Programmable matter by folding
Open accessAbstract
Programmable matter is a material whose properties can be programmed to achieve specific shapes or stiffnesses upon command. This concept requires constituent elements to interact and rearrange intelligently in order to meet the goal. This paper considers achieving programmable sheets that can form themselves in different shapes autonomously by folding. Past approaches to creating transforming machines have been limited by the small feature sizes, the large number of components, and the associated complexity of communication among the units. We seek to mitigate these difficulties through the unique concept of self-folding origami with universal crease patterns. This approach exploits a single sheet composed of interconnected triangular sections. The sheet is able to fold into a set of predetermined shapes using embedded actuation. To implement this self-folding origami concept, we have developed a scalable end-to-end planning and fabrication process. Given a set of desired objects, the system computes an optimized design for a single sheet and multiple controllers to achieve each of the desired objects. The material, called programmable matter by folding, is an example of a system capable of achieving multiple shapes for multiple functions.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The proposal is conservative-it does not require specific directional information at hinges, temporal staging, or using nonflat sheets.
“Thus, our proposal is conservative—it does not require specific directional information at hinges6, temporal staging45, or using nonflat sheets37.”
From Shaping the topology of folding pathways in mechanical systems (2018) · cites this paper as [45]
Cited by
Sorted by citations
Flexible mechanical metamaterials
Bertoldi, K., Vitelli, V., Christensen, J., & van Hecke, M. (2017) · Nature Reviews Materials · doi:10.1038/natrevmats.2017.66 · Cited by 1,867 · see citing works
Using origami design principles to fold reprogrammable mechanical metamaterials
Silverberg, J. L., Evans, A. A., McLeod, L., Hayward, R. C., Hull, T., Santangelo, C. D., & Cohen, I. (2014) · Science · doi:10.1126/science.1252876 · Cited by 1,011 · see citing works
Reprogrammable recovery and actuation behaviour of shape-memory polymers
Lendlein, A., & Gould, O. E. C. (2019) · Nature Reviews Materials · doi:10.1038/s41578-018-0078-8 · Cited by 723 · see citing works
Active printed materials for complex self-evolving deformations
Raviv, D., Zhao, W., McKnelly, C., Papadopoulou, A., Kadambi, A., Shi, B., Hirsch, S., Dikovsky, D., Zyracki, M., Olguin, C., et al. (2014) · Scientific Reports · doi:10.1038/srep07422 · Cited by 568 · see citing works
Self-folding of polymer sheets using local light absorption
Liu, Y., Boyles, J. K., Genzer, J., & Dickey, M. D. (2012) · Soft Matter · doi:10.1039/c1sm06564e · Cited by 523 · see citing works
Reversible bidirectional shape-memory polymers
Behl, M., Kratz, K., Zotzmann, J., Nöchel, U., & Lendlein, A. (2013) · Advanced Materials · doi:10.1002/adma.201300880 · Cited by 496 · see citing works
Untethered soft robotic matter with passive control of shape morphing and propulsion
Kotikian, A., McMahan, C., Davidson, E. C., Muhammad, J. M., Weeks, R. D., Daraio, C., & Lewis, J. A. (2019) · Science Robotics · doi:10.1126/scirobotics.aax7044 · Cited by 476 · see citing works
Origami-inspired active structures: a synthesis and review
Peraza-Hernandez, E. A., Hartl, D. J., Malak Jr, R. J., & Lagoudas, D. C. (2014) · Smart Materials and Structures · doi:10.1088/0964-1726/23/9/094001 · Cited by 421 · see citing works
4D Printing Technology: A Review
Choi, J., Kwon, O.-C., Jo, W., Lee, H. J., & Moon, M.-W. (2015) · 3D Printing and Additive Manufacturing · doi:10.1089/3dp.2015.0039 · Cited by 365 · see citing works
Sequential self-folding of polymer sheets
Liu, Y., Shaw, B., Dickey, M. D., & Genzer, J. (2017) · Science Advances · doi:10.1126/sciadv.1602417 · Cited by 335 · see citing works
Self-folding with shape memory composites
Felton, S. M., Tolley, M. T., Shin, B., Onal, C. D., Demaine, E. D., Rus, D., & Wood, R. J. (2013) · Soft Matter · doi:10.1039/c3sm51003d · Cited by 269 · see citing works
Self-citationDesolvation Induced Origami of Photocurable Polymers by Digit Light Processing
Zhao, Z., Wu, J., Mu, X., Chen, H., Qi, H. J., & Fang, D. (2017) · Macromolecular Rapid Communications · doi:10.1002/marc.201600625 · Cited by 153 · see citing works
A Review on Origami Simulations: From Kinematics, To Mechanics, Toward Multiphysics
Zhu, Y., Schenk, M., & Filipov, E. T. (2022) · Applied Mechanics Reviews · doi:10.1115/1.4055031 · Cited by 137 · see citing works
Advanced Artificial Muscle for Flexible Material‐Based Reconfigurable Soft Robots
Jiao, Z., Zhang, C., Wang, W., Pan, M., Yang, H., & Zou, J. (2019) · Advanced Science · doi:10.1002/advs.201901371 · Cited by 135 · see citing works
Extreme Mechanics: Self-Folding Origami
Santangelo, C. D. (2017) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031016-025316 · Cited by 81 · see citing works
Self-Foldability of Rigid Origami
Tachi, T., & Hull, T. C. (2017) · Journal of Mechanisms and Robotics · doi:10.1115/1.4035558 · Cited by 66 · see citing works
Self-folding origami at any energy scale
Pinson, M. B., Stern, M., Carruthers Ferrero, A., Witten, T. A., Chen, E., & Murugan, A. (2017) · Nature Communications · doi:10.1038/ncomms15477 · Cited by 56 · see citing works
Shaping the topology of folding pathways in mechanical systems
Stern, M., Jayaram, V., & Murugan, A. (2018) · Nature Communications · doi:10.1038/s41467-018-06720-1 · Cited by 38 · see citing works
- Authors
- Hawkes, E., An, B., Benbernou, N. M., Tanaka, H., Kim, S., Demaine, E. D., Rus, D., & Wood, R. J.
- Affiliations
- Harvard University (US)
- Massachusetts Institute of Technology (US)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2010-06-28
- Volume
- 107
- Issue
- 28
- Pages
- 12441-12445
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC2906559
- OpenAlex
- W1980587781
- Cited by
- 658
- References
- 0
- Citations by year
- 2026: 17 · 2025: 35 · 2024: 25 · 2023: 33 · 2022: 59 · 2021: 47 · 2020: 45 · 2019: 47 · 2018: 57 · 2017: 63 · 2016: 48 · 2015: 46 · 2014: 52 · 2013: 37 · 2012: 20
- FWCI
- 50.53
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- Institutional Repositories DataBase (IRDB) (submittedVersion)
- Tokyo Tech Research Repository (Tokyo Institute of Technology) (submittedVersion)
- Topics
- Physical Sciences › Engineering › Mechanical Engineering › Modular Robots and Swarm Intelligence
- Physical Sciences › Engineering › Mechanical Engineering › Advanced Materials and Mechanics
- Physical Sciences › Engineering › Biomedical Engineering › Soft Robotics and Applications
- Keywords
- programmable matter
- MeSH terms
- Algorithms, Computer Simulation, Models, Theoretical, Robotics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review