Journal of the Korean Society for Precision Engineering (한국정밀공학회지)

Korean Society for Precision Engineering (한국정밀공학회)
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Inverse Kinematics Analysis of 7-DOF Anthropomorphic Robot Arm using Conformal Geometric Algebra

등각 기하대수를 이용한 7자유도 로봇 팔의 역기구학 해석

  • 김제석 (한양대학교 자동차공학과) ;
  • 지용관 (한양대학교 자동차공학과) ;
  • 박장현 (한양대학교 미래자동차공학과)
  • Received : 2011.10.14
  • Accepted : 2012.06.12
  • Published : 2012.10.01
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Abstract

In this paper, we present an inverse kinematics of a 7-dof Anthropomorphic robot arm using conformal geometric algebra. The inverse kinematics of a 7-dof Anthropomorphic robot arm using CGA can be computed in an easy way. The geometrically intuitive operations of CGA make it easy to compute the joint angles of a 7-dof Anthropomorphic robot arm which need to be set in order for the robot to reach its goal or the positions of a redundant robot arm's end-effector. In order to choose the best solution of the elbow position at an inverse kinematics, optimization techniques have been proposed to minimize an objective function while satisfying the euler-lagrange equation.

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References

  1. Baillieul, J., "Kinematic Programming Alternatives for Redundant Manipulators," IEEE International Conference on Robotics and Automation, Vol. 2, pp. 722-728, 1985.
  2. Liegeois, A., "Automatic Supervisory Control of the Configuration and Behavior of Multibody Mechanisms," IEEE Trans. Sys. Man and Cybernetics, Vol. 7, No. 12, pp. 868-871, 1977. https://doi.org/10.1109/TSMC.1977.4309644
  3. Whitney, D. E., "The Mathematics of Coordinated Control of Prostheses and Manipulators," DTIC Document, pp. 207-220, 1972.
  4. Tolani, D., Goswami, A., and Badler, N. I., "Real-Time Inverse Kinematics Techniques for Anthropomorphic Limbs," Graphical Models, Vol. 62, No. 5, pp. 353-388, 2000. https://doi.org/10.1006/gmod.2000.0528
  5. Hildenbrand, D., Lange, H., Stock, F., and Koch, A., "Efficient Inverse Kinematics Algorithm Based on Conformal Geometric Algebra Using Reconfigurable Hardware," GRAPP Conference Madeira, 2008.
  6. Hildenbrand, D., "Geometric Computing in Computer Graphics Using Conformal Geometric Algebra," Computers & Graphics, Vol. 29, No. 5, pp. 795-803, 2005. https://doi.org/10.1016/j.cag.2005.08.028
  7. Hildenbrand, D., Bayro-Corrochano, E., and Zamora, J., "Advanced Geometric Approach for Graphics and Visual Guided Robot Object Manipulation," IEEE International Conference on Robotics and Automation, pp. 4727-4732, 2005.
  8. Hildenbrand, D., Fontijne, D., Perwass, C., and Dorst, L., "Geometric Algebra and Its Application to Computer Graphics," EUROGRAPHICS, 2004.
  9. Zamora, J. and Bayro-Corrochano, E., "Inverse Kinematics, Fixation and Grasping Using Conformal Geometric Algebra," IEEE/RSJ International Conference on Intelligent Robots and Systems, Vol. 4, pp. 3841-3846, 2004.
  10. Park, H. W., "Design and control of a redundant manipulator for humanoid robot," M.Sc. Thesis, Mechanical Engineering, KAIST, 2002.
  11. Moon, I. K., "Inverse kinematics for improving repeatability and manipulability of redundant robot arms," M.Sc. Thesis, Mechanical Design Engineering, Hanyang University, 2000.
  12. Lee, J. H., "A Study on Optimal Path Planning of 4- DOF Redundant Robot Based on Dexterity," M.Sc. Thesis, Mechanical Engineering, Yonsei University, 2000.
  13. Dorst, L., "Honing Geometric Algebra for Its Use in the Computer Sciences," Geometric Computing with Clifford Algebra, pp. 127-151, 2001.
  14. Lasenby, J., Fitzgerald, W. J., Lasenby, A. N., and Doran, C. J. L., "New Geometric Methods for Computer Vision: An Application to Structure and Motion Estimation," International Journal of Computer Vision, Vol. 26, No. 3, pp. 191-213, 1998. https://doi.org/10.1023/A:1007901028047
  15. Li, H., Hestenes, D., and Rockwood, A., "Generalized Homogeneous Coordinates for Computational Geometry," Geometric Computing with Clifford Algebra, Vol. 24, pp. 27-60, 2001.
  16. Fowles, G. R. and Cassiday, G. L., "Analytical Mechanics," Saunders College Pub., pp. 423-425, 1999.
  17. Haykin, S. S., "Adaptive Filter Theory," Prentice Hall, pp. 483-532, 1991.
  18. Wong, D. S. H. and Sandler, S. I., "A Theoretically Correct Mixing Rule for Cubic Equations of State," AIChE Journal, Vol. 38, No. 5, pp. 671-680, 1992. https://doi.org/10.1002/aic.690380505

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