Shape-changing robots adapt their own morphology to address a wider range of functions or environments than is possible with a fixed or rigid structure. Akin to biological organisms, the ability to alter shape or configuration emerges from the underlying mechanical structure, materials or control methods. Soft robots, for instance, employ malleable materials to adapt to their environment, modular robots assemble multiple units into various three-dimensional configurations and insect-like swarm robots interact in large numbers to fulfil tasks. However, the promise of broad functional versatility in shape-changing robots has so far been constrained by the practical implications of either increasing the degree of morphological flexibility or addressing specific applications. Here we report a method for creating robotic systems that realizes both sides of this trade-off through the introduction of physical polygon meshing. By abstracting functional three-dimensional structures, collections of shape-changing robotic modules can recreate diverse three-dimensional shapes and dynamically control the resulting morphology. We demonstrate this approach by developing a system of polygon robots that change their own shape, attach to each other, communicate and reconfigure to form functional and articulated structures. Applying the system to three distinct application areas of robotics involving user interaction, locomotion and manipulation, our work demonstrates how physical polygon meshing provides a new framework for more versatile intelligent machines.
This is a preview of subscription content, access via your institution
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$119.00 per year
only $9.92 per issue
Rent or buy this article
Prices vary by article type
Prices may be subject to local taxes which are calculated during checkout
Alliez, P., Ucelli, G., Gotsman, C. & Attene, M. in Shape Analysis and Structuring (eds. De Floriani, L. & Spagnuolo, M.) 53–82 (Springer, 2008).
Landreneau, E. & Schaefer, S. Simplification of articulated meshes. Comput. Graph. Forum 28, 347–353 (2009).
Botsch, M., Kobbelt, L., Pauly, M., Alliez, P. & Levy, B. Polygon Mesh Processing (A K Peters/CRC Press, 2010).
Shah, D. et al. Shape changing robots: bioinspiration, simulation, and physical realization. Adv. Mater. 33, 1–12 (2021).
Rus, D. & Tolley, M. T. Design, fabrication and control of soft robots. Nature 521, 467–475 (2015).
Wehner, M. et al. An integrated design and fabrication strategy for entirely soft, autonomous robots. Nature 536, 451–455 (2016).
Billard, A. & Kragic, D. Trends and challenges in robot manipulation. Science. 364, eaat8414 (2019).
Bartlett, N. W. et al. A 3D-printed, functionally graded soft robot powered by combustion. Science. 349, 161–165 (2015).
Graule, M. A. et al. Perching and takeoff of a robotic insect on overhangs using switchable electrostatic adhesion. Science. 352, 978–982 (2016).
Chen, Y. et al. Controlled flight of a microrobot powered by soft artificial muscles. Nature 575, 324–329 (2019).
Rubenstein, M., Cornejo, A. & Nagpal, R. Programmable self-assembly in a thousand-robot swarm. Science. 345, 795–799 (2014).
Garattoni, L. & Birattari, M. Autonomous task sequencing in a robot swarm. Sci. Robot. 3, eaat0430 (2018).
Seo, J., Paik, J. & Yim, M. Modular reconfigurable robotics. Annu. Rev. Control Robot. Auton. Syst. 2, 63–88 (2019).
Hawkes, E. et al. Programmable matter by folding. Proc. Natl Acad. Sci. USA 107, 12441–12445 (2010).
Rus, D. & Tolley, M. T. Design, fabrication and control of origami robots. Nat. Rev. Mater. 3, 101–112 (2018).
Zhakypov, Z., Mori, K., Hosoda, K. & Paik, J. Designing minimal and scalable insect-inspired multi-locomotion millirobots. Nature 571, 381–386 (2019).
Li, S. et al. Particle robotics based on statistical mechanics of loosely coupled components. Nature 567, 361–365 (2019).
Swissler, P. & Rubenstein, M. FireAnt: a modular robot with full-body continuous docks. In Proc. 2018 IEEE International Conference on Robotics and Automation (ed.) 6812–6817 (IEEE, 2018).
Kriegman, S., Blackiston, D., Levin, M. & Bongard, J. A scalable pipeline for designing reconfigurable organisms. Proc. Natl Acad. Sci. USA 117, 1853–1859 (2020).
Støy, K. in Springer Handbook of Computational Intelligence (eds Kacprzyk, J. & Pedrycz, W.) 1407–1421 (Springer, 2015).
Romanishin, J. W., Gilpin, K., Claici, S. & Rus, D. 3D M-blocks: self-reconfiguring robots capable of locomotion via pivoting in three dimensions. In Proc. 2015 IEEE International Conference on Robotics and Automation (ed.) 1925–1932 (IEEE, 2015).
Nawroj, A. I. & Dollar, A. M. Shape control of compliant, articulated meshes: towards modular active-cell robots (MACROs). IEEE Robot. Autom. Lett. 2, 1878–1884 (2017).
Usevitch, N. S. et al. An untethered isoperimetric soft robot. Sci. Robot. 5, eaaz0492 (2020).
Lyder, A., Garcia, R. & Stoy, K. Mechanical design of Odin, an extendable heterogeneous deformable modular robot. In Proc. 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems (ed.) 883–888 (IEEE, 2008).
Benson, E. et al. DNA rendering of polyhedral meshes at the nanoscale. Nature 523, 441–444 (2015).
Tachi, T. Origamizing polyhedral surfaces. IEEE Trans. Vis. Comput. Graph. 16, 298–311 (2010).
Kim, W. et al. Bioinspired dual-morphing stretchable origami. Sci. Robot. 4, eaay3493 (2019).
Belke, C. H. & Paik, J. Mori: a modular origami robot. IEEE/ASME Trans. Mechatron. 22, 2153–2164 (2017).
Pieber, M., Neurauter, R. & Gerstmayr, J. An adaptive robot for building in-plane programmable structures. In Proc. 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (ed.) 1–9 (IEEE, 2018).
Chirikjian, G. & Pamecha, A. Bounds for self-reconfiguration of metamorphic robots. Proc. IEEE Int. Conf. Robot. Autom. 2, 1452–1457 (1996).
Booth, J. W. et al. OmniSkins: robotic skins that turn inanimate objects into multifunctional robots. Sci. Robot. 3, 1–10 (2018).
Belke, C. H. From Modular Origami Robots to Polygon-Based Modular Systems: a New Paradigm in Reconfigurable Robotics. PhD thesis, EPFL (2020).
Isenburg, M., Gumhold, S. & Gotsman, C. Connectivity shapes. In Proc. Visualization, 2001. (ed.) 135–552 (IEEE, 2001).
Belke, C. H. & Paik, J. Automatic couplings with mechanical overload protection for modular robots. IEEE/ASME Trans. Mechatron. 24, 1420–1426 (2019).
Leithinger, D., Follmer, S., Olwal, A. & Ishii, H. Shape displays: spatial interaction with dynamic physical form. IEEE Comput. Graph. Appl. 35, 5–11 (2015).
Everitt, A. & Alexander, J. 3D printed deformable surfaces for shape-changing displays. Front. Robot. AI 6, 1–13 (2019).
Spinos, A., Carroll, D., Kientz, T. & Yim, M. Topological reconfiguration planning for a variable topology truss. J. Mech. Robot. 13, 1–12 (2021).
Rosen, D. & Nguyen, A. Simulation methods for formable crust skins of digital clay human–computer interface devices. In Proc. 25th Computers and Information in Engineering Conference (ed.) vol. 3B, 1099–1109 (ASMEDC, 2005).
Felton, S., Tolley, M., Demaine, E., Rus, D. & Wood, R. A method for building self-folding machines. Science. 345, 644–646 (2014).
Nygaard, T. F., Martin, C. P., Torresen, J., Glette, K. & Howard, D. Real-world embodied AI through a morphologically adaptive quadruped robot. Nat. Mach. Intell. 3, 410–419 (2021).
Martín, A., Barrientos, A. & del Cerro, J. The natural-CCD algorithm, a novel method to solve the inverse kinematics of hyper-redundant and soft robots. Soft Robot. 5, 242–257 (2018).
Belke, C. H., Holdcroft, K., Sigrist, A. (2022). Mori3 code and data repository. Zenodo https://doi.org/10.5281/zenodo.7452297
We thank A. Thomas of the Atelier de l’Institut de production et robotique and M. Raton of the Atelier de l’institut de génie mécanique and their teams at École Polytechnique Fédérale de Lausanne for their outstanding work towards manufacturing the Mori3 robots. We also thank S. Bennani for his input towards applicability in space, and L. Noseda for his help in refining the coupling mechanism. Figure 1a image courtesy of Saab AB. This work was partly funded by European Space Agency grants NPI 645-2018 (to C.H.B. and J.P.) and NPI 646-2018 (to K.H. and J.P.), the Swiss National Center of Competence in Research (NCCR) Robotics and the École Polytechnique Fédérale de Lausanne Center for Intelligent Systems.
The authors declare no competing interests
Peer review information
Nature Machine Intelligence thanks Rebecca Kramer-Bottiglio and Johannes Gerstmayr for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Mori3 mechanical and electronic design description and figures (Supplementary Figs. 1–3), Mori3 etymology.
A Mori3 module changes its own polygonal shape.
Two Mori3 modules automatically connect to each other.
A user manipulates a true-3D reconfigurable surface consisting of six Mori3 modules through a virtual interface.
A Mori3 module drives on a flat surface.
A loop consisting of ten Mori3 modules in the form of a continuous track demonstrates rolling locomotion.
A quadruped consisting of ten Mori3 modules stands up from a flat configuration and starts walking.
A quadruped consisting of ten Mori3 modules demonstrates walking locomotion using a static gait.
A robotic arm consisting of five Mori3 modules manipulates an object.
About this article
Cite this article
Belke, C.H., Holdcroft, K., Sigrist, A. et al. Morphological flexibility in robotic systems through physical polygon meshing. Nat Mach Intell 5, 669–675 (2023). https://doi.org/10.1038/s42256-023-00676-8