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Morphological flexibility in robotic systems through physical polygon meshing


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.

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Fig. 1: From virtual to physical polygon meshing: a shape-changing robotic system of polygon-based modules realizes articulated and functional 3D shapes.
Fig. 2: Recreating and manipulating virtual surfaces in true three dimensions using physical polygon meshing with user interaction.
Fig. 3: Different configurations of shape-changing polygon modules enable different types of locomotion and varying degrees of manoeuvrability.
Fig. 4: Object manipulation with a high-DoF robotic arm enabled by an RS-based CCD IK algorithm.

Data availability

All data generated during the experiments are available at42 or

Code availability

All code used during experiments and modelling efforts is available at the repository42 or


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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.

Author information

Authors and Affiliations



C.H.B. and J.P. conceptualized the research. C.H.B. and K.H. carried out research. C.H.B. and A.S. designed and built the robots. C.H.B., K.H. and A.S. implemented methodology and software. C.H.B. and K.H. conducted the experiments. C.H.B. wrote the manuscript, with feedback from all authors.

Corresponding authors

Correspondence to Christoph H. Belke or Jamie Paik.

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The authors declare no competing interests

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Peer review information

Nature Machine Intelligence thanks Rebecca Kramer-Bottiglio and Johannes Gerstmayr for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Mori3 mechanical and electronic design description and figures (Supplementary Figs. 1–3), Mori3 etymology.

Supplementary Video 1

A Mori3 module changes its own polygonal shape.

Supplementary Video 2

Two Mori3 modules automatically connect to each other.

Supplementary Video 3

A user manipulates a true-3D reconfigurable surface consisting of six Mori3 modules through a virtual interface.

Supplementary Video 4

A Mori3 module drives on a flat surface.

Supplementary Video 5

A loop consisting of ten Mori3 modules in the form of a continuous track demonstrates rolling locomotion.

Supplementary Video 6

A quadruped consisting of ten Mori3 modules stands up from a flat configuration and starts walking.

Supplementary Video 7

A quadruped consisting of ten Mori3 modules demonstrates walking locomotion using a static gait.

Supplementary Video 8

A robotic arm consisting of five Mori3 modules manipulates an object.

Algorithm S1

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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).

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