Multimodal collective swimming of magnetically articulated modular nanocomposite robots

Magnetically responsive composites can impart maneuverability to miniaturized robots. However, collective actuation of these composite robots has rarely been achieved, although conducting cooperative tasks is a promising strategy for accomplishing difficult missions with a single robot. Here, we report multimodal collective swimming of ternary-nanocomposite-based magnetic robots capable of on-demand switching between rectilinear translational swimming and rotational swimming. The nanocomposite robots comprise a stiff yet lightweight carbon nanotube yarn (CNTY) framework surrounded by a magnetic polymer composite, which mimics the hierarchical architecture of musculoskeletal systems, yielding magnetically articulated multiple robots with an agile above-water swimmability (~180 body lengths per second) and modularity. The multiple robots with multimodal swimming facilitate the generation and regulation of vortices, enabling novel vortex-induced transportation of thousands of floating microparticles and heavy semi-submerged cargos. The controllable collective actuation of these biomimetic nanocomposite robots can lead to versatile robotic functions, including microplastic removal, microfluidic vortex control, and transportation of pharmaceuticals.


Supplementary Table 1. Dimensions, body lengths, body masses, and saturation magnetization (Ms) values of carbon nanotube yarn (CNTY)
robots. The vol.% notation refers to the concentration of iron particles dispersed in the PDMS prepolymer. Toothed whale (odontocete cetaceans) Underwater 4550 1. 4 11 Supplementary  19 GPa/SG) and 46.9 ± 4.5 N tex −1 , respectively (n= 10). SG denotes specific gravity, the density of the materials divided by the density of water. The bulk density of MWNT fiber was 2.6 g cm −3 .

Supplementary Fig. 3 Raman spectra (inset: polarized Raman spectra) of synthesized MWNT.
The intensity ratio of the D-band to G-band (ID/IG) in the Raman spectra, which states the crystallinity of MWNT, was approximately 0.43 ± 0.11 (n= 5). The G peak intensity ratio (IG∥/IG⊥) of the parallel direction to the perpendicular direction along to the CNTY axis in the polarized Raman spectrum, which states the orientation of MWNT, was 2.54 ± 0.77 (n= 5). For lightweight nanoporous structure, high densification was intentionally restrained in the MWNT fiber, confirmed by the crystallinity and orientation 24,25 . (c) Cargo placement process, confirmed by high-speed camera. When six 30 vol.% CNTY robots moved through assembled rotational swimming, they were able to push the cargo by elastic energy transfer. As a result, cargo delivery was successful. Although the CNTY robots disassembled, they instantaneously reassembled by magnetic attractive force among the robots and could swim through assembled rotational swimming. Since CNTY robots spontaneously assembled even after disassembly, location control of multiple CNTY robots was achieved with ease. By simply moving the CNTY robots away from the cargo before pushing the cargo again, all robots could be separated immediately from the cargo. The positioning and separating process of the cargo were implemented solely through manipulation of the motorized stage location without varying the magnetic frequency of the magnetic field.
Supplementary Fig. 30 Transportation of cargos with sliding resistance by above-water swimming and underwater swimming. Multiple 30 vol.% CNTY robots were manipulated by moving the electromagnetic coils coupled with the motorized stage having two degrees of freedom (2-DoF). (a) Transportation of semi-submerged cuboid cargo with a weight of 42 mg by above-water swimming of 19 CNTY robots. The increased number of CNTY robots resulted in a larger magnitude of vortex due to the larger hydrodynamic volume of the magnetic modular assembly. Therefore, the 19 CNTY robots with assembled rotational swimming transported cuboid cargo with sliding resistance. (b) Transportation of submerged asymmetric cargo with a weight of 39 mg by underwater swimming of two CNTY robots. The underwater swimming was proceeded after the robots were intentionally submerged in water. When the CNTY robots were pressed to the bottom of the water container, the robots sank immediately and remained submerged. When the sunken CNTY robots were relocated on the surface of water, they performed agile above-water swimming without submerging due to water's natural surface tension. The magnetic frequency was 8.3 Hz in (a) and (b).

Supplementary Note 1. Rheological and magnetization properties of ternary nanocomposite
The complex viscosities of the PDMS-iron-particle mixtures were measured using a parallel-plate rheometer (MCR302, Anton Paar) with a plate gap of 5 mm. The experiments were conducted at 23.8 °C and angular frequencies of 1-100 rad s -1 . The complex viscosity was calculated at an angular frequency of 3 rad s -1 .
At low angular frequencies, the storage and loss moduli show slopes of 2 and 1 against the shear rate, respectively, which is a typical rheological characteristic of Newtonian liquids (Supplementary Fig.   8-10). The complex viscosity of the PDMS prepolymer was measured to be 18 Pa·s at an angular frequency of 3 rad s −1 . When 1 and 2 vol.% magnetic particles were dispersed in the PDMS prepolymer, a magnetic composite layer did not appear owing to the insignificant difference in the values of complex viscosity compared to that of the PDMS prepolymer. The viscosity increased to 33, 90, and 371 Pa·s at iron particle loadings of 5, 10, and 20 vol.%, resulting in 10-, 14-, and 21-µm-thick magnetic composite layers on the CNTY after thermal curing, respectively; consequently, Ms was estimated to be 40, 69, and 118 emu g −1 , respectively ( Supplementary Fig. 11). Randomly distributed spherical particles typically exhibit rheological percolation thresholds between 20 and 30 vol.%. Predictably, the viscosity and coating thickness drastically increased to 897 Pa·s and 60 µm, respectively, at an iron particle loading of 30 vol.%, with an Ms of 152 emu g -1 being obtained after the polymerization. Compared to the Ms value of bulk iron particles (237 emu g −1 ), the large Ms of the composites prevented the aggregation of iron particles by the PDMS binder. In the case of the iron particle concentration of 40 vol.%, the highly viscous mixture of the prepolymer composite could not be drained because of its high complex viscosity (2,056 Pa·s), leading to non-uniform coating onto the CNTY surface. The iron particle concentration of 5 vol.% was excluded because of the inability of the resulting robot to swim.

Supplementary Note 2. Swimming mode analysis of a single robot
Rectilinear translational swimming and rotational swimming involve x-axis and y-axis coordinates, as expressed by the following equations representing the Lissajous-Bowditch curve: where ( ) and ( ) are functions of time ( ), denotes the phase difference, 0 and 0 are constants for the amplitude, and is the frequency of the trajectory. Each periodic wave, ( ), of the coordinates was fitted to a Fourier series, as follows: where the upper limit, n, was set to 3 in this study to account for the third harmonics, and and are constants. As shown in Supplementary Fig. 14