Kirigami Makes a Soft Magnetic Sheet Crawl

Abstract Limbless crawling on land requires breaking symmetry of the friction with the ground and exploiting an actuation mechanism to generate propulsive forces. Here, kirigami cuts are introduced into a soft magnetic sheet that allow to achieve effective crawling of untethered soft robots upon application of a rotating magnetic field. Bidirectional locomotion is achieved under clockwise and counterclockwise rotating magnetic fields with distinct locomotion patterns and crawling speed in forward and backward propulsions. The crawling and deformation profiles of the robot are experimentally characterized and combined with detailed multiphysics numerical simulations to extract locomotion mechanisms in both directions. It is shown that by changing the shape of the cuts and orientation of the magnet the robot can be steered, and if combined with translational motion of the magnet, complex crawling paths are programed. The proposed magnetic kirigami robot offers a simple approach to developing untethered soft robots with programmable motion.


Effect of varying the geometrical parameters of kirigami on maximum achievable velocity
We experimentally characterized the effect of varying geometrical parameters of magnetic kirigami sheets on the maximum achievable velocity of the robot compared to a reference design with  = 14 mm,  = 45 mm,  = 7.5 mm, and  = 3.5 mm.Three considered cases are: • Small foot: by decreasing the length of the base cut by 20%.
• Big foot: by increasing the length of the base cut by 20%.
• Small leaf: by downscaling the size of the leaf by 20%.The maximum velocity of the robot decreased in all considered cases compared to the reference design as shown in Figure S1.

Comparing the locomotion mechanisms under CCW and CW actuation
Our analyses suggest that the speed difference is attributed to how the foot deforms, anchors to the ground, and relaxes.We note that under CCW actuation, the locomotion happens while the foot is under compression by friction force, and only the last stages of the bending of the foot contribute to crawling.On the other hand, under CW actuation, the foot is under tension, and the full extent of the relaxation of the deformed foot contributes to propulsion.Hence, the CW actuation is faster than CCW.We illustrated the difference between crawling behavior under CW and CCW actuation in Fig. S3.

Distribution of magnetic particles in the silicone matrix
The distribution of the magnetic particles within the silicone matrix is very homogeneous as shown in Fig. S4.Optical microscopy and SEM images of the prepared composite material with an equivalent mass fraction show the oriented magnetic particles dispersed uniformly within the matrix.

Effect of frequency of rotating magnetic field on robot's velocity
We experimentally analyzed the correlation between crawling speed and rotation frequency of the magnetic field within the operational limits of our experimental setup.This investigation focused on a sample featuring 3 × 3 U-cuts, but we anticipate that this relationship also holds for other designs.Our examination involved progressively increasing the frequency of a clockwise rotating magnetic field from 1.6 Hz to 4.2 Hz.However, excessive vibrations in our setup hindered accurate assessment of the robot's locomotion at frequencies beyond this range.
Our findings revealed that as the frequency of the rotating magnetic field increased, the robot's crawling speed also accelerated.Nevertheless, we anticipate that the inertial effect will prevail beyond a critical frequency, causing a sharp decline in speed as the robot's leaf cannot effectively follow the magnetic field.Fig. S5A and S5B, respectively, show the evolution of the robot's velocity with the walking distance and the maximum velocity as a function of the frequency of the rotating magnetic field.In Fig S5A, we observe that the robot speed increases as the robot crawls over the magnet and declines when it takes distance from it due to a weaker magnetic field.In Fig. S5B, we notice that the gain in the speed by increasing the frequency is at a lower rate for higher frequencies.

Figure S1 .
Figure S1.Effect of varying the size of the foot and the leaf on maximum velocity (n=3) of the robot compared to a reference design with  = 14 mm,  = 45 mm,  = 7.5 mm, and  = 3.5 mm.

Figure S2 .
Figure S2.Evolution of the foot angle   of kirigami magnetic robots for different values of hinge width  under CCW and CW magnetic actuation.Snapshots of the deformation of the kirigami magnetic robots at selected angles   of the rotating magnetic field.

Figure S3 .
Figure S3.Comparison between the mechanisms of locomotion under CCW and CW magnetic fields.

Figure S4 .
Figure S4.(A) optical microscopy and (B) scanning electron microscopy (SEM) images through the thickness of a composite prepared with Strontium Ferrite magnetic particles.

Figure S5 .
Figure S5.(A)Evolution of the robot's velocity with crawling distance, and (B) maximum velocity for different frequencies of the rotating magnetic field.The experiments were performed for a magnetic kirigami robot with 3 × 3 U-cuts.In this frequency range, the speed increases with increasing frequency.We could not go beyond 4.2 Hz due to the limitations of the setup.