Collective dynamics in entangled worm and robot blobs

Abstract

Living systems at all scales aggregate in large numbers for a variety of functions including mating, predation, and survival. The majority of such systems consist of unconnected individuals that collectively flock, school, or swarm. However, some aggregations involve physically entangled individuals, which can confer emergent mechanofunctional material properties to the collective. Here, we study in laboratory experiments and rationalize in theoretical and robophysical models the dynamics of physically entangled and motile self-assemblies of 1-cm-long California blackworms (Lumbriculus variegatus, Annelida: Clitellata: Lumbriculidae). Thousands of individual worms form braids with their long, slender, and flexible bodies to make a three-dimensional, soft, and shape-shifting "blob." The blob behaves as a living material capable of mitigating damage and assault from environmental stresses through dynamic shape transformations, including minimizing surface area for survival against desiccation and enabling transport (negative thermotaxis) from hazardous environments (like heat). We specifically focus on the locomotion of the blob to understand how an amorphous entangled ball of worms can break symmetry to move across a substrate. We hypothesize that the collective blob displays rudimentary differentiation of function across itself, which when combined with entanglement dynamics facilitates directed persistent blob locomotion. To test this, we develop a robophysical model of the worm blobs, which displays emergent locomotion in the collective without sophisticated control or programming of any individual robot. The emergent dynamics of the living functional blob and robophysical model can inform the design of additional classes of adaptive mechanofunctional living materials and emergent robotics.

Keywords: collective behavior; emergent mechanics; entangled active matter; organismal collective; swarming robot.

Fig. 1.

Worm blobs form via physical entanglements. (A) An entangled worm blob composed of $\sim$50,000 worms. (B) The worm blob behaves as a non-Newtonian fluid, which can flow at long timescales and maintain shape as a solid at short timescales (Movie S1). (C and D) Blob formation in water. The experiment starts in water at $\sim {\mathrm{30}}^{○}$C in which the worms are mainly untangled with each other. As the water cools down to 25 °C, the worms aggregate initially into two smaller blobs (t = 1 min), which ultimately merge to form one large blob (t = 20 min; Movie S1). (E) Close view of braid formation within a blob.

Fig. 2.

Water evaporation response of the worm blob. (A) When water is scarce, worms spontaneously form hemispherical blobs as a survival strategy to minimize evaporative losses. Shown is a time snapshot from the experiment (side view, N = 100 worms) for 450 min (Movie S2). The worms first undergo a stereotypical search mode for a water source and, after a certain time, spontaneously transition into a shrink mode to reduce surface area. (B) The shape changes of the worm blobs in the air as a function of blob size (N = 5, 10, 20, 100, 1,000). See Movie S2 for the example experiments with N = 1 and N = 1,000. (C) Projected surface area (A) as a function of cluster size (N = 1, 5, 10, 20 100, and 1,000 worms, 10 replicates per condition) under controlled laboratory conditions ($24{\hspace{1em}}^{○}$C, humidity $48\%$). The red star on the light blue curve indicates the time when the shrink mode starts. The worm blobs achieve a steady-state area (${\mathrm{A}}_s$) indicated by a plateau in the curve, where the change in surface area is minimal (${\mathrm{A}}_s$ = dA/dt $<1$%). (D) Comparison of experimental steady-state projected surface area (${\mathrm{A}}_s$) (black) with theoretical estimation of surface area (red) across three orders of magnitude of blob size (N) reveals good agreement between model and experiments. $V_w$ and $V_b$ are the total volume of N worms with a cylindrical body and the volume of a sphere shape worm blob, respectively. The final worm radius ($r_w$) is calculated from experimental measurements (SI Appendix, Fig. S7).

Fig. 3.

Worm blobs exhibit emergent locomotion under thermal gradients. (A) Schematic of the experimental setup to study worm blob locomotion under thermal gradients and different light conditions. The worm blob is placed ($N=600$ worms) into the center of a metal plate (30 × 20 × 5 cm³) filled with water. We establish thermal gradients on the surface of the plate by setting the temperature of the cold and the hot side to $\mathrm{15}{\hspace{1em}}^{○}$C and $\mathrm{50}{\hspace{1em}}^{○}$C, respectively (see SI Appendix, Fig. S8 for the details of the setup). Color bar represents the temperature of the water. (B) Time snapshots (t = 0, 7.5, 15, and 30 min) from the thermotaxis navigation experiments under room light (400 lux, Left) and spotlight (5,500 lux, Right). In both cases, the worms exhibit negative thermotaxis, but under low light conditions, they move individually, while under high light intensities, they move collectively as a blob. Dashed lines divide the plate into five equal areas for tracking movement of worms across the plate. For both experiments, overlap space–time heat maps of worm locomotion are shown in SI Appendix, Figs. S10 and S11. (C) During the same duration, by moving together as a blob, $>90\%$ of the worms make it to the colder side (zone 4), while moving individually $>70\%$ of the worms make it to the cold side (zone 5). Dashed lines (red, 5,500 lux; blue, 400 lux) show the time when the same amount of the worms ($70\%$) reach the cold sides in both experiments.

Fig. 4.

Mechanism of emergent locomotion of a worm blob through differentiation of activity. (A) Schematic of the experimental setup with enforced temperature gradient. The black dot shows the center of blob (CoB). (B) Snapshots from the quasi-2D experiment, where a small worm blob (N = 20) exhibits negative thermotaxis, crawling toward the cold side (Right) in response to a temperature gradient (Movie S4). (C) Proposed mechanism of how an entangled worm blob breaks symmetry to exhibit directed motion. The worm blob moves through differentiation of activity: Worms at the leading edge (blue) act as pullers, while worms at the trailing edge (red) curl up and lift the blob to potentially reduce friction. $\mathrm{\Delta }L$ is the contraction amount of leading worms and $\mathrm{\Delta }{\text{x}}_c$ is the forward displacement of a worm blob. (D) Correlation plot of changes in the length of the leading-edge puller worms, $\mathrm{\Delta }L=l\left({\text{t}}_f\right)-l\left({\text{t}}_i\right)$, and the blob’s forward position, $\mathrm{\Delta }{\text{x}}_c={\text{x}}_c\left({\text{t}}_f\right)-{\text{x}}_c\left({\text{t}}_i\right)$, where $t_i$ and $t_f$ represents the initial and final times of the peak forward movement (total 17 events from N = 3 trials). Color represents the maximum height of the blob (max ${\text{y}}_c$) during the forward displacement. (E) Horizontal displacement of the center of blob for N = 20 (dark and light purple) and N $>$ 300 (dark and light yellow) in response to thermal gradients. Red dots on the N = 20 case indicate where the pulling events begin (the events [1–7] and [8–12] are shown in D) (Movie S4). (F) Schematic of the experimental setup to measure pulling force of individual worms. The pegs are mounted on a plastic petri dish (100 × 15 mm) and the tail of the worm is glued to a force-calibrated elastic beam (SI Appendix, Fig. S13). By measuring the deflection of the beam by the worms, pulling force is estimated. (G) Illustration describing the observed behavior of worms during measurements at $\mathrm{20}{\hspace{1em}}^{○}$C (blue) and $\mathrm{30}{\hspace{1em}}^{○}$C (red) as shown in Movie S4. (H) Force measurements for single worms in cold ($\mathrm{20}{\hspace{1em}}^{○}$C, blue) and hot water ($\mathrm{30}{\hspace{1em}}^{○}$C, red). The black dots on the blue curve indicate the start time of successive pulling events by worms as seen in Movie S4. Inset shows the mean and standard deviation of the maximum pulling forces in cold (five trials) and hot water (three trials).

Fig. 5.

Robophysical model of a worm blob consisting of three-dimensional (3D) printed robots. (A) Each robot is a three-link, planar robot equipped with two photoresistors and the arms are connected to the body via servos controlled by Arduino Pro-Mini (38). (B) Motion sequences of two gaits as a function of arm angles (${\alpha }_1$ and ${\alpha }_2$), wiggle (Top), and crawl (Bottom). We define ${\alpha }_1>0$ when it is above the centerline and ${\alpha }_2>0$ when it is below the center line. The arrows show the direction of the arm movement sequence. Note that the wiggle gait does not lead to forward motion while the crawl does (to the left). For the binder robots, when they are rigid, the robots are powered and their arms are held at the centerline such that ${\alpha }_{\mathrm{1,2}}=0$, while for the flexible case, the robots are not powered and the arms are free to deform based on interactions with neighboring robots. (C) To enhance the physical entanglement of the robots, the arms are covered with a plastic mesh and L-shape pins are inserted to the edge of the arms. (D) Six robots entangle to form a robophysical model of the worm blob.

Fig. 6.

Collective locomotion of a physically entangled robotic blob. (A) Snapshots from the experiment where all of the robots are active and change their gaits from wiggling ($<200$ lux) to crawling ($>800$ lux) according to light intensity (Fig. 5B). At intermediate light intensity ($200\text{to}800$ lux) the robots kept their arms straight (rigid), i.e., ${\alpha }_1={\alpha }_2=0$ (Movie S5). (B) The robots with red dots are inactive (unpowered) and their arms can move flexibly to enable them to act as binders for the robotic blob. The remaining robots changed their gaits according to light intensity thresholds described previously (Fig. 5B and Movie S5). (C) Space–time overlap heatmaps of robot positions (x axis), revealing collective motion in the flexible case. Color represents the normalized density of the robots. (D) Mean displacement of the individual robots in a run for the flexible (n = 17 trials) and rigid (n = 11) cases. (E) Distribution of the vertical arm position $\mathrm{\Delta }y=$ y(t) − y(0) with respect to initial arm position of the robots in a blob for four different gaits (blue, all crawl; orange, half crawl; yellow, rigid; purple, flexible). Each dataset has 10,000 data points randomly chosen from two to five experiments. Inset shows schematic illustration of $\mathrm{\Delta }y$ measurement. (F) Mean displacement of all of the robots per cycle in a run for the all crawl (n = 6 trials), semicrawl (n = 15 trials), flexible (n = 17 trials), and rigid (n = 11) cases (see Table 1 for the details). The activity level is defined as how much the robots move their arms on a vertical plane.