{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T10:59:30Z","timestamp":1776250770280,"version":"3.50.1"},"reference-count":37,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2011,1,14]],"date-time":"2011-01-14T00:00:00Z","timestamp":1294963200000},"content-version":"unspecified","delay-in-days":13,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>This paper considers planning and control algorithms that enable a programmable sheet to realize different shapes by autonomous folding. Prior work on self-reconfiguring machines has considered modular systems in which independent units coordinate with their neighbors to realize a desired shape. A key limitation in these prior systems is the typically many operations to make and break connections with neighbors, which lead to brittle performance. We seek to mitigate these difficulties through the unique concept of self-folding origami with a universal fixed set of hinges. 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.<\/jats:p><jats:p>We describe the planning algorithms underlying these self-folding sheets, forming a new family of reconfigurable robots that fold themselves into origami by actuating edges to fold by desired angles at desired times. Given a flat sheet, the set of hinges, and a desired folded state for the sheet, the algorithms (1) plan a continuous folding motion into the desired state, (2) discretize this motion into a practicable sequence of phases, (3) overlay these patterns and factor the steps into a minimum set of groups, and (4) automatically plan the location of actuators and threads on the sheet for implementing the shape-formation control.<\/jats:p>","DOI":"10.1017\/s0263574710000731","type":"journal-article","created":{"date-parts":[[2011,1,14]],"date-time":"2011-01-14T15:37:39Z","timestamp":1295019459000},"page":"87-102","source":"Crossref","is-referenced-by-count":31,"title":["Planning to fold multiple objects from a single self-folding sheet"],"prefix":"10.1017","volume":"29","author":[{"given":"Byoungkwon","family":"An","sequence":"first","affiliation":[]},{"given":"Nadia","family":"Benbernou","sequence":"additional","affiliation":[]},{"given":"Erik D.","family":"Demaine","sequence":"additional","affiliation":[]},{"given":"Daniela","family":"Rus","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2011,1,14]]},"reference":[{"key":"S0263574710000731_ref34","unstructured":"34. Tachi T. , \u201cSimulation of Rigid Origami,\u201d Origami4: Proceedings of the 4th International Meeting of Origami Science, Math and Education (2009), pp. 175\u2013187."},{"key":"S0263574710000731_ref29","doi-asserted-by":"publisher","DOI":"10.1201\/b15735-24"},{"key":"S0263574710000731_ref25","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1109\/70.864227","article-title":"Folding cartons with fixtures: A motion planning approach","volume":"16","author":"Lu","year":"2000","journal-title":"IEEE Trans. Robot. Autom."},{"key":"S0263574710000731_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.tifs.2009.10.007"},{"key":"S0263574710000731_ref20","doi-asserted-by":"publisher","DOI":"10.1177\/0278364907085557"},{"key":"S0263574710000731_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(79)90002-4"},{"key":"S0263574710000731_ref3","doi-asserted-by":"crossref","unstructured":"3. Balkcom D. , Robotic Origami Folding PhD Thesis (Pittsburgh, PA: Robotics Institute, Carnegie Mellon University, Aug. 2004).","DOI":"10.1109\/ROBOT.2004.1308754"},{"key":"S0263574710000731_ref33","unstructured":"33. Belcastro S.-M. and Hull T. C. , \u201cA Mathematical Model for Non-Flat Origami,\u201d Origami3: Proceedings of the 3rd International Meeting of Origami Mathematics, Science and Education (2002) pp. 39\u201351."},{"key":"S0263574710000731_ref17","doi-asserted-by":"publisher","DOI":"10.1109\/M-RA.2007.908971"},{"key":"S0263574710000731_ref36","doi-asserted-by":"crossref","unstructured":"36. Yim M. , Shen W-M. , Salemi B. , Rus D. , Lipson H. , Klavins E. and Chirikjian G. , \u201cModular self-reconfiguring robot systems: Opportunities and challenges,\u201d IEEE\/ASME Trans. Mechatronics (2006).","DOI":"10.1109\/MRA.2007.339623"},{"key":"S0263574710000731_ref28","unstructured":"28. Nagpal R. , Programmable Self-assembly: Constructing Global Shape Using Biologically-Inspired Local Interactions and Origami Mathematics PhD Thesis (Massachusetts Institute of Technology, 2001)."},{"key":"S0263574710000731_ref8","doi-asserted-by":"publisher","DOI":"10.1177\/0278364908090235"},{"key":"S0263574710000731_ref23","volume-title":"Robotics: Science and Systems","author":"Klavins","year":"2006"},{"key":"S0263574710000731_ref7","unstructured":"7. Balkcom D. J. and Mason M. T. , \u201cIntroducing Robotic Origami Folding,\u201d IEEE International Conference on Robotics and Automation (2004), pp. 3245\u20133250."},{"key":"S0263574710000731_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0515-9"},{"key":"S0263574710000731_ref9","doi-asserted-by":"publisher","DOI":"10.1177\/02783649030229002"},{"key":"S0263574710000731_ref21","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0914069107"},{"key":"S0263574710000731_ref6","doi-asserted-by":"publisher","DOI":"10.1177\/0278364904044409"},{"key":"S0263574710000731_ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2002.806230"},{"key":"S0263574710000731_ref26","doi-asserted-by":"crossref","first-page":"974","DOI":"10.1038\/35023115","article-title":"Automatic design and manufacture of robotic lifeforms","volume":"406","author":"Lipson","year":"2000","journal-title":"Nature"},{"key":"S0263574710000731_ref37","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026544419097"},{"key":"S0263574710000731_ref27","first-page":"2210","volume-title":"Proceedings of the International Conference on Intelligent Robots and Systems","author":"Murata","year":"2000"},{"key":"S0263574710000731_ref10","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026552720914"},{"key":"S0263574710000731_ref4","doi-asserted-by":"crossref","unstructured":"4. Benbernou N. , Demaine E. D. , Demaine M. L. and Ovadya A. , \u201cA universal crease pattern for folding orthogonal shapes,\u201d arXiv:0909.5388 (Sep. 2009). http:\/\/arXiv.org\/abs\/0909.5388.","DOI":"10.21236\/ADA524705"},{"key":"S0263574710000731_ref14","first-page":"64","volume-title":"Proceedings of the 16th Canadian Conference on Computational Geometry","author":"Demaine","year":"2004"},{"key":"S0263574710000731_ref24","doi-asserted-by":"publisher","DOI":"10.1109\/70.508439"},{"key":"S0263574710000731_ref30","doi-asserted-by":"publisher","DOI":"10.1109\/70.611311"},{"key":"S0263574710000731_ref11","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1145\/997817.997840","volume-title":"Proceedings of the 20th Annual ACM Symposium on Computational Geometry","author":"Cantarella","year":"2004"},{"key":"S0263574710000731_ref35","unstructured":"35. Varshavskaya P. , Kaelbling L. P. and Rus D. , \u201cAutomated design of adaptive controllers for modular robots using reinforcement learning,\u201d Int. J. Robot. Res. Special Issue on Self-Reconfigurable Modular Robots (2007)."},{"key":"S0263574710000731_ref32","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-006-6475-7"},{"key":"S0263574710000731_ref16","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511735172"},{"key":"S0263574710000731_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(00)00023-0"},{"key":"S0263574710000731_ref1","first-page":"3149","volume-title":"Proceedings of the IEEE International Conference on Robotics and Automation","author":"An","year":"2008"},{"key":"S0263574710000731_ref22","first-page":"2888","volume-title":"Proceedings of the IEEE International Conference on Robotics and Automation","author":"White","year":"2004"},{"key":"S0263574710000731_ref18","unstructured":"18. 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