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A general stiffness model for programmable matter and modular robotic structures

Published online by Cambridge University Press:  14 January 2011

Paul J. White ,
Shai Revzen ,
Chris E. Thorne  and
Mark Yim
Paul J. White*
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, USA
Shai Revzen
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, USA
Chris E. Thorne
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, USA
Mark Yim
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, USA
*
*Corresponding author. E-mail: whitepj@seas.upenn.edu
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Summary

The fields of modular reconfigurable robotics and programmable matter study how to compose functionally useful systems from configurations of modules. In addition to the external shape of a module configuration, the internal arrangement of modules and bonds between them can greatly impact functionally relevant mechanical properties such as load bearing ability. A fast method to evaluate the mechanical property aids the search for an arrangement of modules achieving a desired mechanical property as the space of possible configurations grows combinatorially. We present a fast approximate method where the bonds between modules are represented with stiffness matrices that are general enough to represent a wide variety of systems and follows the natural modular decomposition of the system. The method includes nonlinear modeling such as anisotropic bonds and properties that vary as components flex. We show that the arrangement of two types of bonds within a programmable matter systems enables programming the apparent elasticity of the structure. We also present a method to experimentally determine the stiffness matrix for chain style reconfigurable robots. The efficacy of applying the method is demonstrated on the CKBot modular robot and two programmable matter systems: the Rubik's snake folding chain toy and a right angle tetrahedron chain called RATChET7mm. By allowing the design space to be rapidly explored we open the door to optimizing modular structures for desired mechanical properties such as enhanced load bearing and robustness.

Keywords

Modular RoboticsProgrammable MatterLumped Parameter Stiffness Model
Type
Article
Information
Robotica , Volume 29 , Special Issue 1: Robotic Self-X Systems , January 2011 , pp. 103 - 121
Copyright
Copyright © Cambridge University Press 2011

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