Fig. 6: Magnetic gradient-assisted collective navigation through confined environments and contact-based object transport.

a Locomotion speed comparison for the rotation (blue), static (red), oscillation (green), and chain (black) modes with N = 126 micro-disks driven at different frequencies when the gradient is F = 0.7 Gauss/mm. The chains move faster than other modes. The error bars represent standard deviations over 5 s. b Displacement of each mode over time when at \({\Omega }_{y}=30\) Hz. The chains move faster and get slowed down due to the physical boundary around 2.5 s. This contributes to large standard deviations in chain speed in (a). c Representative images showing the trajectories of static (left), oscillating (middle left), rotating (middle right), and chain (right) collectives under the influence of a magnetic field gradient along the y axis. d Y chain of seven micro-disks driven with magnetic field gradients to produce MPI and C trajectories (Supplementary Movie 7). e 17 micro-disks transition between different modes to navigate through narrow passages (Supplementary Movie 8). (f) The collective switches between the modes static, X chains, and Y chains to locomote and push an object. The brightness of the images in (c–f) is enhanced using photoshop for better visualization. The symbols on the sub-images at the bottom, in (c), and top, in (e, f), represent the mode the collective exhibits. These symbols correspond to those shown in Fig. 1a. The sub-images in (f) are labeled at the bottom with the function that the collective performs.