Skip to main content
SpringerLink
Log in

Assembling and Configuring

  • Chapter
  • First Online:
Implementing Polytope Projects for Smart Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 92))

  • 490 Accesses

Abstract

This chapter examines self-assembly and self-configuring at different scales from molecular to macro systems. Case studies refer to biochemical systems and to self-reconfiguring robots. The relation between flexible self-assembling of tiles and computing is outlined. Computation in living cells is correlated to permutation trees . Configuration trees , shifted shapes and skew strips shapes allow the study of metamorphic robotic systems as collections of modules that can dynamically self-reconfigure.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Adleman, L.: Molecular computation of solutions of combinatorial problems. Science 266, 1021–1024 (1994)

    Article  Google Scholar 

  • Aloupis, G., Collette, S., Damian, M., Demaine, E.D., Flatland, R., Langerman, S., O’Rourke, J., Ramaswami, S., Sacristan, V., Wuhrer, S.: Linear reconfiguration of cube-style modular robots. In: Computational Geometry—Theory and Applications, pp. 652–663 (2009)

    Google Scholar 

  • Bergeron, N., Lam, T., Li, H.: Combinatorial Hopf algebras and towers of algebras—dimension, quantization and functorality. Algebras Represent. Theory 15(4), 675–696 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Blasiak, P.: Combinatorial route to algebra: the art of composition & de-composition. Discrete Math. Theor. Comput. Sci. 12(2), 381–400 (2010)

    MathSciNet  Google Scholar 

  • Carbone, A., Seeman, N.C.: Circuits and programmable self-assembling DNA structures. Proc. Natl. Acad. Sci. U.S.A. 99, 12577–12582 (2002)

    Article  MathSciNet  Google Scholar 

  • Chen I.M., Burdick J.W.: Determining task optimal modular robot assembly configurations. In: IEEE International Conference on Robotics and Automation, Proceedings, vol. 1, 21 May 1995, pp. 132–137. IEEE (1995)

    Google Scholar 

  • Chen, I.M., Burdick, J.W.: Enumerating the non-isomorphic assembly configurations of modular robotic systems. Int. J. Robot. Res. 17(7), 702–719 (1998)

    Article  Google Scholar 

  • Chiang, C.H., Chirikjian, G.: Modular robot motion planning using similarity metrics. Auton. Robots 10, 91–106 (2001)

    Article  MATH  Google Scholar 

  • Chirikjian G.: Kinematics of a metamorphic robotic system. In: IEEE International Conference on Robotics and Automation, Proceedings, 8 May 1994, pp. 449–455. IEEE (1994)

    Google Scholar 

  • Drees, M., Hüllmann, M., Koutsopoulos, A., Scheideler, C.: Self-organizing particle systems. In: Parallel & Distributed Processing Symposium (IPDPS), 2012 IEEE 26th International, pp. 1272–1283. IEEE (2012)

    Google Scholar 

  • Fomin, S.: Duality of graded graphs. J. Algebraic Comb. 3, 357–404 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Gilpin, K., Rus, D.: Modular robot systems: from self-assembly to self-disassembly. IEEE Robot. Autom. Mag. 17(3), 38–53 (2010)

    Article  Google Scholar 

  • Gilpin, K., Rus D.: A distributed algorithm for 2D shape duplication with smart pebble robots. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 3285–3292, IEEE (2012)

    Google Scholar 

  • Goldstein, S.C., Campbell, J.D., Mowry, T.C.: Programmable matter. Computer 38(6), 99–101 (2005)

    Article  Google Scholar 

  • Hivert, F.: An introduction to combinatorial Hopf algebras: examples and realizations. In: Nato Advanced Study Institute School on Physics and Computer Science, vol. 1, Cargese, France, pp. 17–29 (2005)

    Google Scholar 

  • Iordache, O.: Self-evolvable Systems. Machine Learning in Social Media. Springer, Berlin, Heidelberg (2012)

    Book  Google Scholar 

  • Iordache, O.: Polytope Projects. Taylor & Francis CRC Press, Boca Raton (2013)

    Book  Google Scholar 

  • Joni, S.A., Rota, G.C.: Coalgebras and bialgebras in combinatorics. Stud. Appl. Math. 61(2), 93–139 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  • Jonoska, N., McColm, G.L.: Complexity classes for self-assembling flexible tiles. Theoret. Comput. Sci. 410(4–5), 332–346 (2000)

    MathSciNet  MATH  Google Scholar 

  • Jonoska, N., McColm, G.L., Staninska, A.: On stoichiometry for the assembly of flexible tile DNA complexes. Nat. Comput. 10(3), 1121–1141 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Kari, L., Mahalingam, K.: DNA computing: a research snapshot. In: Atallah, M., Blanton, M. (eds.) Algorithms and Theory of Computation Handbook, 2nd edn (two volume set). Special Topics and Techniques, pp. 31-1–31-24. CRC Press, Boca Raton (2010)

    Google Scholar 

  • Landweber, L.F., Kari, L.: The evolution of cellular computing: nature’s solution to a computational problem. Biosystems 52(1), 3–13 (1999)

    Article  Google Scholar 

  • Malvenuto, C., Reutenauer, C.: Duality between quasi-symmetrical functions and the solomon descent algebra. J. Algebra 177(3), 967–982 (1995)

    Article  MATH  Google Scholar 

  • Martins, D., Simoni, R.: Enumeration of planar metamorphic robots configurations. In: ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, ReMAR 2009, 22 June 2009, pp. 580–588. IEEE (2009)

    Google Scholar 

  • Pamecha, A., Chiang, C.J., Stein, D., Chirikjian, G.: Design and implementation of metamorphic robots. In: Proceedings of the 1996 ASME Design Engineering Technical Conference and Computers in Engineering Conference 1996, vol. 10, Irvine, California, USA. ASME (1996)

    Google Scholar 

  • Prescott, D.M.: The DNA of ciliated protozoa. Microbiol. Rev. 58(2), 233–267 (1994)

    Google Scholar 

  • Ruch, E.: Algebraic aspects of the chirality phenomenon in chemistry. Acc. Chem. Res. 5(2), 49–56 (1972)

    Article  Google Scholar 

  • Sauerbrei, S., Sydow, U., Plath, P.J.: On the characterization of foam decay with diagram lattices and majorization. Zeitschrift für Naturforschung A 61(3–4), 153–165 (2006)

    MATH  Google Scholar 

  • Schweikardt, E., Gross, M.D.: Experiments in design synthesis when behaviour is determined by shape. Pers. Ubiquit. Comput. 13, 123–132 (2011)

    Article  Google Scholar 

  • Seo, J., Yim, M., Kumar, V.: Assembly sequence planning for constructing planar structures with rectangular modules. In: IEEE International Conference on Robotics and Automation (ICRA) 2016, pp. 5477–5482. IEEE (2016)

    Google Scholar 

  • Stanley, R.P.: Differential posets. J. Am. Math. Soc. 1, 919–961 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  • Stanley, R.P.: Variations on differential posets. In: Invariant theory and tableaux. IMA Vol. Math. Appl. 19, 145–165. Springer, New York (1990)

    Google Scholar 

  • Tolley, M.T., Lipson, H.: On-line assembly planning for stochastically reconfigurable systems. Int. J. Robot. Res. 30(13), 1566–1584 (2011)

    Article  Google Scholar 

  • Winfree, E.: Algorithmic self-assembly of DNA: theoretical motivations and 2D assembly experiments. J. Biomol. Struct. Dyn. 11, 263–270 (2000)

    Article  Google Scholar 

  • Yim, M., Shen, W.M., Salemi, B., Rus, D., Moll, M., Lipson, H., Klavins, E., Chirikjian, G.S.: Modular self-reconfigurable robot systems [grand challenges of robotics]. IEEE Robot. Autom. Mag. 14(1), 43–52 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Montreal, QC, Canada

    Octavian Iordache

Authors
  1. Octavian Iordache
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Octavian Iordache .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Iordache, O. (2017). Assembling and Configuring. In: Implementing Polytope Projects for Smart Systems. Studies in Systems, Decision and Control, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-52551-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-52551-8_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52550-1

  • Online ISBN: 978-3-319-52551-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation