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. 2024 Jan 3;19(4):494–503. doi: 10.1038/s41565-023-01567-0

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© The Author(s) 2024, corrected publication 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 6 — a, Schematic snapshots of the micropenguin gait under an orientation-switching control strategy. The dark and transparent structures show the current and previous orientations of the micropenguin at a certain position, respectively. Yellow curved arrows indicate the magnetic torques (τ) that facilitate the flippers closing and opening. Red curved arrows indicate the micropenguin rotation. The magnetic torques under the magnetic actuation field (B_x) close the micropenguin flippers to generate a forward movement (phases 1–2 and 3–4) while the elastic torques under the magnetic base field (B_z) open the flippers for shape recovery (phases 2–3 and 4–1) after the micropenguin rotates 90° along the y axis. From phases 1–4, the micropenguin moves along the +x, −z, +x and +z directions sequentially. The base field (2 mT) is necessary to keep the micropenguin’s orientation. b, Stacked images of the micropenguin locomotion under the sequential magnetic field with a cycle duration of 5.5 s. c, Time-sequential images of the microturtle gait during one movement cycle. Red dashed lines indicate the starting position. Solid and hollow arrows show the respective magnetic field directions lasting till and starting from the current time points. The elastic potential energy stored in the z picosprings independently actuates the non-magnetic torso. The presence of the non-magnetic torso helps the microturtle to avoid undesired rotation of the whole body under the magnetic field. When the left/right picosprings actuate the microturtle forwards, the right/left picosprings buffer the rotation of the torso. When the magnetic fields cycle among 0°, 15°, −75° and −105° to the axial direction of the microturtle, the microturtle gains a net displacement by utilizing the phase difference between the rotations of its left and right flippers, owing to the programmed release of the stored energy in the picospring linkages. d, Locomotion sequence of the microturtle under a magnetic actuation field of 16 mT. The orange arrow indicates the locomotion direction. Scale bar, 20 μm.