Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-24T07:57:04.159Z Has data issue: false hasContentIssue false

Curve shortening-inspired self-reconfiguration of heterogenous hexagonal-shaped modules toward a straight chain

Published online by Cambridge University Press:  02 December 2013

Yizhou Miao
Affiliation:
State Key Laboratory of Industrial Control Technology, College of Electrical Engineering, Zhejiang University, 38 Zheda Road, Hangzhou, 310027P. R. China
Gangfeng Yan
Affiliation:
State Key Laboratory of Industrial Control Technology, College of Electrical Engineering, Zhejiang University, 38 Zheda Road, Hangzhou, 310027P. R. China
Zhiyun Lin*
Affiliation:
State Key Laboratory of Industrial Control Technology, College of Electrical Engineering, Zhejiang University, 38 Zheda Road, Hangzhou, 310027P. R. China
*
*Corresponding author. E-mail: linz@zju.edu.cn

Summary

This study deals with a self-reconfiguration problem of hexagonal-shaped modules from an arbitrary initial configuration to a straight chain. Modules are modeled as the same-sized rigid bodies. Two categories of modules with different functionalities are used. One category comprises two powerful modules, which are expected to play the role of terminal modules in a goal configuration. The other category comprises several ordinary modules, which are expected to fill in the middle portion in a goal configuration. A distributed control strategy, inspired by the idea of curve shortening, is developed for each module to act cooperatively to attain a goal configuration. It is verified that under the proposed strategy, modules eventually converge to a straight chain.

Type
Articles
Copyright
Copyright © Cambridge University Press 2013 

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.Chiang, C. J. and Chirikjian, G. S., “Modular robot motion planning using similarity metrics,” Auton. Robots 10 (1), 91106 (2001).Google Scholar
2.Chirikjian, G., Pamecha, A. and Ebert-Uphoff, I., “Evaluating efficiency of self-reconfiguration in a class of modular robots,” J. Robot. Syst. 13 (5), 317338 (1996).Google Scholar
3.Yim, M., Zhang, Y., Lamping, J. and Mao, E., “Distributed control for 3D metamorphosis,” Auton. Robots 10 (1), 4156 (2001).Google Scholar
4.Stoy, K., “Controlling Self-Reconfiguration Using Cellular Automata and Gradients,” In: Proceedings of the 8th International Conference on Intelligent Autonomous Systems (2004) pp. 693–702.Google Scholar
5.Harada, K., Oetomo, D., Susilo, E., Menciassi, A., Daney, D., Merlet, J. P. and Dario, P., “A reconfigurable modular robotic endoluminal surgical system: Vision and preliminary results,” Robotica 28, 171183 (2010).Google Scholar
6.Chirikjian, G. S., “Kinematics of a Metamorphic Robotic System,” In: Proceedings of the 1994 IEEE International Conference on Robotics and Automation (1994) pp. 449–455.Google Scholar
7.Murata, S., Kurokawa, H. and Kokaji, S., “Self-Assembling Machine,” In: Proceedings of the 1994 IEEE International Conference on Robotics and Automation (1994) pp. 441–448.Google Scholar
8.Pamechal, A., Uphoff, I. E. and Chirikjian, G. S., “Useful metrics for modular robot motion planning,” IEEE Trans. Robot. Autom. 13 (4), 531545 (1997).Google Scholar
9.Walter, J. E., Welch, J. L. and Amato, N. M., “Concurrent metamorphosis of hexagonal robot chains into simple connected configurations,” IEEE Trans. Robot. Autom. 18 (6), 945956 (2002).Google Scholar
10.Walter, J. E., Welch, J. L. and Amato, N. M., “Distributed reconfiguration of metamorphic robot chains,” Distrib. Comput. 17 (2), 171189 (2004).Google Scholar
11.Ghrist, R. and Peterson, V., “The geometry and topology of reconfiguration,” Adv. Appl. Math. 38 (3), 302323 (2007).CrossRefGoogle Scholar
12.Zhang, L. and Dai, J. S., “Metamorphic Techniques and Geometric Reconfiguration Principles,” In: International Conference on Reconfigurable Mechanisms and Robots 2009 (2009) pp. 32–40.Google Scholar
13.Matysik, S. and Walter, J., “Using a Pocket-Filling Strategy for Distributed Reconfiguration of a System of Hexagonal Metamorphic Robots in an Obstacle-Cluttered Environment,” In: Proceedings of the 2009 IEEE International Conference on Robotics and Automation (2009) pp. 3266–3273.Google Scholar
14.Walter, J. E., Tsai, E. M. and Amato, N. M., “Algorithms for fast concurrent reconfiguration of hexagonal metamorphic robots,” IEEE Trans. Robot. 21, 621631 (2005)Google Scholar
15.Hou, F. and Shen, W., “On the Complexity of Optimal Reconfiguration Planning for Modular Reconfigurable Robots,” In: 2010 IEEE International Conference on Robotics and Automation (2010) pp. 2791–2796.Google Scholar
16.Guan, E., Fu, Z., Yan, W., Jiang, D. and Y. Zhao, “Self-reconfiguration path planning design for M-lattice robot based on genetic algorithm,” Intell. Robot. Appl. 7102, 505514 (2011).Google Scholar
17.Ivanov, P. and Walter, J., “Layering Algorithm for Collision-Free Traversal Using Hexagonal Self-Reconfigurable Metamorphic Robots,” In: Proceedings of 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (2010) pp. 521–528.Google Scholar
18.Miao, Y., Yan, G. and Lin, Z., “A Distributed Reconfiguration Strategy for Target Enveloping with Hexagonal Metamorphic Modules,” In: Proceedings of the 2011 IEEE International Conference on Robotics and Automation (2011) pp. 4804–4809.Google Scholar
19.Larkworthy, T. and Ramamoorthy, S., “A characterization of the reconfiguration space of self-reconfiguring robotic systems,” Robotica 29 (1), 7385 (2011).Google Scholar
20.Pamecha, A., chiang, C., Stein, D. and Chirikjian, G., “Design and Implementation of Metamorphic Robots,” In: Proceedings of the 1996 ASME Design Engineering Technical Conferences and Computers in Engineering Conference (1996) pp. 1–10.Google Scholar
21.Murata, S., Kurokawa, H., Yoshida, E., Tomita, K. and S. Kokaji, “A 3-D Self-Reconfigurable Structure,” In: Proceedings of the 1998 IEEE International Conference on Robotics and Automation (1998) pp. 432–439.Google Scholar
22.Castano, A., Shen, W. M. and Will, P., “CONRO: Towards deployable robots with inter-robots metamorphic capabilities,” Auton. Robots 8 (3), 309324 (2000).Google Scholar
23.Salemi, B., Moll, M. and Shen, W., “SUPERBOT: A Deployable, Multi-Functional, and Modular Self-Reconfigurable Robotic System,” In: Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems (2006) pp. 3636–3641.Google Scholar
24.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).Google Scholar
25.Gilpin, K., Knaian, A. and Rus, D., “Robot Pebbles: One Centimeter Modules for Programmable Matter Through Self-Disassembly,” In: Proceedings of the 2010 IEEE International Conference on Robotics and Automation (2010) pp. 2485–2492.Google Scholar
26.Grayson, M. A., “The heat equation shrinks embedded plane curves to round points,” J. Differ. Geom. 26 (2), 285314 (1987).CrossRefGoogle Scholar
27.Grayson, M. A., “Shortening embedded curves,” Ann. Math. 129, 71111 (1989).Google Scholar
28.Yamins, D. and Nagpal, R., “Automated Global-to-Local Programming in 1-D Spatial Multi-Agent Systems,” In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems (2008) 615–622.Google Scholar