Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T17:41:41.716Z Has data issue: false hasContentIssue false
  • English
  • Français

Efficient constant-velocity reconfiguration of crystalline robots**

Published online by Cambridge University Press:  14 January 2011

Greg Aloupis ,
Sébastien Collette ,
Mirela Damian ,
Erik D. Demaine ,
Robin Flatland ,
Stefan Langerman ,
Joseph O'Rourke ,
Val Pinciu ,
Suneeta Ramaswami  and
Vera Sacristán
...Show all authors
Greg Aloupis*
Affiliation:
Université Libre de Bruxelles, Belgique. E-mail: aloupis.greg@gmail.com (Supported by the Communauté française de Belgique - ARC)
Sébastien Collette
Affiliation:
Chargé de Recherches du FRS-FNRS, Université Libre de Bruxelles, Belgique. E-mail: sebastien.collette@ulb.ac.be
Mirela Damian
Affiliation:
Villanova University, Villanova, PA, USA. E-mail: mirela.damian@villanova.edu
Erik D. Demaine
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA, USA. E-mail: edemaine@mit.edu (Partially supported by NSF CAREER award CCF-0347776, DOE grant DE-FG02-04ER25647, and AFOSR grant FA9550-07-1-0538)
Robin Flatland
Affiliation:
Siena College, Loudonville, NY, USA. E-mail: flatland@siena.edu
Stefan Langerman
Affiliation:
Maítre de Recherches du FRS-FNRS, Université Libre de Bruxelles, Belgique. E-mail: stefan.langerman@ulb.ac.be
Joseph O'Rourke
Affiliation:
Smith College, Northampton, MA, USA. E-mail: orourke@cs.smith.edu
Val Pinciu
Affiliation:
Southern Connecticut State University, New Haven, CT, USA. E-mail: pinciu@scsu.ctstateu.edu
Suneeta Ramaswami
Affiliation:
Rutgers University, Camden, NJ, USA. E-mail: rsuneeta@camden.rutgers.edu. (Partially supported by NSF grant CCR-0204293)
Vera Sacristán
Affiliation:
Universitat Politècnica de Catalunya, Barcelona, Spain. E-mail: vera.sacristan@upc.edu (Partially supported by projects MCI MTM2009-07242 and Gen. Cat. DGR 2009SGR1040)
Stefanie Wuhrer
Affiliation:
Carleton University, Ottawa, Canada. E-mail: swuhrer@scs.carleton.ca
*
*Corresponding author. E-mail: aloupis.greg@gmail.com
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2 × 2 × 2 modules. We respect certain physical constraints: each atom reaches at most constant velocity and can displace at most a constant number of other atoms. We assume that one of the atoms has access to the coordinates of atoms in the target configuration.

Our algorithms involve a total of O(n2) atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n2) parallel steps or do not respect the constraints mentioned above. In fact, in the settings considered, our algorithms are optimal. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configuration space, and only requires local communication.

Keywords

Control of robotic systemsMobile robotsModular robotsMotion planningPath planning
Type
Article
Information
Robotica , Volume 29 , Special Issue 1: Robotic Self-X Systems , January 2011 , pp. 59 - 71
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.)

Footnotes

**

A short version appeared at WAFR 2008,2 with title Realistic reconfiguration of crystalline (and telecube) robots

References

1.Aloupis, G., Benbernou, N., Damian, M., Demaine, E., Flatland, R., Iacono, J. and Wuhrer, S., “Efficient Reconfiguration of Lattice-Based Modular Robots,” European Conference on Mobile Robots, Mlini/Dubrovnik, Croatia, (Sep. 23–25, 2009a) pp. 81–86.Google Scholar
2.Aloupis, G., Collette, S., Damian, M., Demaine, E. D., El-Khechen, D., Flatland, R., Langerman, S., O'Rourke, J., Pinciu, V., Ramaswami, S., Sacristán, V. and Wuhrer, S., “Realistic Reconfiguration of Crystalline and Telecube Robots. In: 8th International Workshop on the Algorithmic Foundations of Robotics (WAFR) (Chirikjian, G. S. et al. Eds.), Springer Tracts in Advanced Robotics, vol. 57, (2008a) pp. 433–447.Google Scholar
3.Aloupis, G., Collette, S., Damian, M., Demaine, E. D., Flatland, R., Langerman, S., O'Rourke, J., Ramaswami, S., Sacristán, V. and Wuhrer, S., “Linear reconfiguration of cube-style modular robots,” Comput. Geom., Theor. Appl. 42 (6–7), 652–663 (2009b).CrossRefGoogle Scholar
4.Aloupis, G., Collette, S., Demaine, E. D., Langerman, S., Sacristán, V. and Wuhrer, S., “Reconfiguration of Cube-Style Modular Robots Using O(logn) Parallel Moves,” Proceedings of the International Symposium on Algorithms and Computation (ISAAC 2008), volume 5369 of LNCS, (2008b) pp. 342–353.CrossRefGoogle Scholar
5.Aloupis, G., Collette, S., Demaine, E. D., Langerman, S., Sacristán, V. and Wuhrer, S., “Reconfiguration of 3D Crystalline Robots in O(logn) Parallel Steps. Technical Report arXiv:0908.2440 (2009c) p. 21.CrossRefGoogle Scholar
6.Brener, N., Amar, F. B. and Bidaud, P., “Designing modular lattice systems with chiral space groups,” Int. J. Robot. Res. 27 (3–4), 279–297 (2008).CrossRefGoogle Scholar
7.Butler, Z., Byrnes, S. and Rus, D., “Distributed Motion Planning for Modular Robots with Unit-Compressible Modules,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Maui, Hawaii, USA, vol. 2, (2001) pp. 790–796.Google Scholar
8.Butler, Z., Fitch, R. and Rus, D., “Distributed control for unit-compressible robots: Goal-recognition, locomotion and splitting,” IEEE/ASME Trans. Mechatron. 7 (4), 418–430 (2002).CrossRefGoogle Scholar
9.Butler, Z., Kotay, K., Rus, D. and Tomita, K., “Generic decentralized control for lattice-based self-reconfigurable robots,” Int. J. Robot. Res. 23, 919–937 (2004).CrossRefGoogle Scholar
10.Butler, Z. and Rus, D., “Distributed planning and control for modular robots with unit-compressible modules,” Int. J. Robot. Res. 22 (9), 699–715 (2003).CrossRefGoogle Scholar
11.Chiang, C.-J. and Chirikjian, G., “Similarity metric with applications in modular robot motion planning,” Auton. Robots 10 (1), 91–106 (2001).CrossRefGoogle Scholar
12.Chirikjian, G., “Kinematics of a Metamorphic Robotic System,” Proceedings of the IEEE International Conference on Robotic Automation (May 8–13, 1994) pp. 449–455.Google Scholar
13.Chirikjian, G., Pamecha, A. and Ebert-Uphoff, I., “Evaluating efficiency of self-reconfiguration in a class of modular robots,” J. Robot. Syst. 13 (5), 317–338 (1996).3.0.CO;2-T>CrossRefGoogle Scholar
14.Fukuda, T. and Nakagawa, S., “Approach to the dynamically reconigurable robotic system,” J. Intell. Robot. Syst. 1 (1), 55–72 (1988).CrossRefGoogle Scholar
15.Hosokawa, K., Tsujimori, T., Fujii, T., Kaetsu, H., Asama, H., Kuroda, Y. and Endo, I., “Self-Organizing Collective Robots with Morphogenesis in a Vertical Plane,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Leuven, Belgium (May 16–20, 1998) pp. 2858–2863.Google Scholar
16.Jørgensen, M. W., Østergaard, E. H. and Lund, H. H., “Modular ATRON: Modules for a Self-Reconfigurable Robot,” Proceedings of the of the International Conference on Intelligient Robots and Systems (2004) pp. 2068–2073.Google Scholar
17.Kotay, K. and Rus, D., “Algorithms for Self-Reconfiguring Molecule Motion Planning,” Proceedings of the International Conference on Intelligent Robots and Systems, Kagawa University, Takamatsu, Japan (Oct. 30–Nov. 5, 2000) pp. 2184–2193.Google Scholar
18.Kurokawa, H., Tomita, K., Kamimura, A., Kokaji, S., Hasuo, T. and Murata, S., “Self-reconfigurable Modular Robot M-TRAN: Distributed Control and Communication,” In: RoboComm '07: Proceedings of the 1st International Conference on Robot Communication and Coordination, Piscataway, NJ, USA. (IEEE Press, 2007) pp. 1–7.Google Scholar
19.Kurokawa, H., Tomita, K., Kamimura, A., Kokaji, S., Hasuo, T. and Murata, S., “Distributed self-reconfiguration of M-TRAN III modular robotic system,” Int. J. Robot. Res. 27, 373–386 (2008).CrossRefGoogle Scholar
20.Murata, S. and Kurokawa, H., “Self-reconfigurable robots: Shape-changing cellular robots can exceed conventional robot flexibility,” IEEE Robot. Autom. Mag. 14 (1), 43–52 (2007).CrossRefGoogle Scholar
21.Murata, S., Kurokawa, H. and Kokaji, S., “Self-Assembling Machine,” Proceedings of the IEEE International Conferance Robotic Automation, San Diego, CA, USA (May 1994) pp. 441–448.Google Scholar
22.Pamecha, A., Chiang, C., Stein, D. and Chirikjian, G., “Design and Implementation of Metamorphic Robots,” In: Proceedings of the ASME Design Engineering Technical Conference and Computers in Engineering Conference (McCarthy, J., ed.), Irvine, CA, (1996) pp. 1–10.Google Scholar
23.Pamecha, A., Ebert-Uphoff, I. and Chirikjian, G., “Useful metrics for modular robot motion planning,” IEEE Trans. Robot. Autom. 13 (4), 531–545 (1997).CrossRefGoogle Scholar
24.Reif, J. H. and Slee, S., “Optimal Kinodynamic Motion Planning for Self-Reconfigurable Robots Between Arbitrary 2D Configurations,” Robotics: Science and Systems Conference, Georgia Institute of Technology, Atlanta, GA, USA (June 27–30, 2007).Google Scholar
25.Rus, D. and Vona, M., “Crystalline robots: Self-reconfiguration with compressible unit modules,” Auton. Robot 10 (1), 107–124 (2001).CrossRefGoogle Scholar
26.Salemi, B., Will, P. and Shen, W.-M., “Distributed task negotiation in modular robots,” J. Robot. Soc. Japan, (Special Issue on “Modular Robots”) 21 (8), 32–39 (2003).Google Scholar
27.Stoy, K., “Using cellular automata and gradients to control self-reconfiguration,” Robot. Auton. Syst. (Special issue IAS-04) 54, 135–141 (2006).CrossRefGoogle Scholar
28.Suh, J. W., Homans, S. B. and Yim, M., “Telecubes: Mechanical Design of a Module for Self-Reconfigurable Robotics,” Proceedings of the IEEE International Conference on Robotics and Automation, Washington, DC (May 11–15, 2002) pp. 4095–4101.Google Scholar
29.Ünsal, C., Kilite, H., Patton, M. and Khosla, P., “Motion Planning for a Modular Self-Reconfiguring Robotic System,” Proceedings of the 5th International Symposium on Distributed Autonomous Robotic Systems, Knoxville, Tennessee, USA (Oct. 4–6, 2000).Google Scholar
30.Vassilvitskii, S., Yim, M. and Suh, J., “A Complete, Local and Parallel Reconfiguration Algorithm for Cube Style Modular Robots,” Proceedings of the of the IEEE International Conference on Robotics and Automation (2002) pp. 117–122.Google Scholar
31.Walter, J. E., Tsai, E. M. and Amato, N. M., Choosing Good Paths for Fast Distributed Reconfiguration of Hexagonal Metamorphic Robots,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), (2002) pp. 102–109.Google Scholar
32.Yim, M., “New Locomotion Gaits,” Proceedings of the IEEE International Conference Robotic Automation, San Diego, CA, USA (May 1994).Google Scholar
33.Yim, M., Duff, D. G. and Roufas, K. D., “Polybot: A Modular Reconfigurable Robot.” Proceedings of the 2000 IEEE International Conference on Robotics and Automation (2000) pp. 514–520.Google Scholar
34.Yim, M., Shen, W.-M., Salemi, B., Rus, D., Moll, M., Lipson, H., Klavins, E. and Chirikjian, G. S., “Modular self-reconfigurable robots systems: Challenges and opportunities for the future,” IEEE Robot. Autom. Mag. 14 (1), 43–52 (2007).CrossRefGoogle Scholar
35.Yoshida, E., Murata, S., Kamimura, A., Tomita, K., Kurokawa, H. and Kokaji, S., “A self-reconfigurable modular robot: Reconfiguration planning and experiments,” Int. J. Robot. Res. 21 (10–11), 903–915 (2002).CrossRefGoogle Scholar