Research Papers

Optimal Distribution of Active Modules in Reconfiguration Planning of Modular Robots

[+] Author and Article Information
Meibao Yao

Deep Space Exploration Research Center,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: meibaoyao@gmail.com

Xueming Xiao

School of Opto-Electronic Engineering,
Changchun University of
Science and Technology,
Changchun 130022, China
e-mail: alexcapshow@gmail.com

Christoph H. Belke

Reconfigurable Robotics Lab,
École Polytechnique Fédérale de Lausanne,
Lausanne 1015, Switzerland
e-mail: christoph.belke@epfl.ch

Hutao Cui

Deep Space Exploration Research Center,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: cuiht@hit.edu.cn

Jamie Paik

Reconfigurable Robotics Lab,
École Polytechnique Fédérale de Lausanne,
Lausanne 1015, Switzerland
e-mail: jamie.paik@epfl.ch

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received March 31, 2018; final manuscript received November 5, 2018; published online December 17, 2018. Assoc. Editor: Robert J. Wood.

J. Mechanisms Robotics 11(1), 011017 (Dec 17, 2018) (9 pages) Paper No: JMR-18-1092; doi: 10.1115/1.4041972 History: Received March 31, 2018; Revised November 05, 2018

Reconfigurability in versatile systems of modular robots is achieved by appropriately actuating individual modular units. Optimizing the distribution of active and passive modules in modular architecture can significantly reduce both cost and energy of a reconfiguration task. This paper presents a methodology for planning this distribution in modular robots, resulting in a minimum number of active modules that guarantees the capability to reconfigure. We discuss the optimal distribution problem in layout-based and target-based planning schemes such that modular robots can instantly respond to reconfiguration commands with either an initial planar layout or a target configuration as input. We propose heuristic algorithms as solutions for the different scenarios, which we demonstrate by applying them to Mori, a modular origami robot, in simulation. The results show that our algorithms yield high-quality distribution schemes in reduced time, and are thus viable for real-time applications in modular robotic systems.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Pfotzer, L. , Ruehl, S. , Heppner, G. , Rönnau, A. , and Dillmann, R. , 2014, “ Kairo 3: A Modular Reconfigurable Robot for Search and Rescue Field Missions,” IEEE International Conference on Robotics and Biomimetics (ROBIO), Bali, Indonesia, Dec. 5–10, pp. 205–210.
Schmitz, A. , Maiolino, P. , Maggiali, M. , Natale, L. , Cannata, G. , and Metta, G. , 2011, “ Methods and Technologies for the Implementation of Large-Scale Robot Tactile Sensors,” IEEE Trans. Rob., 27(3), pp. 389–400. [CrossRef]
Harada, K. , Oetomo, D. , Susilo, E. , Menciassi, A. , Daney, D. , Merlet, J.-P. , and Dario, P. , 2010, “ A Reconfigurable Modular Robotic Endoluminal Surgical System: Vision and Preliminary Results,” Robotica, 28(2), pp. 171–183. [CrossRef]
Yim, M. , Roufas, K. , Duff, D. , Zhang, Y. , Eldershaw, C. , and Homans, S. , 2003, “ Modular Reconfigurable Robots in Space Applications,” Auton. Rob., 14(2/3), pp. 225–237. [CrossRef]
Yao, M. , Xiao, X. , Tian, Y. , and Cui, H. , 2018, “ A Two-Time Scale Control Scheme for On-Orbit Manipulation of Large Flexible Module,” Acta Astronaut., (accepted).
Chen, I. M. , and Yang, G. , 1998, “ Automatic Model Generation for Modular Reconfigurable Robot Dynamics,” ASME J. Dyn. Syst. Meas. Control, 120(3), pp. 346–352. [CrossRef]
Meister, E. , Nosov, E. , and Levi, P. , 2013, “ Automatic Onboard and Online Modelling of Modular and Self-Reconfigurable Robots,” Sixth IEEE Conference on Robotics, Automation and Mechatronics (RAM), Manila, Philippines, Nov. 12–15, pp. 91–96.
Yao, M. , Belke, C. H. , Cui, H. , and Paik, J. , 2018, “ A Reconfiguration Strategy for Modular Robots Using Origami Folding,” Int. J. Rob. Res., (accepted).
Yang, G. , and Chen, I.-M. , 2000, “ Task-Based Optimization of Modular Robot Configurations: Minimized Degree-of-Freedom Approach,” Mech. Mach. Theory, 35(4), pp. 517–540. [CrossRef]
Bi, Z. , and Zhang, W.-J. , 2001, “ Concurrent Optimal Design of Modular Robotic Configuration,” J. Rob. Syst., 18(2), pp. 77–87. [CrossRef]
Wu, W. , Guan, Y. , Yang, Y. , and Dong, B. , 2016, “ Multi-Objective Configuration Optimization of Assembly-Level Reconfigurable Modular Robots,” IEEE International Conference on Information and Automation (ICIA), Ningbo, China, Aug. 1–3, pp. 528–533.
Yao, M. , Cui, H. , Xiao, X. , Belke, C. H. , and Paik, J. , 2018, “ Towards Peak Torque Minimization for Modular Self-Folding Robots,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain, Oct. 1–5, pp. 7975–7982.
Casal, A. , and Yim, M. H. , 1999, “ Self-Reconfiguration Planning for a Class of Modular Robots,” Proc. SPIE, 3839, pp. 246–257.
Hou, F. , and Shen, W.-M. , 2010, “ On the Complexity of Optimal Reconfiguration Planning for Modular Reconfigurable Robots,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 2791–2796.
Spröwitz, A. , Moeckel, R. , Vespignani, M. , Bonardi, S. , and Ijspeert, A. , 2014, “ Roombots: A Hardware Perspective on 3D Self-Reconfiguration and Locomotion With a Homogeneous Modular Robot,” Rob. Auton. Syst., 62(7), pp. 1016–1033. [CrossRef]
Huang, J.-L. , Zhakypov, Z. , Sonar, H. , and Paik, J. , 2018, “ A Reconfigurable Interactive Interface for Controlling Robotic Origami in Virtual Environments,” Int. J. Rob. Res., 37(6), pp. 629–647. [CrossRef]
Gilpin, K. , and Rus, D. , 2010, “ Modular Robot Systems,” IEEE Rob. Autom. Mag., 17(3), pp. 38–55. [CrossRef]
Moubarak, P. , and Ben-Tzvi, P. , 2012, “ Modular and Reconfigurable Mobile Robotics,” Rob. Auton. Syst., 60(12), pp. 1648–1663. [CrossRef]
Kurokawa, H. , Tomita, K. , Kamimura, A. , Kokaji, S. , Hasuo, T. , and Murata, S. , 2008, “ Distributed Self-Reconfiguration of m-Tran III Modular Robotic System,” Int. J. Rob. Res., 27(3–4), pp. 373–386. [CrossRef]
Yim, M. , Duff, D. G. , and Roufas, K. D. , 2000, “ PolyBot: A Modular Reconfigurable Robot,” IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, Apr. 24–28, pp. 514–520.
Jorgensen, M. W. , Ostergaard, E. H. , and Lund, H. H. , 2004, “ Modular ATRON: Modules for a Self-Reconfigurable Robot,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Sendai, Japan, Sept. 28–Oct. 2, pp. 2068–2073.
Detweiler, C. , Vona, M. , Yoon, Y. , Yun, S.-K. , and Rus, D. , 2007, “ Self-Assembling Mobile Linkages,” IEEE Rob. Autom. Mag., 14(4), pp. 45–55. [CrossRef]
Detweiler, C. , Vona, M. , Kotay, K. , and Rus, D. , 2006, “ Hierarchical Control for Self-Assembling Mobile Trusses With Passive and Active Links,” IEEE International Conference on Robotics and Automation (ICRA), Orlando, FL, May 15–19, pp. 1483–1490.
Yun, S.-K. , and Rus, D. , 2011, “ Optimal Self Assembly of Modular Manipulators With Active and Passive Modules,” Auton. Rob., 31(2–3), pp. 183–207. [CrossRef]
Yun, S.-K. , and Rus, D. , 2008, “ Self Assembly of Modular Manipulators With Active and Passive Modules,” IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, May 19–23, pp. 1477–1482.
Christensen, D. J. , Schultz, U. P. , and Stoy, K. , 2013, “ A Distributed and Morphology-Independent Strategy for Adaptive Locomotion in Self-Reconfigurable Modular Robots,” Rob. Auton. Syst., 61(9), pp. 1021–1035. [CrossRef]
Baca, J. , Pagala, P. , Rossi, C. , and Ferre, M. , 2015, “ Modular Robot Systems Towards the Execution of Cooperative Tasks in Large Facilities,” Rob. Auton. Syst., 66, pp. 159–174. [CrossRef]
Werfel, J. , and Nagpal, R. , 2008, “ Three-Dimensional Construction With Mobile Robots and Modular Blocks,” Int. J. Rob. Res., 27(3–4), pp. 463–479. [CrossRef]
Paik, J. K. , Byoungkwon, A. , Rus, D. , and Wood, R. J. , 2012, “ Robotic Origamis: Self-Morphing Modular Robot,” Second International Conference on Morphological Computation (ICMC), Venice, Italy, Sept. 12–14, Paper No. EPFL-CONF-206919.
Firouzeh, A. , and Paik, J. , 2015, “ Robogami: A Fully Integrated Low-Profile Robotic Origami,” ASME J. Mech. Rob., 7(2), p. 021009. [CrossRef]
An, B. , and Rus, D. , 2014, “ Designing and Programming Self-Folding Sheets,” Rob. Auton. Syst., 62(7), pp. 976–1001. [CrossRef]
Zuliani, F. , Liu, C. , Paik, J. , and Felton, S. M. , 2018, “ Minimally Actuated Transformation of Origami Machines,” IEEE Rob. Autom. Lett., 3(3), pp. 1426–1433. [CrossRef]
Zhakypov, Z. , Falahi, M. , Shah, M. , and Paik, J. , 2015, “ The Design and Control of the Multi-Modal Locomotion Origami Robot, Tribot,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany, Sept. 28–Oct. 2, pp. 4349–4355.
Zhakypov, Z. , and Paik, J. , 2017, “ Design Methodology for Constructing Multimaterial Origami Robots and Machines,” IEEE Trans. Rob., 34(1), pp. 151–165. [CrossRef]
Salerno, M. , Firouzeh, A. , and Paik, J. , 2017, “ A Low Profile Electromagnetic Actuator Design and Model for an Origami Parallel Platform,” ASME J. Mech. Rob., 9(4), p. 041005. [CrossRef]
Belke, C. H. , and Paik, J. , 2017, “ Mori: A Modular Origami Robot,” IEEE/ASME Trans. Mechatronics, 22(5), pp. 2153–2164. [CrossRef]
Straub, R. , and Prautzsch, H. , 2011, “ Creating Optimized Cut-out Sheets for Paper Models From Meshes,” KIT, Fakultät für Informatik, Karlsruhe, Baden-Württemberg, Germany.
Pardalos, P. M. , Mavridou, T. , and Xue, J. , 1998, “ The Graph Coloring Problem: A Bibliographic Survey,” Handbook of Combinatorial Optimization, Springer, Berlin, pp. 1077–1141.
Karp, R. M. , 1972, “ Reducibility Among Combinatorial Problems,” Complexity of Computer Computations, Springer, Berlin, pp. 85–103.
Bender, E. A. , and Wilf, H. S. , 1985, “ A Theoretical Analysis of Backtracking in the Graph Coloring Problem,” J. Algorithms, 6(2), pp. 275–282. [CrossRef]
Salari, E. , and Eshghi, K. , 2008, “ An ACO Algorithm for the Graph Coloring Problem,” Int. J. Contemp. Math. Sci., 3(6), pp. 293–304.


Grahic Jump Location
Fig. 1

An overview of our method for planning distribution of active modules in modular robots

Grahic Jump Location
Fig. 7

A scalable tetrahedron, its optimal initial layout, and the distribution of active modules

Grahic Jump Location
Fig. 3

An initial layout resulting in two feasible 3D shapes, a boat and a quadruped, using the layout-based planner. A simplified actuation sequence is shown for each 3D shape.

Grahic Jump Location
Fig. 4

Four initial layouts with two distribution schemes each, generated by two layout-based planning algorithms

Grahic Jump Location
Fig. 5

Computational efficiency of the layout-based algorithm compared to the k-coloring approach

Grahic Jump Location
Fig. 6

Two 3D shapes with three initial layouts each, generated by the target-based approach, one of which is optimal: (a) an octahedron and (b) a quadruped

Grahic Jump Location
Fig. 2

The reconfiguration procedure of the Mori robotic platform: (a) an initial layout is shaped when each triangular module connects to other modular units, (b) the aggregates are actuated with a controlled sequence of modules to perform folding motion during the reconfiguration (robotic motion), and (c) the desired 3D configuration of a quadruped comes into conformation



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In