Reconfiguring Chain-Type Modular Robots Based on the Carpenter’s Rule Theorem

  • Jungwon Seo
  • Steven Gray
  • Vijay Kumar
  • Mark Yim
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 68)


Reconfiguring chain-type modular robots has been considered a difficult problem scaling poorly with increasing numbers of modules. We address the reconfiguration problem for robots in 2D by presenting centralized and decentralized algorithms based on the Carpenter’s Rule Theorem [4]. The theorem guarantees the existence of instantaneous collision-free unfolding motions which monotonically increase the distance between all joint pairs until an open chain is straightened or a closed chain is convexified. The motions can be found by solving a convex program. Compared to the centralized version, the decentralized algorithm utilizes local proximity sensing and limited communications between subsets of nearby modules. Because the decentralized version reduces the number of joint pairs considered in each convex optimization, it is a practical solution for large number of modules.


Joint Angle Integral Curve Master Problem Convex Program Open Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jungwon Seo
    • 1
  • Steven Gray
    • 1
  • Vijay Kumar
    • 1
  • Mark Yim
    • 1
  1. 1.Department of Mechanical Engineering and Applied MechanicsUniversity of Pennsylvania 

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