Programmable Assembly With Universally Foldable Strings (Moteins)

Understanding how linear strings fold into 2-D and 3-D shapes has been a long sought goal in many fields of both academia and industry. This paper presents a technique to design self-assembling and self-reconfigurable systems that are composed of strings of very simple robotic modules. We show that physical strings that are composed of a small set of discrete polygonal or polyhedral modules can be used to programmatically generate any continuous area or volumetric shape. These modules can have one or two degrees of freedom (DOFs) and simple actuators with only two or three states. We describe a subdivision algorithm to produce universal polygonal and polyhedral string folding schemas, and we prove the existence of a continuous motion to reach any such folding. This technique is validated with dynamics simulations as well as experiments with chains of modules that pack on a regular cubic lattice. We call robotic programmable universally foldable strings “moteins” as motorized proteins.

[1]  Gregory S. Chirikjian,et al.  Modular Robot Motion Planning Using Similarity Metrics , 2001, Auton. Robots.

[2]  G. Peano Sur une courbe, qui remplit toute une aire plane , 1890 .

[3]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[4]  Sheung-Hung Poon,et al.  On Unfolding 3D Lattice Polygons and 2D Orthogonal Trees , 2008, COCOON.

[5]  Devin J. Balkcom,et al.  Robotic origami folding , 2008, Int. J. Robotics Res..

[6]  Nancy M. Amato,et al.  Using motion planning to study protein folding pathways , 2001, J. Comput. Biol..

[7]  Gregory S. Chirikjian,et al.  Useful metrics for modular robot motion planning , 1997, IEEE Trans. Robotics Autom..

[8]  Jayme Luiz Szwarcfiter,et al.  Hamilton Paths in Grid Graphs , 1982, SIAM J. Comput..

[9]  George M Whitesides,et al.  Biomimetic self-assembly of a functional asymmetrical electronic device , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Gregory S. Chirikjian,et al.  Kinematics of a metamorphic robotic system , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[11]  Mark Yim,et al.  A general stiffness model for programmable matter and modular robotic structures , 2011, Robotica.

[12]  Erik D. Demaine,et al.  Reconfigurable asynchronous logic automata: (RALA) , 2010, POPL '10.

[13]  D. Hilbert Ueber die stetige Abbildung einer Line auf ein Flächenstück , 1891 .

[14]  David Eppstein,et al.  Hinged dissections of polyominoes and polyforms , 1999, CCCG.

[15]  Fumihito Arai,et al.  Control strategy for a network of cellular robots-determination of a master cell for cellular robotic network based on a potential energy , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[16]  Mark Yim,et al.  Right Angle Tetrahedron Chain Externally-Actuated Testbed (RATChET): A Shape-Changing System , 2009 .

[17]  Nancy M. Amato,et al.  A motion-planning approach to folding: from paper craft to protein folding , 2001, IEEE Transactions on Robotics and Automation.

[18]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[19]  Liang Lu,et al.  Folding cartons with fixtures: a motion planning approach , 1999, IEEE Trans. Robotics Autom..

[20]  Thierry Siméon,et al.  A random loop generator for planning the motions of closed kinematic chains using PRM methods , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[21]  N. Seeman,et al.  Synthesis from DNA of a molecule with the connectivity of a cube , 1991, Nature.

[22]  Fumio Hara,et al.  Dynamic distributed knowledge system in self-organizing robotic system: CEBOT , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[23]  H Tanaka,et al.  Programmable matter by folding , 2010, Proceedings of the National Academy of Sciences.

[24]  G. Whitesides,et al.  Self-Assembly at All Scales , 2002, Science.

[25]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

[26]  Erik D. Demaine,et al.  Reconfigurable Asynchronous Logic Automata , 2010 .

[27]  Hod Lipson,et al.  Robotics: Self-reproducing machines , 2005, Nature.

[28]  Joseph S. B. Mitchell,et al.  Locked and Unlocked Chains of Planar Shapes , 2010, Discret. Comput. Geom..

[29]  K. Dill,et al.  A simple protein folding algorithm using a binary code and secondary structure constraints. , 1995, Protein engineering.

[30]  Gregory S. Chirikjian,et al.  Modular Self-Reconfigurable Robot Systems [Grand Challenges of Robotics] , 2007, IEEE Robotics & Automation Magazine.

[31]  Philippe Bidaud,et al.  Designing Modular Lattice Systems with Chiral Space Groups , 2008, Int. J. Robotics Res..

[32]  George M. Whitesides,et al.  Beyond molecules: Self-assembly of mesoscopic and macroscopic components , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Ara Knaian,et al.  Electropermanent magnetic connectors and actuators: devices and their application in programmable matter , 2010 .

[34]  Erik D. Demaine,et al.  Hinged Dissection of Polypolyhedra , 2005, WADS.