JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Solution Space of Inverse Differential Kinematics
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Solution Space of Inverse Differential Kinematics
Kang, Chul-Goo;
  PDF(new window)
 Abstract
Continuous-path motion control such as resolved motion rate control requires online solving of the inverse differential kinematics for a robot. However, the solution space of the inverse differential kinematics related to Jacobian J is not well-established. In this paper, the solution space of inverse differential kinematics is analyzed through categorization of mapping conditions between joint velocities and end-effector velocity of a robot. If end-effector velocity is within the column space of J, the solution or the minimum norm solution is obtained. If it is not within the column space of J, an approximate solution by least-squares is obtained. Moreover, this paper introduces an improved mapping diagram showing orthogonality and mapping clearly between subspaces, and concrete examples numerically showing the concept of several subspaces. Finally, a solver and graphics user interface (GUI) for inverse differential kinematics are developed using MATLAB, and the solution of inverse differential kinematics using the GUI is demonstrated for a vertically articulated robot.
 Keywords
Differential kinematics;Robot manipulator;Jacobian;Range;Nullspace;Moore-Penrose pseudoinverse;
 Language
Korean
 Cited by
 References
1.
J. Denavit, and R. S. Hartenberg, "A kinematic notation for lower-pair mechanisms based on matrices," ASME Journal of Applied Mechanics, vol. 22, pp. 215-221, 1955.

2.
R.P. Paul, B.E. Shimano, and G. Mayer, "Kinematic control equations for simple manipulators," IEEE Transactions on Systems, Man, and Cybernetics, vol. 11, no. 6, pp. 449-455, 1981. crossref(new window)

3.
M.W. Spong, S. Hutchinson, and M. Vidyasagar, Robot Modeling and Control, John Wiley & Sons, 2006.

4.
H. Asada, and J.-J. E. Slotine, Robot Analysis and Control, John Wiley & Sons, 1986.

5.
B. Siciliano, L. Sciavicco, L. Villani, and G. Oriolo, Robotics: Modelling, Planning and Control, Springer, 2010.

6.
J.J. Craig, Introduction to Robotics: Mechanics and Control, 3rd ed., Pearson Prentice Hall, 2005.

7.
D.L. Pieper, "The kinematics of manipulators under computer control," Ph.D. Thesis, Stanford University, 1968.

8.
D. Manocha, and J.F. Canny, "Efficient inverse kinematics for general 6R manipulators," IEEE Transactions on Robotics and Automation, vol. 10, no. 5, pp. 648-657, 1994. crossref(new window)

9.
C.S.G. Lee, and M. Ziegler, "A geometric approach in solving the inverse kinematics of PUMA robots," IEEE Transactions on Aerospace and Electronic Systems, vol. AES-20, no. 6, pp. 695-706, 1984. crossref(new window)

10.
D. Kohli, and A.H. Soni, "Kinematic analysis of spatial mechanisms via successive screw displacements," ASME Journal of Engineering for Industry, vol. 97, no. 2, pp. 739-747, 1975. crossref(new window)

11.
K.H. Hunt, Kinematic Geometry of Mechanisms, Oxford Science Publications, 1978.

12.
A.T. Yang, and R. Freudenstein, "Application of dual number quaternion algebra to the analysis of spatial mechanisms," ASME Journal of Applied Mechanics, vol. 31, no. 2, pp. 300-308, 1964. crossref(new window)

13.
J. Angeles, Rotational Kinematics, Springer-Verlag, 1988.

14.
J.J. Uicker, J. Denavit, and R.S. Hartenberg, "An iterative method for the displacement analysis of spatial mechanisms," ASME Journal of Applied Mechanics, vol. 31, no. 2, pp. 309-314, 1964. crossref(new window)

15.
D. Tolani, A. Goswami, and N. I. Badler, "Real-time inverse kinematics techniques for anthropomorphic limbs," Graphical Models, vol. 62, pp. 353-388, 2000. crossref(new window)

16.
J. Lee, J. Kim, J. Lee, D.-H. Kim, H.-K. Lim, and S.-H. Ryu, "Inverse kinematics solution and optimal motion planning for industrial robots with redundancy," Journal of Korea Robotics Society, vol. 7, no. 1, pp. 35-44, 2012. crossref(new window)

17.
M. Benati, P. Morasso, and V. Tagliasco, "The inverse kinematic problem for anthropomorphic manipulator arms," ASME Journal of Dynamic Systems, Measurement, and Control, vol. 104, no. 1, pp. 110-113, 1982. crossref(new window)

18.
S. Elgazzar, "Efficient kinematic transformation for the PUMA 560 robot," IEEE Journal of Robotics and Automation, vol. 1, pp. 142-151, 1985. crossref(new window)

19.
R.P. Paul, and H. Zhang, "Computationally efficient kinematics for manipulators with spherical wrists based on the homogenous transformation representation," The International Journal of Robotics Research, vol. 5, pp. 32-44, 1986. crossref(new window)

20.
J. Cote, C. Gosselin, and D. Laurendeau, "Generalized inverse kinematic functions for the PUMA manipulators," IEEE Transactions on Robotics and Automation, vol. 11, no. 3, pp. 404-408, 1995. crossref(new window)

21.
A.A. Goldenberg, B. Benhabib, and R.G. Fenton, "A complete generalized solution to the inverse kinematics of robots," IEEE Journal of Robotics and Automation, vol. RA-1, no. 1, pp. 14-20, 1985.

22.
J.M. Hollerbach, and G. Sahar, "Wrist-partitioned, inverse kinematic accelerations and manipulator dynamics," The International Journal of Robotics Research, vol. 2, no. 4, pp. 61-76, 1983. crossref(new window)

23.
Y.-L. Kim, and J.-B. Song, "Analytical inverse kinematics algorithm for a 7 DOF anthropomorphic robot arm using intuitive elbow direction," Journal of Korea Robotics Society, vol. 6, no. 1, pp. 27-33, 2011. crossref(new window)

24.
C.-G. Kang, "Online trajectory planning for a PUMA robot," International Journal of Precision Engineering and Manufacturing, vol. 8, pp. 16-21, 2007.

25.
T. Ho, C.-G. Kang, and S. Lee, "Efficient closed-form solution of inverse kinematics for a specific six-DOF arm," International Journal of Control, Automation, and Systems, vol. 10, no. 3, pp. 567-573, 2012. crossref(new window)

26.
Y. Nakamura, Advanced Robotics: Redundancy and Optimization, Addison-Wesley Publishing, 1991.

27.
D.E. Whitney, "The mathematics of coordinated control of prosthetic arms and manipulators," ASME Journal of Dynamic Systems, Measurement, and Control, vol. 94. no. 4, pp. 303-309, 1972. crossref(new window)

28.
R.P. Paul, Robot Manipulators: Mathematics, Programming, and Control, MIT Press, 1981.

29.
D.E. Orin, and W.W. Schrader, "Efficient computation of the Jacobian for robot manipulators," The International Journal of Robotics Research, vol. 3, no. 4, pp. 66-75, 1984. crossref(new window)

30.
R.M. Murray, Z. Li, and S.S. Sastry, A Mathematical Introduction to Robotic Manipulation, CRC Press, 1994.

31.
O. Khatib, "A unified approach for motion and force control of robot manipulators: The operational space formulation," IEEE Journal of Robotics and Automation, vol. 3, no. 1, pp. 43-53, 1987. crossref(new window)

32.
C.W. Wampler, "Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods," IEEE Transactions on Systems, Man, and Cybernetics, vol. 16, no. 1, pp. 93-101, 1986. crossref(new window)

33.
Y. Nakamura, and H. Hanafusa, "Inverse kinematic solutions with singularity robustness for robot manipulator control," ASME Journal of Dynamic Systems, Measurement, and Control, vol. 108, pp. 163-171, 1986. crossref(new window)

34.
C.A. Klein, and C.-H. Huang, "Review of pseudoinverse control for use with kinematically redundant manipulators," IEEE Transactions on Systems, Man, and Cybernetics, vol. 13, no. 2, pp. 245-250, 1983.

35.
R.J. Schilling, Fundamentals of Robotics: Analysis and Control, Prentice Hall, 1990.

36.
A. Koivo, Fundamentals for Control of Robotic Manipulators, John Wiley & Sons, 1989.

37.
D.E. Whitney, "Resolved motion rate control of manipulators and human prostheses," IEEE Transactions on Man-Machine Systems, vol. 10, no. 2, pp. 47-53, 1969. crossref(new window)

38.
K.S. Fu, R.C. Gonzalez, and C.S.G. Lee, Robotics: Control, Sensing, Vision, and Intelligence, McGraw-Hill, 1987.

39.
G. Strang, Linear Algebra and Its Applications, 4th ed., Thomson Brooks/Cole, 2006.

40.
G.H. Golub, and C.F. Van Loan, Matrix Computations, 3rd ed., The Johns Hopkins University Press, 1996.

41.
S.L. Campbell, and C.D. Meyer, Jr., Generalized Inverses of Linear Transformations, Pitman, 1979.