Hostname: page-component-594f858ff7-x2rdm Total loading time: 0 Render date: 2023-06-07T00:35:29.142Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": false, "coreDisableEcommerce": false, "corePageComponentUseShareaholicInsteadOfAddThis": true, "coreDisableSocialShare": false, "useRatesEcommerce": true } hasContentIssue false

Planning to fold multiple objects from a single self-folding sheet

Published online by Cambridge University Press:  14 January 2011

Byoungkwon An
Affiliation:
MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA 02139, USA
Nadia Benbernou
Affiliation:
MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA 02139, USA
Erik D. Demaine*
Affiliation:
MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA 02139, USA
Daniela Rus
Affiliation:
MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA 02139, USA
*
*Corresponding author. E-mail: edemaine@mit.edu

Summary

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.

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.

Type
Article
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.An, B., “Em-Cube: Cube-Shaped, Self-Reconfigurable Robots Sliding on Structure Surfaces,” Proceedings of the IEEE International Conference on Robotics and Automation, New York (May 2008) pp. 31493155.Google Scholar
2.Aspvall, B., Plass, M. F. and Tarjan, R. E., “A linear-time algorithm for testing the truth of certain quantified boolean formulas,” Inf. Process. Lett. 8 (3), 121123 (1979).CrossRefGoogle Scholar
3.Balkcom, D., Robotic Origami Folding PhD Thesis (Pittsburgh, PA: Robotics Institute, Carnegie Mellon University, Aug. 2004).Google Scholar
4.Benbernou, N., Demaine, E. D., Demaine, M. L. and Ovadya, A., “A universal crease pattern for folding orthogonal shapes,” arXiv:0909.5388 (Sep. 2009). http://arXiv.org/abs/0909.5388.Google Scholar
5.Butler, Z., Fitch, R. and Rus, D., “Distributed control for unit-compressible robots: Goal-recogition, locomotion and splitting,” IEEE/ASME Trans. Mechatronics 7 (4), 418–30 (2002).CrossRefGoogle Scholar
6.Butler, Z., Kotay, K., Rus, D. and Tomita, K., “Generic decentralized control for lattice-based self-reconfigurable robots,” Int. J. Robot. Res. 23 (9), 919937 (2004).CrossRefGoogle Scholar
7.Balkcom, D. J. and Mason, M. T., “Introducing Robotic Origami Folding,” IEEE International Conference on Robotics and Automation (2004), pp. 3245–3250.Google Scholar
8.Balkcom, D. and Mason, M., “Robotic origami folding,” Int. J. Robot. Res. 27 (5), 613627 (May 2008).CrossRefGoogle Scholar
9.Butler, Z. J. and Rus, D., “Distributed planning and control for modular robots with unit-compressible modules,” Int. J. Robot. Res. 22 (9), 699716 (2003).CrossRefGoogle Scholar
10.Chiang, C.-H. and Chirikjian, G., “Modular robot motion planning using similarity metrics,” Auton. Robots 10 (1), 91106 (2001).CrossRefGoogle Scholar
11.Cantarella, J. H., Demaine, E. D., Iben, H. N. and O'Brien, J. F., “An Energy-Driven Approach to Linkage Unfolding,” Proceedings of the 20th Annual ACM Symposium on Computational Geometry Brooklyn, New York (June 2004) pp. 134143.Google Scholar
12.Díaz-Báñez, J. M. and Mesa, J. A., “Fitting rectilinear polygonal curves to a set of points in the plane,” Eur. J. Oper. Res. 130 (1), 214222 (2001).CrossRefGoogle Scholar
13.Dai, J. S. and Caldwell, D. G., “Origami-based robotic paper-and-board packaging for food industry,” Trends Food Sci. Technol. 21 (3), 153157 (2010).CrossRefGoogle Scholar
14.Demaine, E. D., Devadoss, S. L., Mitchell, J. S. B. and O'Rourke, J., “Continuous Foldability of Polygonal Paper,” Proceedings of the 16th Canadian Conference on Computational Geometry Montréal, Canada (Aug. 2004), pp. 6467.Google Scholar
15.Downey, R. G. and Fellows, M. R., Parameterized Complexity (Springer-Verlag, New York 1999).CrossRefGoogle Scholar
16.Demaine, E. D. and O'Rourke, J., Geometric Folding Algorithms: Linkages, Origami, Polyhedra, (Cambridge University Press, Cambridge, July 2007).CrossRefGoogle Scholar
17.Detweiler, C., Vona, M., Yoon, Y., Yun, S. and Rus, D., “Self-assembling mobile linkages with active and passive modules,” IEEE Robot. Autom. Mag. 14 (4), 4555 (2007).CrossRefGoogle Scholar
18.Fukuda, T. and Kawakuchi, Y., “Cellular robotic system (CEBOT) as one of the realization of self-organizing intelligent universal manipulator,” Proceedings of IEEE International Conference on Robotics and Automation (1990) pp. 662–667.Google Scholar
19.Gilpin, K., Kotay, K., Rus, D. and Vasilescu, I., “Miche: Modular shape formation by self-disassembly,” Int. J. Robot. Res. 27 (3–4), 345372 (2008).CrossRefGoogle Scholar
20.Gilpin, K., Kotay, K., Rus, D. and Vasilescu, I., “Miche: Self-assembly by self-disassembly,” Int. J. Robot. Res. 27 (3–4), 345372 (2008).CrossRefGoogle Scholar
21.Hawkes, E., An, B. K., Benbernou, N. M., Tanaka, H., Kim, S., Demaine, E. D., Rus, D. and Wood, R. J., “Programmable matter by folding,” Proc. Natl. Acad. Sci. U. S. A. 107 (28), 1244112445 (2010).CrossRefGoogle ScholarPubMed
22.White, P. J., Kopanski, K. and Lipson, H., “Stochastic self-reconfigurable cellular robotics,” Proceedings of the IEEE International Conference on Robotics and Automation, New Orleans, LA (May 2004) pp. 28882893.Google Scholar
23.Klavins, E., Burden, S. and Napp, N., “Optimal rules for programmed stochastic self-assembly,” Robotics: Science and Systems, Philadelphia, PA (2006).Google Scholar
24.Kavraki, L. E., Svestka, P., Latombe, J.-C. and Overmars, M. H., “Probabilistic roadmaps for path planning in high-dimensional configuration spaces,” IEEE Trans. Robot. Autom. 12 (4), 566580 (1996).CrossRefGoogle Scholar
25.Lu, L. and Akella, S., “Folding cartons with fixtures: A motion planning approach,” IEEE Trans. Robot. Autom. 16 (4), 346356 (2000).Google Scholar
26.Lipson, H. and Pollack, J., “Automatic design and manufacture of robotic lifeforms,” Nature 406, 974978 (2000).Google ScholarPubMed
27.Murata, S., Yoshida, E., Tomita, K., Kurokawa, H., Kamimura, A. and Kokaji, S., “Hardware Design of Modular Robotic System,” Proceedings of the International Conference on Intelligent Robots and Systems, Takamatsu, Japan (2000) pp. 22102217.Google Scholar
28.Nagpal, R., Programmable Self-assembly: Constructing Global Shape Using Biologically-Inspired Local Interactions and Origami Mathematics PhD Thesis (Massachusetts Institute of Technology, 2001).Google Scholar
29.Nagpal, R., “Self-Assembling Global Shape, Using Ideas From Biology and Origami,” Origami3: Third International Meeting of Origami Science, Math and Education (Hull, T., ed.) (A K Peters, 2002) pp. 219231.CrossRefGoogle Scholar
30.Pamecha, A., Ebert-Uphoff, I. and Chirikjian, G., “Useful metrics for modular robot motion planning,” IEEE Trans. Robot. Autom. 13 (4), 531–45 (1997).CrossRefGoogle Scholar
31.Song, G. and Amato, N. M., “A motion-planning approach to folding: from paper craft to protein folding,” IEEE Trans. Robot. Autom. 20 (1), 6071 (Feb. 2004).CrossRefGoogle Scholar
32.Shen, W.-M., Krivokon, M., Chiu, H., Everist, J., Rubenstein, M. and Venkatesh, J., “Multimode locomotion for reconfigurable robots,” Auton. Robots 20 (2), 165177 (2006).CrossRefGoogle Scholar
33.Belcastro, S.-M. and Hull, T. C., “A Mathematical Model for Non-Flat Origami,” Origami3: Proceedings of the 3rd International Meeting of Origami Mathematics, Science and Education (2002) pp. 39–51.Google Scholar
34.Tachi, T., “Simulation of Rigid Origami,” Origami4: Proceedings of the 4th International Meeting of Origami Science, Math and Education (2009), pp. 175–187.Google Scholar
35.Varshavskaya, P., Kaelbling, L. P. and Rus, D., “Automated design of adaptive controllers for modular robots using reinforcement learning,” Int. J. Robot. Res. Special Issue on Self-Reconfigurable Modular Robots (2007).Google Scholar
36.Yim, M., Shen, W-M., Salemi, B., Rus, D., Lipson, H., Klavins, E. and Chirikjian, G., “Modular self-reconfiguring robot systems: Opportunities and challenges,” IEEE/ASME Trans. Mechatronics (2006).Google Scholar
37.Yim, M., Zhang, Y., Lamping, J. and Mao, E., “Distributed control for 3D shape metamorphosis,” Auton. Robots 10 (1), 4156 (2001).CrossRefGoogle Scholar