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Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers

Authors:

Hugo A. Akitaya,

Esther M. Arkin,

Erik D. Demaine,

Vida Dujmović,

Robin Flatland,

André van Renssen,

Vera SacristánAuthors Info & Claims

Algorithmica, Volume 83, Issue 5

Pages 1316 - 1351

https://doi.org/10.1007/s00453-020-00784-6

Published: 01 May 2021 Publication History

Abstract

We present the first universal reconfiguration algorithm for transforming a modular robot between any two facet-connected square-grid configurations using pivot moves. More precisely, we show that five extra “helper” modules (“musketeers”) suffice to reconfigure the remaining n modules between any two given configurations. Our algorithm uses

O (n^{2})

pivot moves, which is worst-case optimal. Previous reconfiguration algorithms either require less restrictive “sliding” moves, do not preserve facet-connectivity, or for the setting we consider, could only handle a small subset of configurations defined by a local forbidden pattern. Configurations with the forbidden pattern do have disconnected reconfiguration graphs (discrete configuration spaces), and indeed we show that they can have an exponential number of connected components. But forbidding the local pattern throughout the configuration is far from necessary, as we show that just a constant number of added modules (placed to be freely reconfigurable) suffice for universal reconfigurability. We also classify three different models of natural pivot moves that preserve facet-connectivity, and show separations between these models.

References

[1]

Abel, Z., Kominers, S.D.: Pushing hypercubes around. CoRR abs/0802.3414 (2008)

[2]

An, B.K.: EM-Cube: cube-shaped, self-reconfigurable robots sliding on structure surfaces. In: Proceedings of IEEE International Conference on Robotics and Automation (ICRA), pp. 3149–3155 (2008)

[3]

Ayanian, N., White, P.J., Hálász, Á., Yim, M., Kumar, V.: Stochastic control for self-assembly of XBots. In: Proceedings of ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC-CIE) (2008)

[4]

Benbernou, N.M.: Geometric algorithms for reconfigurable structures. Ph.D. Thesis, Massachusetts Institute of Technology (2011)

[5]

Chennareddy S, Agrawal A, and Karuppiah A Modular self-reconfigurable robotic systems: a survey on hardware architectures J. Robot. 2017 2017 5013532

[6]

Chirikjian, G.S.: Kinematics of a metamorphic robotic system. In: Proceedings of IEEE international conference on robotics and automation (ICRA), vol. 1, pp. 449–455 (1994)

[7]

Dumitrescu A and Pach J Pushing squares around Graphs Comb. 2006 22 1 37-50

[8]

Dumitrescu A, Suzuki I, and Yamashita M Motion planning for metamorphic systems: feasibility, decidability, and distributed reconfiguration IEEE Trans. Robot. 2004 20 3 409-418

[9]

Fitch, R., Butler, Z., Rus, D.: Reconfiguration planning for heterogeneous self-reconfiguring robots. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), vol. 3, pp. 2460–2467 (2003)

[10]

Hemmerling A Labyrinth Problems: Labyrinth-Searching Abilities of Automata, Teubner-Texte zur Mathematik (TTZM) 1989 Berlin Springer

[11]

Kurokawa, H., Murata, S., Yoshida, E., Tomita, K., Kokaji, S.: A 3-D self-reconfigurable structure and experiments. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), vol. 2, pp. 860–865 (1998)

[12]

Larkworthy T and Ramamoorthy S A characterization of the reconfiguration space of self-reconfiguring robotic systems Robotica 2011 29 1 73-85

[13]

Michail O, Skretas G, and Spirakis PG On the transformation capability of feasible mechanisms for programmable matter J. Comput. Syst. Sci. 2019 102 18-39

[14]

Murata, S., Kurokawa, H., Kokaji, S.: Self-assembling machine. In: Proceedings of IEEE International Conference on Robotics and Automation (ICRA), vol. 1, pp. 441–448 (1994)

[15]

Murata S, Yoshida E, Kamimura A, Kurokawa H, Tomita K, and Kokaji S M-TRAN: self-reconfigurable modular robotic system IEEE/ASME Trans. Mechatron. 2002 7 4 431-441

[16]

Nguyen, A., Guibas, L.J., Yim, M.: Controlled module density helps reconfiguration planning. In: Proceedings of 4th International Workshop on Algorithmic Foundations of Robotics (WAFR), pp. 23–36 (2000)

[17]

Østergaard EH, Kassow K, Beck R, and Lund HH Design of the ATRON lattice-based self-reconfigurable robot Auton. Robots 2006 21 2 165-183

[18]

Rus, D., Vona, M.: A physical implementation of the self-reconfiguring crystalline robot. In: Proceedings of IEEE International Conference on Robotics and Automation (ICRA), vol. 2, pp. 1726–1733 (2000)

[19]

Salemi, B., Moll, M., Shen, W.M.: SUPERBOT: a deployable, multi-functional, and modular self-reconfigurable robotic system. In: Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3636–3641 (2006)

[20]

Stoy K, Brandt D, and Christensen DJ Self-Reconfigurable Robots: An Introduction 2010 Cambridge MIT Press

[21]

Sung, C., Bern, J., Romanishin, J., Rus, D.: Reconfiguration planning for pivoting cube modular robots. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp. 1933–1940 (2015)

[22]

Unsal, C., Kiliccote, H., Khosla, P.: I(CES)-Cubes: a modular self-reconfigurable bipartite robotic system. In: Proceedings of SPIE Conference on Mobile Robots and Autonomous Systems, vol. 3839, pp. 258–269 (1999)

[23]

Yim M, Shen W, Salemi B, Rus D, Moll M, Lipson H, Klavins E, and Chirikjian GS Modular self-reconfigurable robot systems IEEE Robot. Autom. Mag. 2007 14 1 43-52

[24]

Zykov, V., Chan, A., Lipson, H.: Molecubes: an open-source modular robotic kit. In: IROS-2007 Self-Reconfigurable Robotics Workshop (2007)

Cited By

Fekete SKramer PRieck CScheffer CSchmidt A(2024)Efficiently reconfiguring a connected swarm of labeled robotsAutonomous Agents and Multi-Agent Systems10.1007/s10458-024-09668-338:2Online publication date: 7-Aug-2024
https://dl.acm.org/doi/10.1007/s10458-024-09668-3
Almalki NGupta SMichail O(2024)On the Exponential Growth of Geometric ShapesAlgorithmics of Wireless Networks10.1007/978-3-031-74580-5_2(16-30)Online publication date: 5-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-74580-5_2
Fei JJia QChen GLi TWang RZhang X(2023)Genetic algorithm-based optimal design of modular robot topology based on distributed parallel kinematic modeling and analysisEngineering Applications of Artificial Intelligence10.1016/j.engappai.2023.106251123:PAOnline publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1016/j.engappai.2023.106251
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Published In

cover image Algorithmica

Algorithmica Volume 83, Issue 5

May 2021

439 pages

ISSN:0178-4617

Issue’s Table of Contents

© Springer Science+Business Media, LLC, part of Springer Nature 2021.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 May 2021

Accepted: 13 November 2020

Received: 11 September 2019

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Cited By

Fekete SKramer PRieck CScheffer CSchmidt A(2024)Efficiently reconfiguring a connected swarm of labeled robotsAutonomous Agents and Multi-Agent Systems10.1007/s10458-024-09668-338:2Online publication date: 7-Aug-2024
https://dl.acm.org/doi/10.1007/s10458-024-09668-3
Almalki NGupta SMichail O(2024)On the Exponential Growth of Geometric ShapesAlgorithmics of Wireless Networks10.1007/978-3-031-74580-5_2(16-30)Online publication date: 5-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-74580-5_2
Fei JJia QChen GLi TWang RZhang X(2023)Genetic algorithm-based optimal design of modular robot topology based on distributed parallel kinematic modeling and analysisEngineering Applications of Artificial Intelligence10.1016/j.engappai.2023.106251123:PAOnline publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1016/j.engappai.2023.106251
Fekete SKeldenich PKosfeld RRieck CScheffer C(2023)Connected coordinated motion planning with bounded stretchAutonomous Agents and Multi-Agent Systems10.1007/s10458-023-09626-537:2Online publication date: 17-Oct-2023
https://dl.acm.org/doi/10.1007/s10458-023-09626-5
Connor MMichail O(2022)Centralised Connectivity-Preserving Transformations by Rotation: 3 Musketeers for All Orthogonal Convex ShapesAlgorithmics of Wireless Networks10.1007/978-3-031-22050-0_5(60-76)Online publication date: 8-Sep-2022
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Michail OSkretas GSpirakis P(2021)Distributed computation and reconfiguration in actively dynamic networksDistributed Computing10.1007/s00446-021-00415-535:2(185-206)Online publication date: 19-Dec-2021
https://dl.acm.org/doi/10.1007/s00446-021-00415-5
Connor MMichail OPotapov I(2021)Centralised Connectivity-Preserving Transformations for Programmable Matter: A Minimal Seed ApproachAlgorithms for Sensor Systems10.1007/978-3-030-89240-1_4(45-60)Online publication date: 9-Sep-2021
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Almethen AMichail OPotapov I(2021)Distributed Transformations of Hamiltonian Shapes Based on Line MovesAlgorithms for Sensor Systems10.1007/978-3-030-89240-1_1(1-16)Online publication date: 9-Sep-2021
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