Skip to main content
Top
Published in: Autonomous Robots 4/2019

28-04-2018

Distributed configuration formation with modular robots using (sub)graph isomorphism-based approach

Authors: Ayan Dutta, Prithviraj Dasgupta, Carl Nelson

Published in: Autonomous Robots | Issue 4/2019

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We consider the problem of configuration formation in modular robot systems where a set of modules that are initially in different configurations and located at different locations are required to assume appropriate positions so that they can get into a new, user-specified, target configuration. We propose a novel algorithm based on (sub)graph isomorphism, where the modules select locations or spots in the target configuration using a utility-based framework, while retaining their original configuration to the greatest extent possible, to reduce the time and energy required by the modules to disconnect and connect multiple times to form the target configuration. We have shown analytically that our proposed algorithm is complete and guarantees a Pareto-optimal allocation. Experimental simulations of our algorithm with different numbers of modules in different initial configurations and located initially at different locations, show that the planning time of our algorithm is nominal (order of msec for 100 modules). We have also compared our algorithm against a market-based allocation algorithm and shown that our proposed algorithm performs better in terms of time and number of messages exchanged.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Footnotes
1
A common coordinate system can be maintained by modules for localizing themselves following the model described in Suzuki and Yamashita (1997).
 
Literature
go back to reference Ahmadzadeh, H., & Masehian, E. (2015). Modular robotic systems: Methods and algorithms for abstraction, planning, control, and synchronization. Artificial Intelligence, 223, 27–64.MathSciNetCrossRefMATH Ahmadzadeh, H., & Masehian, E. (2015). Modular robotic systems: Methods and algorithms for abstraction, planning, control, and synchronization. Artificial Intelligence, 223, 27–64.MathSciNetCrossRefMATH
go back to reference Aho, A. V., & Hopcroft, J. E. (1974). The design and analysis of computer algorithms. Bengaluru: Pearson Education India.MATH Aho, A. V., & Hopcroft, J. E. (1974). The design and analysis of computer algorithms. Bengaluru: Pearson Education India.MATH
go back to reference Akutsu, T. (1993). A polynomial time algorithm for finding a largest common subgraph of almost trees of bounded degree. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 76(9), 1488–1493. Akutsu, T. (1993). A polynomial time algorithm for finding a largest common subgraph of almost trees of bounded degree. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 76(9), 1488–1493.
go back to reference Alonso-Mora, J., Breitenmoser, A., Rufli, M., Siegwart, R., & Beardsley, P. (2011). Multi-robot system for artistic pattern formation. In 2011 IEEE international conference on robotics and automation (ICRA) (pp. 4512–4517). IEEE. Alonso-Mora, J., Breitenmoser, A., Rufli, M., Siegwart, R., & Beardsley, P. (2011). Multi-robot system for artistic pattern formation. In 2011 IEEE international conference on robotics and automation (ICRA) (pp. 4512–4517). IEEE.
go back to reference Asadpour, M., Sproewitz, A., Billard, A., Dillenbourg, P., & Ijspeert, A.J. (2008). Graph signature for self-reconfiguration planning. In IEEE/RSJ international conference on intelligent robots and systems, 2008. IROS 2008 (pp. 863–869). IEEE. Asadpour, M., Sproewitz, A., Billard, A., Dillenbourg, P., & Ijspeert, A.J. (2008). Graph signature for self-reconfiguration planning. In IEEE/RSJ international conference on intelligent robots and systems, 2008. IROS 2008 (pp. 863–869). IEEE.
go back to reference Baca, J., Hossain, S., Dasgupta, P., Nelson, C. A., & Dutta, A. (2014). Modred: Hardware design and reconfiguration planning for a high dexterity modular self-reconfigurable robot for extra-terrestrial exploration. Robotics and Autonomous Systems, 62(7), 1002–1015.CrossRef Baca, J., Hossain, S., Dasgupta, P., Nelson, C. A., & Dutta, A. (2014). Modred: Hardware design and reconfiguration planning for a high dexterity modular self-reconfigurable robot for extra-terrestrial exploration. Robotics and Autonomous Systems, 62(7), 1002–1015.CrossRef
go back to reference Baca, J., Woosley, B., Dasgupta, P., Dutta, A., & Nelson, C. (2016). Coordination of modular robots by means of topology discovery and leader election: Improvement of the locomotion case. In Distributed autonomous robotic systems (pp. 447–458). Berlin: Springer. Baca, J., Woosley, B., Dasgupta, P., Dutta, A., & Nelson, C. (2016). Coordination of modular robots by means of topology discovery and leader election: Improvement of the locomotion case. In Distributed autonomous robotic systems (pp. 447–458). Berlin: Springer.
go back to reference Bertsekas, D. P. (1990). The auction algorithm for assignment and other network flow problems: A tutorial. Interfaces, 20(4), 133–149.CrossRef Bertsekas, D. P. (1990). The auction algorithm for assignment and other network flow problems: A tutorial. Interfaces, 20(4), 133–149.CrossRef
go back to reference Brandes, U. (2001). A faster algorithm for betweenness centrality*. Journal of Mathematical Sociology, 25(2), 163–177.CrossRefMATH Brandes, U. (2001). A faster algorithm for betweenness centrality*. Journal of Mathematical Sociology, 25(2), 163–177.CrossRefMATH
go back to reference Chen, I. M., & Burdick, J. W. (1998). Enumerating the non-isomorphic assembly configurations of modular robotic systems. The International Journal of Robotics Research, 17(7), 702–719.CrossRef Chen, I. M., & Burdick, J. W. (1998). Enumerating the non-isomorphic assembly configurations of modular robotic systems. The International Journal of Robotics Research, 17(7), 702–719.CrossRef
go back to reference Chirikjian, G., Pamecha, A., & Ebert-Uphoff, I. (1996). Evaluating efficiency of self-reconfiguration in a class of modular robots. Journal of Field Robotics, 13(5), 317–338.MATH Chirikjian, G., Pamecha, A., & Ebert-Uphoff, I. (1996). Evaluating efficiency of self-reconfiguration in a class of modular robots. Journal of Field Robotics, 13(5), 317–338.MATH
go back to reference Cordella, L. P., Foggia, P., Sansone, C., & Vento, M. (2004). A (sub) graph isomorphism algorithm for matching large graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(10), 1367–1372.CrossRef Cordella, L. P., Foggia, P., Sansone, C., & Vento, M. (2004). A (sub) graph isomorphism algorithm for matching large graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(10), 1367–1372.CrossRef
go back to reference Dasgupta, P., Ufimtsev, V., Nelson, C., & Hossain, S. (2012). Dynamic reconfiguration in modular robots using graph partitioning-based coalitions. In Proceedings of the 11th international conference on autonomous agents and multiagent systems-volume 1. International foundation for autonomous agents and multiagent systems (pp. 121–128). Dasgupta, P., Ufimtsev, V., Nelson, C., & Hossain, S. (2012). Dynamic reconfiguration in modular robots using graph partitioning-based coalitions. In Proceedings of the 11th international conference on autonomous agents and multiagent systems-volume 1. International foundation for autonomous agents and multiagent systems (pp. 121–128).
go back to reference Davis, J. D., Sevimli, Y., Eldridge, B. R., & Chirikjian, G. S. (2016). Module design and functionally non-isomorphic configurations of the Hex-DMR II system. Journal of Mechanisms and Robotics, 8(5), 051,008.CrossRef Davis, J. D., Sevimli, Y., Eldridge, B. R., & Chirikjian, G. S. (2016). Module design and functionally non-isomorphic configurations of the Hex-DMR II system. Journal of Mechanisms and Robotics, 8(5), 051,008.CrossRef
go back to reference Dutta, A., Chaudhuri, S.G., Datta, S., & Mukhopadhyaya, K. (2012). Circle formation by asynchronous fat robots with limited visibility. In Distributed Computing and Internet Technology (pp. 83–93). Berlin: Springer. Dutta, A., Chaudhuri, S.G., Datta, S., & Mukhopadhyaya, K. (2012). Circle formation by asynchronous fat robots with limited visibility. In Distributed Computing and Internet Technology (pp. 83–93). Berlin: Springer.
go back to reference Dutta, A., & Dasgupta, P. (2016). Simultaneous configuration formation and information collection by modular robotic systems. In 2016 IEEE international conference on robotics and automation (ICRA) (pp. 5216–5221). Dutta, A., & Dasgupta, P. (2016). Simultaneous configuration formation and information collection by modular robotic systems. In 2016 IEEE international conference on robotics and automation (ICRA) (pp. 5216–5221).
go back to reference Dutta, A., Dasgupta, P., & Nelson, C. (2018). Distributed adaptive locomotion learning in modred modular self-reconfigurable robot. In Distributed Autonomous Robotic Systems (pp. 345–357). Cham: Springer. Dutta, A., Dasgupta, P., & Nelson, C. (2018). Distributed adaptive locomotion learning in modred modular self-reconfigurable robot. In Distributed Autonomous Robotic Systems (pp. 345–357). Cham: Springer.
go back to reference Enner, F., Rollinson, D., & Choset, H. (2013). Motion estimation of snake robots in straight pipes. In International conference on robotics and automation (pp. 5148–5153). Enner, F., Rollinson, D., & Choset, H. (2013). Motion estimation of snake robots in straight pipes. In International conference on robotics and automation (pp. 5148–5153).
go back to reference Fitch, R., & Butler, Z. (2008). Million module march: Scalable locomotion for large self-reconfiguring robots. The International Journal of Robotics Research, 27(3–4), 331–343.CrossRef Fitch, R., & Butler, Z. (2008). Million module march: Scalable locomotion for large self-reconfiguring robots. The International Journal of Robotics Research, 27(3–4), 331–343.CrossRef
go back to reference Hossain, S., Nelson, C. A., Chu, K. D., & Dasgupta, P. (2014). Kinematics and interfacing of modred: A self-healing capable, four-dof modular self-reconfigurable robot. JMR, 13, 1256. Hossain, S., Nelson, C. A., Chu, K. D., & Dasgupta, P. (2014). Kinematics and interfacing of modred: A self-healing capable, four-dof modular self-reconfigurable robot. JMR, 13, 1256.
go back to reference Hou, F., & Shen, W.M. (2008). Distributed, dynamic, and autonomous reconfiguration planning for chain-type self-reconfigurable robots. In IEEE international conference on robotics and automation, 2008. ICRA 2008 (pp. 3135–3140). IEEE. Hou, F., & Shen, W.M. (2008). Distributed, dynamic, and autonomous reconfiguration planning for chain-type self-reconfigurable robots. In IEEE international conference on robotics and automation, 2008. ICRA 2008 (pp. 3135–3140). IEEE.
go back to reference Hou, F., & Shen, W. M. (2014). Graph-based optimal reconfiguration planning for self-reconfigurable robots. Robotics and Autonomous Systems, 62(7), 1047–1059.CrossRef Hou, F., & Shen, W. M. (2014). Graph-based optimal reconfiguration planning for self-reconfigurable robots. Robotics and Autonomous Systems, 62(7), 1047–1059.CrossRef
go back to reference Kamimura, A., Kurokawa, H., Yoshida, E., Tomita, K., Kokaji, S., & Murata, S. (2004). Distributed adaptive locomotion by a modular robotic system, M-TRAN II. In Proceedings. 2004 IEEE/RSJ international conference on intelligent robots and systems, 2004.(IROS 2004) (Vols. 3, pp. 2370–2377). IEEE. Kamimura, A., Kurokawa, H., Yoshida, E., Tomita, K., Kokaji, S., & Murata, S. (2004). Distributed adaptive locomotion by a modular robotic system, M-TRAN II. In Proceedings. 2004 IEEE/RSJ international conference on intelligent robots and systems, 2004.(IROS 2004) (Vols. 3, pp. 2370–2377). IEEE.
go back to reference Klavins, E. (2007). Programmable self-assembly. IEEE, Control Systems, 27(4), 43–56.CrossRef Klavins, E. (2007). Programmable self-assembly. IEEE, Control Systems, 27(4), 43–56.CrossRef
go back to reference Knight, S., Rabideau, G., Chien, S., Engelhardt, B., & Sherwood, R. (2001). Casper: Space exploration through continuous planning. IEEE Intelligent Systems, 16(5), 70–75.CrossRef Knight, S., Rabideau, G., Chien, S., Engelhardt, B., & Sherwood, R. (2001). Casper: Space exploration through continuous planning. IEEE Intelligent Systems, 16(5), 70–75.CrossRef
go back to reference Kobler, J., Schöning, U., & Torán, J. (2012). The graph isomorphism problem: Its structural complexity. Berlin: Springer.MATH Kobler, J., Schöning, U., & Torán, J. (2012). The graph isomorphism problem: Its structural complexity. Berlin: Springer.MATH
go back to reference Kurokawa, H., Tomita, K., Kamimura, A., Kokaji, S., Hasuo, T., & Murata, S. (2008). Distributed self-reconfiguration of M-TRAN III modular robotic system. The International Journal of Robotics Research, 27(3–4), 373–386.CrossRef Kurokawa, H., Tomita, K., Kamimura, A., Kokaji, S., Hasuo, T., & Murata, S. (2008). Distributed self-reconfiguration of M-TRAN III modular robotic system. The International Journal of Robotics Research, 27(3–4), 373–386.CrossRef
go back to reference Nelson, C.A., & Cipra, R.J. (2004). An algorithm for efficient self-reconfiguration of chain-type unit-modular robots. In ASME DETC, (pp. 1283–1291). New York City: American Society of Mechanical Engineers. Nelson, C.A., & Cipra, R.J. (2004). An algorithm for efficient self-reconfiguration of chain-type unit-modular robots. In ASME DETC, (pp. 1283–1291). New York City: American Society of Mechanical Engineers.
go back to reference Neubert, J., & Lipson, H. (2016). Soldercubes: A self-soldering self-reconfiguring modular robot system. Autonomous Robots, 40(1), 139–158.CrossRef Neubert, J., & Lipson, H. (2016). Soldercubes: A self-soldering self-reconfiguring modular robot system. Autonomous Robots, 40(1), 139–158.CrossRef
go back to reference Pamecha, A., Ebert-Uphoff, I., & Chirikjian, G. S. (1997). Useful metrics for modular robot motion planning. IEEE Transactions on Robotics and Automation, 13(4), 531–545.CrossRefMATH Pamecha, A., Ebert-Uphoff, I., & Chirikjian, G. S. (1997). Useful metrics for modular robot motion planning. IEEE Transactions on Robotics and Automation, 13(4), 531–545.CrossRefMATH
go back to reference Park, M., Chitta, S., Teichman, A., & Yim, M. (2008). Automatic configuration recognition methods in modular robots. The International Journal of Robotics Research, 27(3–4), 403–421.CrossRef Park, M., Chitta, S., Teichman, A., & Yim, M. (2008). Automatic configuration recognition methods in modular robots. The International Journal of Robotics Research, 27(3–4), 403–421.CrossRef
go back to reference Raymond, J. W., & Willett, P. (2002). Maximum common subgraph isomorphism algorithms for the matching of chemical structures. Journal of Computer-Aided Molecular Design, 16(7), 521–533.CrossRef Raymond, J. W., & Willett, P. (2002). Maximum common subgraph isomorphism algorithms for the matching of chemical structures. Journal of Computer-Aided Molecular Design, 16(7), 521–533.CrossRef
go back to reference Rosa, M., Goldstein, S., Lee, P., Campbell, J., & Pillai, P. (2006). Scalable shape sculpturing via hole motions. In IEEE international conference on robotics and automation, (pp. 1462–1468). Orlando, FL. Rosa, M., Goldstein, S., Lee, P., Campbell, J., & Pillai, P. (2006). Scalable shape sculpturing via hole motions. In IEEE international conference on robotics and automation, (pp. 1462–1468). Orlando, FL.
go back to reference Rubenstein, M., Cornejo, A., & Nagpal, R. (2014). Programmable self-assembly in a thousand-robot swarm. Science, 345(6198), 795–799.CrossRef Rubenstein, M., Cornejo, A., & Nagpal, R. (2014). Programmable self-assembly in a thousand-robot swarm. Science, 345(6198), 795–799.CrossRef
go back to reference Shamir, R., & Tsur, D. (1997). Faster subtree isomorphism. In Proceedings of the Fifth Israeli symposium on theory of computing and systems, 1997 (pp. 126–131). IEEE. Shamir, R., & Tsur, D. (1997). Faster subtree isomorphism. In Proceedings of the Fifth Israeli symposium on theory of computing and systems, 1997 (pp. 126–131). IEEE.
go back to reference Stoy, K., Brandt, D., & Christensen, D. J. (2010). Self-reconfigurable robots: An introduction. Cambridge: The MIT Press. Stoy, K., Brandt, D., & Christensen, D. J. (2010). Self-reconfigurable robots: An introduction. Cambridge: The MIT Press.
go back to reference Suzuki, I., & Yamashita, M. (1997). Agreement on a common XY coordinate system by a group of mobile robots. In Intelligent Robots—Sensing, Modeling And Planning (pp. 305–321). Suzuki, I., & Yamashita, M. (1997). Agreement on a common XY coordinate system by a group of mobile robots. In Intelligent Robots—Sensing, Modeling And Planning (pp. 305–321).
go back to reference Tolley, M.T., & Lipson, H. (2010). Fluidic manipulation for scalable stochastic 3D assembly of modular robots. In 2010 IEEE international conference on robotics and automation (ICRA) (pp. 2473–2478). IEEE. Tolley, M.T., & Lipson, H. (2010). Fluidic manipulation for scalable stochastic 3D assembly of modular robots. In 2010 IEEE international conference on robotics and automation (ICRA) (pp. 2473–2478). IEEE.
go back to reference Werfel, J., & Nagpal, R. (2008). Three-dimensional construction with mobile robots and modular blocks. The International Journal of Robotics Research, 27(3–4), 463–479.CrossRef Werfel, J., & Nagpal, R. (2008). Three-dimensional construction with mobile robots and modular blocks. The International Journal of Robotics Research, 27(3–4), 463–479.CrossRef
go back to reference Yim, M., Shen, W. M., Salemi, B., Rus, D., Moll, M., Lipson, H., et al. (2007). Modular self-reconfigurable robot systems [grand challenges of robotics]. IEEE Robotics & Automation Magazine, 14(1), 43–52.CrossRef Yim, M., Shen, W. M., Salemi, B., Rus, D., Moll, M., Lipson, H., et al. (2007). Modular self-reconfigurable robot systems [grand challenges of robotics]. IEEE Robotics & Automation Magazine, 14(1), 43–52.CrossRef
Metadata
Title
Distributed configuration formation with modular robots using (sub)graph isomorphism-based approach
Authors
Ayan Dutta
Prithviraj Dasgupta
Carl Nelson
Publication date
28-04-2018
Publisher
Springer US
Published in
Autonomous Robots / Issue 4/2019
Print ISSN: 0929-5593
Electronic ISSN: 1573-7527
DOI
https://doi.org/10.1007/s10514-018-9759-9

Other articles of this Issue 4/2019

Autonomous Robots 4/2019 Go to the issue