Robotic origami folding

Origami, the art of paper sculpture, is a fresh challenge for the field of robotic manipulation, and provides a concrete example of the many difficulties and general manipulation problems faced in robotics. This paper describes our initial exploration, and highlights key problems in the manipulation, modeling, and design of foldable structures. Results include the design of the first origami-folding robot, a complete fold-sequence planner for a simple class of origami, and analysis of the kinematics of more complicated folds, including the common paper shopping bag.

[1]  D. Hilbert,et al.  Geometry and the Imagination , 1953 .

[2]  James E. pLebensohn Geometry and the Imagination , 1952 .

[3]  J. Milnor Topology from the differentiable viewpoint , 1965 .

[4]  T. Mckeown Mechanics , 1970, The Mathematics of Fluid Flow Through Porous Media.

[5]  Marvin Minsky,et al.  Manipulator Design Vignettes , 1972 .

[6]  David A. Huffman,et al.  Curvature and Creases: A Primer on Paper , 1976, IEEE Transactions on Computers.

[7]  J. Thorpe Elementary Topics in Differential Geometry , 1979 .

[8]  J. W. Humberston Classical mechanics , 1980, Nature.

[9]  Carl Friedrich Gauss Disquisitiones generales circa superficies curvas , 1981 .

[10]  Per Lötstedt Coulomb Friction in Two-Dimensional Rigid Body Systems , 1981 .

[11]  Michael A. Erdmann,et al.  On Motion Planning with Uncertainty , 1984 .

[12]  Masayuki INABA,et al.  Hand Eye Coordination in Rope Handling , 1985 .

[13]  H. Lawson The Moduli Space , 1985 .

[14]  John J. Craig,et al.  Introduction to Robotics Mechanics and Control , 1986 .

[15]  Tomas Lozano-Perez A simple motion-planning algorithm for general robot manipulators , 1986, IEEE J. Robotics Autom..

[16]  Gunter Weiss,et al.  Computer-aided treatment of developable surfaces , 1988, Comput. Graph..

[17]  P. Redont Representation and deformation of developable surfaces , 1989 .

[18]  Zexiang Li,et al.  A variational approach to optimal nonholonomic motion planning , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[19]  Phillip J. McKerrow,et al.  Introduction to robotics , 1991 .

[20]  Günter Aumann,et al.  Interpolation with developable Bézier patches , 1991, Comput. Aided Geom. Des..

[21]  Takami Yasuda,et al.  An interactive simulation system of origami based on virtual space manipulation , 1992, [1992] Proceedings IEEE International Workshop on Robot and Human Communication.

[22]  Kazuaki Iwata,et al.  Modeling of deformable thin parts for their manipulation , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[23]  S. Antman Nonlinear problems of elasticity , 1994 .

[24]  Thomas C. Hull On the Mathematics of Flat Origamis , 1994 .

[25]  Tosiyasu L. Kunii,et al.  Bending and creasing virtual paper , 1994, IEEE Computer Graphics and Applications.

[26]  J. Trinkle,et al.  On Dynamic Multi‐Rigid‐Body Contact Problems with Coulomb Friction , 1995 .

[27]  M. Kapovich,et al.  On the moduli space of polygons in the Euclidean plane , 1995 .

[28]  Meng Sun,et al.  A Technique for Constructing Developable Surfaces , 1996, Graphics Interface.

[29]  D. Stewart,et al.  AN IMPLICIT TIME-STEPPING SCHEME FOR RIGID BODY DYNAMICS WITH INELASTIC COLLISIONS AND COULOMB FRICTION , 1996 .

[30]  David Baraff,et al.  Linear-time dynamics using Lagrange multipliers , 1996, SIGGRAPH.

[31]  Kazuaki Iwata,et al.  Static analysis of deformable object grasping based on bounded force closure , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[32]  Shinichi Hirai,et al.  Modeling of plain knitted fabrics for their deformation control , 1997, Proceedings of International Conference on Robotics and Automation.

[33]  R. Connelly,et al.  The Bellows conjecture. , 1997 .

[34]  M. Anitescu,et al.  Formulating Dynamic Multi-Rigid-Body Contact Problems with Friction as Solvable Linear Complementarity Problems , 1997 .

[35]  Gregory S. Chirikjian,et al.  Inverse Kinematics of Binary Manipulators Using a Continuum Model , 1997, J. Intell. Robotic Syst..

[36]  Hirofumi Nakagaki,et al.  Study of deformation and insertion tasks of a flexible wire , 1997, Proceedings of International Conference on Robotics and Automation.

[37]  Hidefumi Wakamatsu,et al.  Dynamic analysis of rodlike object deformation towards their dynamic manipulation , 1997, Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems. Innovative Robotics for Real-World Applications. IROS '97.

[38]  Lydia E. Kavraki,et al.  Towards planning for elastic objects , 1998 .

[39]  Andrew P. Witkin,et al.  Large steps in cloth simulation , 1998, SIGGRAPH.

[40]  Helmut Pottmann,et al.  Approximation of developable surfaces with cone spline surfaces , 1998, Comput. Aided Des..

[41]  Jesse Freeman,et al.  in Morse theory, , 1999 .

[42]  M. Kapovich,et al.  Moduli Spaces of Linkages and Arrangements , 1999 .

[43]  J. Dai,et al.  Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds , 1998 .

[44]  Uri M. Ascher,et al.  Sequential Regularization Methods for Simulating Mechanical Systems with Many Closed Loops , 1999, SIAM J. Sci. Comput..

[45]  Lydia E. Kavraki,et al.  A probabilistic roadmap approach for systems with closed kinematic chains , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[46]  Johannes Wallner,et al.  Approximation algorithms for developable surfaces , 1999, Comput. Aided Geom. Des..

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

[48]  Nancy M. Amato,et al.  A Kinematics-Based Probabilistic Roadmap Method for Closed Chain Systems , 2001 .

[49]  McCarthy,et al.  Geometric Design of Linkages , 2000 .

[50]  M. Rubin Cosserat Theories: Shells, Rods and Points , 2000 .

[51]  Jeffrey C. Trinkle,et al.  Motion planning for planar n-bar mechanisms with revolute joints , 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).

[52]  Hidefumi Wakamatsu,et al.  Modeling of shape bifurcation phenomena in manipulations of deformable string objects , 2001, Adv. Robotics.

[53]  Shinichi Hirai,et al.  Robust manipulation of deformable objects by a simple PID feedback , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[54]  Shinichi Hirai,et al.  Robust grasping manipulation of deformable objects , 2001, Proceedings of the 2001 IEEE International Symposium on Assembly and Task Planning (ISATP2001). Assembly and Disassembly in the Twenty-first Century. (Cat. No.01TH8560).

[55]  Jian S. Dai,et al.  Carton manipulation analysis using configuration transformation , 2002 .

[56]  Devin J. Balkcom,et al.  A sensorless insertion strategy for rigid planar parts , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[57]  Dinesh K. Pai,et al.  STRANDS: Interactive Simulation of Thin Solids using Cosserat Models , 2002, Comput. Graph. Forum.

[58]  Jian S. Dai,et al.  Kinematics and mobility analysis of carton folds in packing manipulation based on the mechanism equivalent , 2002 .

[59]  Erik D. Demaine,et al.  Recent Results in Computational Origami , 2002 .

[60]  Kwang-Jin Choi,et al.  Stable but responsive cloth , 2002, SIGGRAPH 2002.

[61]  Jian S. Dai,et al.  An approach to carton-folding trajectory planning using dual robotic fingers , 2003, Robotics Auton. Syst..

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

[63]  Jeffrey C. Trinkle,et al.  Complete path planning for a planar 2-R manipulator with point obstacles , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[64]  J. Trinkle,et al.  THE GEOMETRY OF CONFIGURATION SPACES FOR CLOSED CHAINS IN TWO AND THREE DIMENSIONS , 2004 .

[65]  Devin J. Balkcom,et al.  Introducing robotic origami folding , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[66]  Dinesh K. Pai,et al.  A unified treatment of elastostatic contact simulation for real time haptics , 2005, SIGGRAPH Courses.

[67]  J. R. Jones,et al.  Matrix Representation of Topological Changes in Metamorphic Mechanisms , 2005 .

[68]  Ronald Fedkiw,et al.  Robust treatment of collisions, contact and friction for cloth animation , 2002, SIGGRAPH Courses.

[69]  Jian S. Dai,et al.  From Origami to a New Class of Centralized 3-DOF Parallel Mechanisms , 2007 .

[70]  R. Ho Algebraic Topology , 2022 .