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The Kinematics of Hyper-Redundant Robots

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Essays on Mathematical Robotics

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 104))

Abstract

Hyper-Redundant robots have a large or infinite degree of kinematic redundancy. This paper reviews some simple hyper-redundant robot modeling and task planning techniques. These methods are based on a ‘backbone curve’ that captures the robot’s macroscopic geometric features. The inverse kinematic, or ‘hyper-redundancy resolution,’ problem reduces to determining the time varying backbone curve behavior. ‘Modal’ and ‘optimal’ hyper-redundancy resolution methods are reviewed. In addition to end-effector placement, we also consider how the backbone curve model can be used to implement locomotion and tentacle-like grasping. These ideas have been implemented on a 30 degree-of-freedom robot prototype.

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References

  1. V.V. Anderson and R.C. Horn, Tensor-arm manipulator design, ASME Trans., 67-DE- 57:1–12, 1967.

    Google Scholar 

  2. J. Baillieul, Kinematic programming alternatives for redundant manipulators, In Proc. IEEE Int., Conf. on Robotics and Automation, pages 722–728, St. Louis, MO, March 1985.

    Google Scholar 

  3. S. Bennet, T. Mcconnel, and S.L. Trubatch, Quantitative analysis of the speed of snakes as a function of peg spacing, J. Experimental Biology, pages 161–165, 1974.

    Google Scholar 

  4. J. Burdick, J. Radford, and S. Chirikjian, A sidewinding gait for hyperredundant robots, In Proc. IEEE. Int. Conf on Robotics and Automation, Atlanta, GA, May 1993.

    Google Scholar 

  5. G.S. Chirikjian, Theory and Applications of Hyper-Redundant Robotic Manipulators, PhD thesis, California Institute of Technology, June 1994.

    Google Scholar 

  6. G.S. Chirikjian and J.W. Burdick, An obstacle avoidance algorithm for hyperredundant manipulators, In IEEE Int. Conf. on Robotics and Automation, Cincinnati, OH, May 14–18, 1990.

    Google Scholar 

  7. G.S. Chirikjian and J.W. Burdick, Design, implementation,and experiments with a thirty degree-of-freedom `hyper-redundant’ robot, In Proc. IEEE Int. Conf. on Robotics and Automation, Atlanta, GA, May 1993.

    Google Scholar 

  8. G.S. Chirikjian and J.W. Burdick, Experiments in hyper-redundant manipulation, In Video Proceedings. IEEE Int. Conf. on Robotics and Automation, Atlanta, GA, May 1993.

    Google Scholar 

  9. G.S. Chirikjian and J.W. Burdick, A modal approach to hyper-redundant manipulator kinematics, IEEE Trans. on Robotics and Automation, 10(3):343–354, 1994.

    Article  Google Scholar 

  10. G.S. Chirikjian and J.W. Burdick, Kinematically optimal hyper-redundant manipulator configurations, (to appear) IEEE Trans. on Robotics and Automation, 1995.

    Google Scholar 

  11. G.S. Chirikjian and J.W. Burdick, The kinematics of hyper-redundant robot locomotion, (to appear) IEEE Trans. on Robotics and Automation, 1995.

    Google Scholar 

  12. T.S. Drozdaa, Spine robot… the verdict’s yet to come, Manufacturing Engineering, 93 (3):110–112, Sept. 1984.

    Google Scholar 

  13. A. Morecki et al., Robotic system - elephant trunk type elastic manipulator combined with a quadruped walking machine,In Proc. Second Int. Conf. on Robotics and Factories of the Future, pages 649–656, San Diego, CA, July 1987.

    Google Scholar 

  14. J. GRAY, The mechanism of locomotion in snakes, J. Experimental Biology,23:101–120, 1946.

    Google Scholar 

  15. A. HAYASHI, J. PARK, and B.J. KUIPERS, Toward planning and control of highly redundant manipulators, In Proc. Fifth IEEE Int. Symp. on Intelligent Control, 1990.

    Google Scholar 

  16. S. Hirose and A. Morishima, Design and control of a mobile robot with articulated body, Int. J. of Robotics Research, 9(2):99–114, 1990.

    Article  Google Scholar 

  17. S. Hirose and Y. Umetani, Kinematic control of active cord mechanism with tactile sensors, In Proc. 2nd Int. CISM-IFT Symp. on Theory and Practice of Robots and Manipulators, pages 241–252, 1976.

    Google Scholar 

  18. M. Ivanescu and I. Badea, Dynamic control for a tentacle manipulator, In Proc. Int. Conf. on Robotics and Factories of the Future, pages 317–328, Charlotte, NC, Dec. 1984.

    Google Scholar 

  19. B.C. Jayne, Kinematics of terrestrial snake locomotion, Copeia, (4):915–927, 1986.

    Article  Google Scholar 

  20. H.D. Jones, Kinematics of terrestrial snake locomotion of agriolimax reticulatus (mollusca: Gastropoda), J. Zool. Lond., 171:489–498, 1973.

    Article  Google Scholar 

  21. C.A. Klein and C.H. Huang, Review of the pseudoinverse for control of kinematically redundant manipulators, IEEE Trans. on Systems, Man, and Cybernetcs, March 1983.

    Google Scholar 

  22. A. Lewis, J. Ostrowski, R. Murray, and J. Burdick, Nonholonomic mechanics and locomotion: the snakeboard example, In Proc. IEEE Int. Conf. on Robotics and Automation,pages 2391–2397, San Diego, CA, May 1994.

    Google Scholar 

  23. H.W. Lissmann, Rectilinear locomotion in a snake (boa occidentalis), J. Experimental Biology, 26:368–379, 1950.

    Google Scholar 

  24. F. Naccarato and P.C. Hughes, An inverse kinematics algorithm for a highly redundant variable-geometry-truss manipulator, In Proc. 3rd Annual Conf. on Aerospace Computational Control, Dec. 1989.

    Google Scholar 

  25. J. Ostrowski, J. Burdick, R. Murray, and A. Lewis, The mechanics of undulatory locomotion: the mixed dynamic and kinematic case,In IEEE Int. Conf. on Robotics and Automation, Nagoya, Japan, May 1995.

    Google Scholar 

  26. J.S. Pettinato and H.E. Stephanou, Manipulability and stability of a tentacle based robot manipulator, In Proc. Int. Conf. on Robotics and Automation, pages 458–463, Scottsdale, AZ, May 1989.

    Google Scholar 

  27. R.J. Salerno, C.F. Reinholtz, and H.H. Robertshaw, Shape control of high degree-of-freedom variable geometry trusses, In Proc. Workshop on Computational Aspects in the Control of Flexible Systems,part 2, Williamsburg, VA, July 1988.

    Google Scholar 

  28. H. Seraji, Configuration control of redundant manipulators: Theory and implementation, IEEE Trans. on Robotics and Automation, 5(4):472–490, August 1989.

    Article  Google Scholar 

  29. M.K. Seymour, Locomotion and coelomic pressure in lumbricus terrestris 1., J. Experimental Biology,51:47–58, 1969.

    Google Scholar 

  30. D. Tesar and M.S. Butler, A generalized modular architecture for robot structures,ASME Manufacturing Review,2(2):91–118, June 1989.

    Google Scholar 

  31. J.F. Wilson and U. Mahajan, The mechanics and positioning of highly flexible manipulator limbs, ASME J. of Mech., Trans., and Automation in Design, 111, 1989.

    Google Scholar 

  32. W.B. Yapp, Locomotion of worms, Nature, Lond., (177):614–615, 1956.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Engineering and Applied Science, California Institute of Technology, Mail Code 104-44, Pasadena, CA, 91125, USA

    Joel W. Burdick & Gregory S. Chirikjian

Authors
  1. Joel W. Burdick
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  2. Gregory S. Chirikjian
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Editor information

Editors and Affiliations

  1. College of Engineering, Boston University, Boston, MA, 02215-2407, USA

    John Baillieul

  2. Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, 94720-1770, USA

    Shankar S. Sastry

  3. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08903, USA

    Hector J. Sussmann

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© 1998 Springer Science+Business Media New York

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Burdick, J.W., Chirikjian, G.S. (1998). The Kinematics of Hyper-Redundant Robots. In: Baillieul, J., Sastry, S.S., Sussmann, H.J. (eds) Essays on Mathematical Robotics. The IMA Volumes in Mathematics and its Applications, vol 104. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1710-7_3

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  • DOI: https://doi.org/10.1007/978-1-4612-1710-7_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7251-9

  • Online ISBN: 978-1-4612-1710-7

  • eBook Packages: Springer Book Archive

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