Skip to main content
Springer Nature Link
Log in

Reconfiguring Massive Particle Swarms with Limited, Global Control

  • Conference paper
  • First Online:
Algorithms for Sensor Systems (ALGOSENSORS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 8243))

  • 1449 Accesses

Abstract

We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal such as gravity or a magnetic field. Upon activation of the field, each particle moves maximally in the same direction, until it hits a stationary obstacle or another stationary particle. In an open workspace, this system model is of limited use because it has only two controllable degrees of freedom—all particles receive the same inputs and move uniformly. We show that adding a maze of obstacles to the environment can make the system drastically more complex but also more useful. The resulting model matches ThinkFun’s Tilt puzzle.

If we are given a fixed set of stationary obstacles, we prove that it is NP-hard to decide whether a given initial configuration can be transformed into a desired target configuration. On the positive side, we provide constructive algorithms to design workspaces that efficiently implement arbitrary permutations between different configurations.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Abelson, H., Allen, D., Coore, D., Hanson, C., Homsy, G., Thomas, J., Knight, F., Nagpal, R., Rauch, E., Sussman, G.J., Weiss, R.: Amorphous computing. Commun. ACM 43(5), 74–82 (2000)

    Article  Google Scholar 

  2. Akella, S., Huang, W.H., Lynch, K.M., Mason, M.T.: Parts feeding on a conveyor with a one joint robot. Algorithmica 26(3), 313–344 (2000)

    MATH  MathSciNet  Google Scholar 

  3. Akella, S., Mason, M.T.: Using partial sensor information to orient parts. Int. J. Robot. Res. 18(10), 963–997 (1999)

    Article  Google Scholar 

  4. Becker, A., Bretl, T.: Approximate steering of a unicycle under bounded model perturbation using ensemble control. IEEE Trans. Robot. 28(3), 580–591 (2012)

    Article  Google Scholar 

  5. Becker, A., Habibi, G., Werfel, J., Rubenstein, M., McLurkin, J.: Massive uniform manipulation: controlling large populations of simple robots with a common input signal. In: IEEE International Conference on Intelligent Robots and Systems, pp. 520–527, November 2013

    Google Scholar 

  6. Becker, A., Onyuksel, C., Bretl, T.: Feedback control of many differential-drive robots with uniform control inputs. In: IEEE International Conference on Intelligent Robots and Systems, October 2012

    Google Scholar 

  7. Becker, A., Ou, Y., Kim, P., Kim, M., Julius, A.: Feedback control of many magnetized tetrahymena pyriformis cells by exploiting phase inhomogeneity. In: IEEE International Conference on Intelligent Robots and Systems, pp. 3317–3323, November 2013

    Google Scholar 

  8. Chanu, A., Felfoul, O., Beaudoin, G., Martel, S.: Adapting the clinical mri software environment for real-time navigation of an endovascular untethered ferromagnetic bead for future endovascular interventions. Magn. Reson. Med. 59(6), 1287–1297 (2008)

    Article  Google Scholar 

  9. Chiang, P.-T., Mielke, J., Godoy, J., Guerrero, J.M., Alemany, L.B., Villagómez, C.J., Saywell, A., Grill, L., Tour, J.M.: Toward a light-driven motorized nanocar: Synthesis and initial imaging of single molecules. ACS Nano 6(1), 592–597 (2011)

    Article  Google Scholar 

  10. Demaine, E.D., Demaine, M.L., O’Rourke, J.: PushPush and Push-1 are NP-hard in 2D. In: Proceedings of the 12th Annual Canadian Conference on Computational Geometry (CCCG), pp. 211–219, August 2000

    Google Scholar 

  11. Demaine, E.D., Hearn, R.A.: Playing games with algorithms: algorithmic combinatorial game theory. In: Albert, M.H., Nowakowski, R.J. (eds.) Games of No Chance 3, vol. 56, pp. 3–56. Mathematical Sciences Research Institute Publications, Cambridge University Press, Cambridge (2009)

    Chapter  Google Scholar 

  12. Donald, B.R., Levey, C.G., Paprotny, I., Rus, D.: Planning and control for microassembly of structures composed of stress-engineered mems microrobots. Int. J. Robot. Res. 32(2), 218–246 (2013)

    Article  Google Scholar 

  13. Dor, D., Zwick, U.: Sokoban and other motion planning problems. Comput. Geom. 13(4), 215–228 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. Engels, B., Kamphans, T.: On the complexity of Randolph’s robot game. Technical report, Rheinische Friedrich-Wilhelms-Universität Bonn Institut für Informatik I, University of Cologne, Germany (2005)

    Google Scholar 

  15. Erdmann, M., Mason, M.: An exploration of sensorless manipulation. IEEE J. Robot. Autom. 4(4), 369–379 (1988)

    Article  Google Scholar 

  16. Fekete S.P., Kröller, A.: Geometry-based reasoning for a large sensor network. In: Proceedings of the 22nd Annual ACM Symposium on Computational Geometry, pp. 475–476 (2006). http://www.computational-geometry.org/SoCG-videos/socg06video/acmvideos/socg06video/

  17. Fekete, S.P., Kröller, A.: Topology and routing in sensor networks. In: Kutyłowski, M., Cichoń, J., Kubiak, P. (eds.) ALGOSENSORS 2007. LNCS, vol. 4837, pp. 6–15. Springer, Heidelberg (2008)

    Google Scholar 

  18. Fekete, S.P., Kröller, A., Pfisterer, D., Fischer, S., Buschmann, C.: Neighborhood-based topology recognition in sensor networks. In: Nikoletseas, S.E., Rolim, J. (eds.) ALGOSENSORS 2004. LNCS, vol. 3121, pp. 123–136. Springer, Heidelberg (2004)

    Google Scholar 

  19. Floyd, S., Diller, E., Pawashe, C., Sitti, M.: Control methodologies for a heterogeneous group of untethered magnetic micro-robots. Int. J. Robot. Res. 30(13), 1553–1565 (2011)

    Article  Google Scholar 

  20. Frutiger, D., Kratochvil, B., Vollmers, K., Nelson, B.J.: Magmites - wireless resonant magnetic microrobots. In: IEEE International Conference on Robotics and Automation, Pasadena, CA, May 2008

    Google Scholar 

  21. Goemans, O.C., Goldberg, K., van der Stappen, A.F.: Blades: a new class of geometric primitives for feeding 3D parts on vibratory tracks. In: International Conference on Robotics and Automation, pp. 1730–1736, May 2006

    Google Scholar 

  22. Goldberg, K., Mirtich, B.V., Zhuang, Y., Craig, J., Carlisle, B.R., Canny, J.: Part pose statistics: estimators and experiments. IEEE Trans. Robot. Autom. 15(5), 849–857 (1999)

    Article  Google Scholar 

  23. Goldberg, K.Y.: Orienting polygonal parts without sensors. Algorithmica 10(2), 201–225 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  24. Hearn R.A., Demaine, E.D.: PSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation. arXiv:cs/0205005, cs.CC/0205005 (2002)

    Google Scholar 

  25. Hoffmann, M.: Motion planning amidst movable square blocks: Push-* is NP-hard. In: Canadian Conference on Computational Geometry, pp. 205–210, June 2000

    Google Scholar 

  26. Holzer, M., Schwoon, S.: Assembling molecules in atomix is hard. Theoret. Comput. Sci. 313(3), 447–462 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  27. Kahn, J., Katz, R., Pister, K.: Emerging challenges: mobile networking for smart dust. J. Comm. Net. 2, 188–196 (2000)

    Google Scholar 

  28. Khalil, I.S.M., Pichel, M.P., Reefman, B.A., Sukas, O.S., Abelmann, L., Misra, S.: Control of magnetotactic bacterium in a micro-fabricated maze. In: IEEE International Conference on Robotics and Automation, Karlsruhe, Germany, pp. 5488–5493, May 2013

    Google Scholar 

  29. Kröller, A., Fekete, S.P., Pfisterer, D., Fischer, S.: Deterministic boundary recognition and topology extraction for large sensor networks. In: Proceedings of the 17th ACM-SIAM Symposium Discrete Algorithms, pp. 1000–1009 (2006)

    Google Scholar 

  30. Leighton, F.T.: Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann, San Mateo (1991)

    Google Scholar 

  31. Lynch, K.M., Northrop, M., Pan, P.: Stable limit sets in a dynamic parts feeder. IEEE Trans. Robot. Autom. 18(4), 608–615 (2002)

    Article  Google Scholar 

  32. Moll, M., Erdmann, M.: Manipulation of pose distributions. Int. J. Robot. Res. 21(3), 277–292 (2002)

    Article  Google Scholar 

  33. Murphey, T.D., Bernheisel, J., Choi, D., Lynch, K.M.: An example of parts handling and self-assembly using stable limit sets. In: International Conference on Robots and System, pp. 1624–1629, August 2005

    Google Scholar 

  34. Murphey, T.D., Burdick, J.W.: Feedback control methods for distributed manipulation systems that involve mechanical contacts. Int. J. Robot. Res. 23(7–8), 763–781 (2004)

    Article  Google Scholar 

  35. Ou, Y., Kim, D.H., Kim, P., Kim, M.J., Julius, A.A.: Motion control of magnetized tetrahymena pyriformis cells by magnetic field with model predictive control. Int. J. Rob. Res. 32(1), 129–139 (2013)

    Article  Google Scholar 

  36. Peyer, K.E., Zhang, L., Nelson, B.J.: Bio-inspired magnetic swimming microrobots for biomedical applications. Nanoscale 5, 1259–1272 (2013)

    Article  Google Scholar 

  37. Rubenstein, M., Ahler, C., Nagpal, R.: Kilobot: a low cost scalable robot system for collective behaviors. In: IEEE International Conference on Robotics and Automation, pp. 3293–3298, May 2012

    Google Scholar 

  38. ThinkFun. Tilt: Gravity fed logic maze. http://www.thinkfun.com/tilt

  39. van der Stappen, A.F., Berretty, R.-P., Goldberg, K., Overmars, M.: Geometry and part feeding. In: Hager, G.D., Christensen, H.I., Bunke, H., Klein, R. (eds.) Sensor Based Intelligent Robots. LNCS, vol. 2238, pp. 259–281. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  40. Vartholomeos, P., Akhavan-Sharif, M., Dupont, P.E.: Motion planning for multiple millimeter-scale magnetic capsules in a fluid environment. In: IEEE International Conference on Robotics and Automation, pp. 1927–1932, May 2012

    Google Scholar 

  41. Vose, T.H., Umbanhowar, P., Lynch, K.M.: Friction-induced velocity fields for point parts sliding on a rigid oscillated plate. In: Robotics: Science and Systems, Zurich, Switzerland, June 2008

    Google Scholar 

  42. Vose, T.H., Umbanhowar, P., Lynch, K.M.: Sliding manipulation of rigid bodies on a controlled 6-DoF plate. Int. J. Robot. Res. 31(7), 819–838 (2012)

    Article  Google Scholar 

  43. Wilfong, G.: Motion planning in the presence of movable obstacles. Ann. Math. Artif. Intell. 3(1), 131–150 (1991)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

We acknowledge the helpful discussion and motivating experimental efforts with T. pyriformis cells by Yan Ou and Agung Julius at RPI and Paul Kim and MinJun Kim at Drexel University. This work was supported by the National Science Foundation under CPS-1035716.

Author information

Authors and Affiliations

  1. Department of Computer Science, Rice University, Houston, TX, 77005, USA

    Aaron Becker, Golnaz Habibi & James McLurkin

  2. Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, MA, 02139, USA

    Erik D. Demaine

  3. Department of Computer Science, TU Braunschweig, Mühlenpfordtstr. 23, 38106, Braunschweig, Germany

    Sándor P. Fekete

Authors
  1. Aaron Becker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik D. Demaine
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sándor P. Fekete
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Golnaz Habibi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. James McLurkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sándor P. Fekete .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, Ontario, Canada

    Paola Flocchini

  2. Stony Brook University, Stonybrook, New York, USA

    Jie Gao

  3. School of Computer Science, Carleton University, Ottawa, Ontario, Canada

    Evangelos Kranakis

  4. University of Paderborn, Paderborn, Germany

    Friedhelm Meyer auf der Heide

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Becker, A., Demaine, E.D., Fekete, S.P., Habibi, G., McLurkin, J. (2014). Reconfiguring Massive Particle Swarms with Limited, Global Control. In: Flocchini, P., Gao, J., Kranakis, E., Meyer auf der Heide, F. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2013. Lecture Notes in Computer Science(), vol 8243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45346-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45346-5_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45345-8

  • Online ISBN: 978-3-642-45346-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics