Shape Complexes for Metamorhpic Robots

A metamorphic robotic system is an aggregate of identical robot units which can individually detach and reattach in such a way as to change the global shape of the system. We introduce a mathematical framework for defining and analyzing general metamorphic systems. This formal structure combined with ideas from geometric group theory leads to a natural extension of a configuration space for metamorphic systems — the shape complex — which is especially adapted to parallelization. We present an algorithm for optimizing reconfiguration sequences with respect to elapsed time. A universal geometric property of shape complexes — non-positive curvature — is the key to proving convergence to the globally time-optimal solution.

[1]  Gregory S. Chirikjian,et al.  Bounds for self-reconfiguration of metamorphic robots , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[2]  Eiichi Yoshida,et al.  Distributed formation control for a modular mechanical system , 1997, Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems. Innovative Robotics for Real-World Applications. IROS '97.

[3]  David B. A. Epstein,et al.  Word processing in groups , 1992 .

[4]  Satoshi Murata,et al.  Self- As sembling Machine , 1994 .

[5]  Craig D. McGray,et al.  Self-reconfigurable molecule robots as 3D metamorphic robots , 1998, Proceedings. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory, Practice and Applications (Cat. No.98CH36190).

[6]  Graham A. Niblo,et al.  The geometry of cube complexes and the complexity of their fundamental groups , 1998 .

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

[8]  Zack J. Butler,et al.  Distributed motion planning for modular robots with unit-compressible 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).

[9]  Xiao-Song Lin,et al.  Configuration spaces and braid groups on graphs in robotics , 2001 .

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

[11]  Nancy M. Amato,et al.  Distributed reconfigurtion of metamorphic robot chains , 2000, PODC.

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

[13]  Nancy M. Amato,et al.  Distributed reconfiguration of metamorphic robot chains , 2004, PODC '00.

[14]  Mark H. Yim,et al.  Rhombic dodecahedron shape for self-assembling robots , 1997 .

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

[16]  Leonidas J. Guibas.  Controlled Module Density Helps Reconfiguration Planning , 2000 .

[17]  Ying Zhang,et al.  Distributed Control for 3D Metamorphosis , 2001, Auton. Robots.

[18]  Zack J. Butler,et al.  Distributed Motion Planning for 3D Modular Robots with Unit-Compressible Modules , 2002, WAFR.

[19]  Craig D. McGray,et al.  The self-reconfiguring robotic molecule: design and control algorithms , 1998 .

[20]  H. Kurokawa,et al.  Self-assembling machine , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.