Abstract
Due to the flexible and robust features, recent advances emerging from computing intelligence in mechanical systems have led to many innovative techniques from signal processing to robotics. However, conventional designs of mechanical computing are typically manifested as deterministic functions with single-task layouts, which show limitations in versatility. This work proposes a versatile mechanical computing architecture, which can integrate both analog and logic operations into a unified robotic system. Inspired by Fourier optics, elastic wave metamaterials are introduced to spatial analog computing with robot crawling, enabling flexible spatiotemporal modulations and self-regulating locomotion. Using serial/parallel strategies, the metamaterial allows nested and cascaded designs from combinational analogs to the extended binary logics. In particular, by encoding analog signals as mechanical qubit-like states, the system can realize higher dimensional logic mappings through reprogrammable matrix operations. Beyond single-task layouts, nonlinear harmonics are also introduced to realize the parallel computing of multiple tasks or their transformation to specific tasks. The versatile strategies are shown to support the parallelism, integration and transformation from analogs to logics, which wish to offer an effective approach for incorporating mechanical intelligence in robotics.
Data availability
All data supporting the findings of this study are available within the Article and its Supplementary Information. Additional data generated in this study are available from the corresponding author on request.
References
Xue, H. R., Yang, Y. H. & Zhang, B. L. Topological acoustics. Nat. Rev. Mater. 7, 974–990 (2022).
Zheng, J. P. et al. Focusing micromechanical polaritons in topologically nontrivial hyperbolic metasurfaces. Adv. Mater. 36, 2311599 (2024).
Jang, Y., Kim, S., Lee, D., Kim, E. & Rho, J. Bound states to bands in the continuum in cylindrical granular crystals. Phys. Rev. Lett. 134, 136901 (2025).
Wang, A. X., Zhou, Y. & Chen, C. Q. Topological mechanics beyond wave dynamics. J. Mech. Phys. Solids 173, 105197 (2023).
Dong, E. Q. et al. Bioinspired metagel with broadband tunable impedance matching. Sci. Adv. 6, eabb3641 (2020).
Pyrialakos, G. G. et al. Bimorphic Floquet topological insulators. Nat. Mater. 21, 634–639 (2022).
Chen, Y. et al. Anomalous frozen evanescent phonons. Nat. Commun. 15, 8882 (2024).
Guzman, M., Guo, X. F., Coulais, C., Carpentier, D. & Bartolo, D. Model-free characterization of topological edge and corner states in mechanical networks. Proc. Natl. Acad. Sci. USA 121, e2305287121 (2024).
Lin, X. et al. A stair-building strategy for tailoring mechanical behavior of re-customizable metamaterials. Adv. Funct. Mater. 31, 2101808 (2021).
Lee, R. H., Mulder, E. A. B. & Hopkins, J. B. Mechanical neural networks: architected materials that learn behaviors. Sci. Robot. 7, eabq7278 (2022).
Mei, T. & Chen, C. Q. In-memory mechanical computing. Nat. Commun. 14, 5204 (2023).
Kwakernaak, L. J. & van Hecke, M. Counting and sequential information processing in mechanical metamaterials. Phys. Rev. Lett. 130, 268204 (2023).
Lin, X. et al. Mechanical Fourier transform for programmable metamaterials. Proc. Natl. Acad. Sci. USA 120, e2305380120 (2023).
He, Q. G., Ferracin, S. & Raney, J. R. Programmable responsive metamaterials for mechanical computing and robotics. Nat. Comput. Sci. 4, 567–573 (2024).
Mei, T., Zhou, Y. & Chen, C. Q. Mechanical neural networks with explicit and robust neurons. Adv. Sci. 11, 2310241 (2024).
Choe, J. K. et al. Digital mechanical metamaterial: encoding mechanical information with graphical stiffness pattern for adaptive soft machines. Adv. Mater. 36, 2304302 (2024).
Pu, H. Y. et al. Magnet-based mechanical logic gates with programmability and continuous operation capability in high-radiation environments. IEEE-ASME Trans. Mechatron. 30, 1–11 (2025).
Howard, D. et al. Evolving embodied intelligence from materials to machines. Nat. Mach. Intell. 1, 12–19 (2019).
Yue, T. Q. et al. Embodying soft robots with octopus-inspired hierarchical suction intelligence. Sci. Robot. 10, eadr4264 (2025).
Novelino, L. S., Ze, Q. J., Wu, S., Paulino, G. H. & Zhao, R. K. Untethered control of functional origami microrobots with distributed actuation. Proc. Natl. Acad. Sci. USA 117, 24096–24101 (2020).
Lee, W. K. et al. A buckling-sheet ring oscillator for electronics-free, multimodal locomotion. Sci. Robot. 7, eabg5812 (2022).
Wu, B. et al. Wave manipulation in intelligent metamaterials: recent progress and prospects. Adv. Funct. Mater. 34, 2316745 (2024).
Preston, D. J. et al. Digital logic for soft devices. Proc. Natl. Acad. Sci. USA 116, 7750–7759 (2019).
Zhang, Y. N., Deshmukh, A. & Wang, K. W. Embodying multifunctional mechano-intelligence in and through phononic metastructures harnessing physical reservoir computing. Adv. Sci. 10, 2305074 (2023).
Zhao, T. et al. Modular chiral origami metamaterials. Nature 640, 931–940 (2025).
Silva, A. et al. Performing mathematical operations with metamaterials. Science 343, 160–163 (2014).
Estakhri, N. M., Edwards, B. & Engheta, N. Inverse-designed metastructures that solve equations. Science 363, 1333–1338 (2019).
Zangeneh-Nejad, F., Sounas, D. L., Alu, A. & Fleury, R. Analogue computing with metamaterials. Nature Review. Materials 6, 207–225 (2021).
Li, Y. N. et al. Memristive field-programmable analog arrays for analog computing. Adv. Mater. 35, 2206648 (2023).
Tzarouchis, D. C., Mencagli, M., Edwards, B. & Engheta, N. Mathematical operations and equation solving with reconfigurable metadevices. Light-Sci. Appl. 11, 263 (2022).
Qiao, H. et al. Splitting phonons: building a platform for linear mechanical quantum computing. Science 380, 1030–1033 (2023).
Cavalluzzi, D., Ige, A. S., Runge, K. & Deymier, P. A. Realizing permutation gates with phi-bits: acoustic quantum analogue computing. J. Appl. Phys. 137, 104901 (2025).
Runge, K., Deymier, P. A., Hasan, M. A., Lata, T. D. & Levine, J. A. Acoustic metamaterials for realizing a scalable multiple phi-bit unitary transformation. AIP Adv. 14, 025010 (2024).
Hasan, M. A., Runge, K. & Deymier, P. A. Experimental classical entanglement in a 16 acoustic qubit-analogue. Sci. Rep. 11, 24248 (2021).
Kuruma, K. et al. Controlling interactions between high-frequency phonons and single quantum systems using phononic crystals. Nat. Phys. 21, 77–82 (2025).
Mei, T., Meng, Z. Q., Zhao, K. J. & Chen, C. Q. A mechanical metamaterial with reprogrammable logical functions. Nat. Commun. 12, 7234 (2021).
Byun, J., Pal, A., Ko, J. K. & Sitti, M. Integrated mechanical computing for autonomous soft machines. Nat. Commun. 15, 2933 (2024).
Mousa, M. & Nouh, M. Parallel mechanical computing: metamaterials that can multitask. Proc. Natl. Acad. Sci. USA 121, e2407431121 (2024).
Ze, Q. J. et al. Soft robotic origami crawler. Sci. Adv. 8, eabm7834 (2022).
Ze, Q. J. et al. Spinning-enabled wireless amphibious origami millirobot. Nat. Commun. 13, 3118 (2022).
Wang, D., Jiang, C. R. & Gu, G. Y. Modeling and design of lattice-reinforced pneumatic soft robots. IEEE Trans. Robot. 40, 606–623 (2024).
Shi, R., Fang, H. B. & Xu, J. Continuum modeling and dynamics of earthworm-like peristaltic locomotion. J. Mech. Phys. Solids 196, 106034 (2025).
Zhang, M. et al. Supercompact photonic quantum logic gate on a silicon chip. Phys. Rev. Lett. 126, 130501 (2021).
He, L. et al. Super-compact universal quantum logic gates with inverse-designed elements. Sci. Adv. 9, adg6685 (2023).
Hauser, H., Ijspeert, A. J., Füchslin, R. M., Pfeifer, R. & Maass, W. Towards a theoretical foundation for morphological computation with compliant bodies. Biol. Cybern. 105, 355–370 (2021).
Nanayakkara, T. et al.Handbook on Soft Robotics. Springer Nature, Switzerland. (2024).
Acknowledgements
The authors wish to express gratitude for the support provided by the National Natural Science Foundation of China (Grant Nos. 12425203 and 12021002 to Y.Z.W.).
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W.Z. performed the derivation and experiment. Y.Z.W. discussed about the results and developed the model, as well as presented the helpful suggestions about the underlying mechanism. Both authors contributed to the writing and editing of the manuscript.
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Nature Communications thanks Keith Runge, who co-reviewed with Araceli Hernandez Granados, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.
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Zhou, W., Wang, YZ. Reprogrammable metamaterial robot with embodied versatile computation and mechanical intelligence. Nat Commun (2026). https://doi.org/10.1038/s41467-026-71368-1
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DOI: https://doi.org/10.1038/s41467-026-71368-1
