Strength analysis of miniature folded right angle tetrahedron chain Programmable Matter

Miniaturization of Programmable Matter is a major challenge. Much of the difficulty stems from size and power requirements of internal actuators. This paper demonstrates that external energy can be used to both move modules and actuate their bonding mechanism. It presents a lattice style Programmable Matter system whose neighbor to neighbor lattice distance is 14mm. Previous work has shown a chain of edge connected right angle tetrahedrons can fold to arbitrary shapes. To form useful shapes such as tools, the chain should be folded to meet the functional requirements of the task such as mechanical strength. This paper also introduces the analysis of the strength of Programmable Matter systems. Module connections are defined by 6DOF stiffness matrices. The paper analyzes the strength of a heterogeneous system with some rigid and some soft connections.

[1]  Pradeep K. Khosla,et al.  A multi-layered planner for self-reconfiguration of a uniform group of I-Cube modules , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[2]  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.

[3]  Shuguang Huang,et al.  The bounds and realization of spatial stiffnesses achieved with simple springs connected in parallel , 1998, IEEE Trans. Robotics Autom..

[4]  Hod Lipson,et al.  Three Dimensional Stochastic Reconfiguration of Modular Robots , 2005, Robotics: Science and Systems.

[5]  Josip Loncaric,et al.  Normal forms of stiffness and compliance matrices , 1987, IEEE Journal on Robotics and Automation.

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

[7]  Mark Yim,et al.  Dynamic Rolling for a Modular Loop Robot , 2006, ISER.

[8]  Eiichi Yoshida,et al.  Miniaturized self-reconfigurable system using shape memory alloy , 1999, Proceedings 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human and Environment Friendly Robots with High Intelligence and Emotional Quotients (Cat. No.99CH36289).

[9]  Gregory S. Chirikjian,et al.  A useful metric for modular robot motion planning , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[10]  W. McCarthy.  Programmable matter , 2000, Nature.

[11]  Kasper Støy,et al.  Using cellular automata and gradients to control self-reconfiguration , 2006, Robotics Auton. Syst..

[12]  Mark Yim,et al.  Reliable External Actuation for Extending Reachable Robotic Modular Self-Reconfiguration , 2008, ISER.

[13]  Sergei Vassilvitskii,et al.  On the general reconfiguration problem for expanding cube style modular robots , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[14]  Bruno Siciliano,et al.  Six-DOF impedance control based on angle/axis representations , 1999, IEEE Trans. Robotics Autom..

[15]  Mark Yim,et al.  Telecubes: mechanical design of a module for self-reconfigurable robotics , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[16]  Mark H. Yim,et al.  Isomorphic Gait Execution in Homogeneous Modular Robots , 2006 .

[17]  Marsette Vona,et al.  Self-reconfiguration planning with compressible unit modules , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[18]  Bruno Siciliano,et al.  Quaternion-based impedance with nondiagonal stiffness for robot manipulators , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[19]  E. Winfree,et al.  Toward reliable algorithmic self-assembly of DNA tiles: a fixed-width cellular automaton pattern. , 2008, Nano letters.

[20]  Eiichi Yoshida,et al.  A 3-D self-reconfigurable structure , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[21]  P. Breedveld,et al.  Modeling of elastically coupled bodies : Part i-General theory and geometric potential function method , 1998 .

[22]  P. Breedveld,et al.  Modeling of Elastically Coupled Bodies: Part II—Exponential and Generalized Coordinate Methods , 1998 .

[23]  Iuliu Vasilescu,et al.  Miche: Modular Shape Formation by Self-Disassembly , 2008, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[24]  Eric Klavins,et al.  Programmable parts: a demonstration of the grammatical approach to self-organization , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[25]  Mark Yim,et al.  Scalable modular self-reconfigurable robots using external actuation , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[26]  Shilong Zhang,et al.  A Finite-Element-Based Method to Determine the Spatial Stiffness Properties of a Notch Hinge , 2001 .

[27]  Henrik Hautop Lund,et al.  Modular ATRON: modules for a self-reconfigurable robot , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

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

[29]  Hod Lipson,et al.  Stochastic self-reconfigurable cellular robotics , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[30]  Seth Copen Goldstein,et al.  Claytronics: A Scalable Basis For Future Robots , 2004 .

[31]  Ernest D. Fasse,et al.  Spatial Compliance Modeling Using a Quaternion-Based Potential Function Method , 2000 .

[32]  I. Shimoyama,et al.  Two-dimensional micro-self-assembly using the surface tension of water , 1996, Proceedings of Ninth International Workshop on Micro Electromechanical Systems.