaled such that active regions moving displacing more than the cutoff distance $D$ are in white, and static regions are in black. The angle of the failure wedge is predicted by the green dashed line. The blue vertical solid line shows the prediction for the size of the fluidized zone, with the dashed blue lines representing the range of possible sizes.

Figure 6

Quantifying local fluidization. (a) Localized fluidization around the end effector. Each histogram corresponds to a different contraction time and depicts void fraction of the substrate as a function of distance from the end effector. The data are normalized with respect to the fluidization void fraction ${\varphi }_0=0.41$. The fluidization void fraction is marked by the black dashed line; fluidization corresponds to data above the line. The position of crossover to fluidization yields plot (b), the size of the fluidized zone, for different contraction times, normalized by the critical advection time. Error bars are smaller than the symbol size. The red vertical dashed line corresponds to the ratio of $t_{\text{in}}$ to the $t_{\text{crit}}$ equaling one. The shaded region bounded by horizontal dashed lines indicates the predicted range of $R_f/R_e$, with the solid horizontal line denoting the specific numerical prediction.