Kinematic Inversion of Robotic Manipulators in the Presence of Redundancies

Abstract

A general algorithm for the solution of the inverse kinematic problem of robotic manipulators in the presence of redundan cies is presented in this article. Redundancies are handled using a constrained nonlinear least-square minimization approach in which a positive definite performance index is minimized subject to the associated kinematic closure equa tions. The arising nonlinear problem is solved as a sequence of linear quadratic programs. The algorithm is aimed at providing an efficient and general solution that avoids the production of undesirable effects such as non-conservative joint motions. Numerical stability of the procedure is en hanced by use of the Newton-Gauss method. Examples are given using the six-axis PUMA and seven-axis CYBOTECH P-15, each performing a task for which five degrees of free dom are required to orient and position an axially-symmetric peg through a continuous path.

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References

Anderson, K. 1987. Inverse kinematics of robot manipulators in the presence of singularities and redundancies Thesis, McGill University, Department of Mechanical Engineering, Montreal.

Angeles, J. 1982. Spatial Kinematic Chains Berlin : Springer-Verlag.

Angeles, J. 1985. On the numerical solution of the inverse kinematic problem Int. J. Robot. Res. 4(2): 21 -37.

Angeles, J. 1986. Iterative kinematic inversion of general five-axis robot manipulators Int. J. Robot. Res. 4(4):59-70.

Angeles, J. 1988a (Salo, Italy). Isotropy criteria in the kinematic design and control of redundant manipulators Proc. NATO Adv. Res. Workshop on Robots with Redundancy : Design, Sensing and Control . In press.

Angeles, J. , 1988b (Ljubljana, Yugoslavia). Special loci of the workspace of spherical wrists Proc. International Meeting on Advances in Robot Kinematics, pp. 36-45.

Angeles, J. , Alivizatos, A. , and Zsombor-Murray, P. 1988. The synthesis of smooth trajectories for pick-and-place operations IEEE Trans. Sys. Man Cybernet. 18(1):173-178.

Angeles, J. , Anderson, K. , Chen, B. , and Cyril, X. 1988. The kinematic inversion of robot manipulators in the presence of singularities ASME J. Dyn. Sys. Meas. Control (110)3:246-254.

Angeles, J. , Anderson, K. , and Gosselin, C. 1987 (Boston). An orthogonal-decomposition algorithm for constrained least-square optimization. Proc. 13th ASME Design A utomation Conference, pp. 215-220.

10.

Angeles, J. , Anderson, K. , and López-Cajún, C. 1987 (New York). KINVERS: An integrated computer package for robot manipulators' forward and inverse kinematics Proc. 1987 ASME International Computers in Engineering Conf., 1:251-258.

11.

Angeles, J. , Habib, M. , and López-Cajún, C. 1987. Efficient algorithms for the kinematic inversion of redundant robot manipulators Int. J. Robot. Automat . (2)3:106-116.

12.

Angeles, J. , and Rojas, A. 1987. Manipulator kinematic inversion via condition-number minimization and continuation. Int. J. Robot. Automat . 2(2):61-69.

13.

Baiflieul, J. 1985 (St. Louis). Kinematic programming alternatives for redundant manipulators Proc. IEEE Conf. on Robot. Automat ., pp. 722-728.

14.

Baillieul, J. 1986 (San Francisco). Avoiding obstacles and resolving kinematic redundancy Proc. IEEE Conf. on Robot. Automat ., pp. 1698-1704.

15.

Baker, D.R. , and Wampler, C.W. 1987 (Raleigh). Some facts concerning the inverse kinematics of redundant manipulators Proc. 1987 IEEE Int. Conf. Robot. Automat., pp. 610-617.

16.

Golub, G.H. , and Van Loan, C. 1983. Matrix Computations. Baltimore : The John Hopkins University Press, pp. 38-43.

17.

Hartenberg, R.S. , and Denavit, J. 1964. Kinematic Synthesis of Linkages, New York: McGraw-Hill.

18.

Hollerbach, J.M. 1984 (Tokyo). Optimum kinematic design of a seven degree of freedom manipulator Proc. II Int. Symp. Robot. Automat ., pp. 707-711.

19.

Hollerbach, J.M. 1985 (Miami Beach). Evaluation of redundant manipulators derived from the PUMA geometry Proc. 1985 ASME Winter Annual Meeting, pp. 187-192.

20.

Klein, C.A. and Blaho, B.E. 1987. Dexterity measures for the design and control of kinematically redundant manipulators, Int. J. Robot. Res . (6)2:72-83.

21.

Klein, C.A. , and Huang, C.H. 1983. Review of pseudoinverse control for use with kinematically redundant manipulators. IEEE Trans. Sys. Man Cybernet . SMC-13(3):245-250.

22.

Liégeois, A. 1975. Commande des systèmes mécaniques articulés. RAIRO. Série Automatique.

23.

Mangasarian, O.L. 1972. Techniques of optimization Trans. ASME J. Eng. for Ind. 93:303-309.

24.

Paul, R.P. , Shimano, B. , and Mayer, G.E. 1981. Kinematic control equations for simple manipulators IEEE Trans. Sys. Man Cybemet. SMC-11(6):449-455.

25.

Salisbury, J.K. , and Craig, J.J. 1982. Articulated hands: force control and kinematic issues Int. J. Robot. Res. 1(1):4-17.

26.

Schittkowski, K. 1985. A unified outline of nonlinear programming algorithms Trans. ASME J. Mech. Trans. Automat. Design 107:449-453.

27.

Spring, K. 1986. Euler parameters and the use of quaternion algebra in the manipulation of finte rotations: A review Mech. Mach. Theory 21(5):365-373.

28.

Stanišić, M. , and Pennock, G. 1985. A nondegenerate kinematic solution of a seven-jointed robot manipulator. Int. J. Robot. Res . 4(2):10-20.

29.

Tsai, L.W. , and Morgan, A.P. 1985. Solving the kinematics of the most general six- and five-degree-of-freedom manipulators by continuation methods Trans. ASME J. Mech. Trans. Automat. Design 107:189-200.

30.

Whitney, D.E. 1972. The mathematics of coordinated control of prosthetic arms and manipulators Trans. ASME J. Dyn. Sys. Meas. Control 94(14):303-309.

31.

Yahşi, O.S. , and Özgören, K. 1984. Minimal joint motion optimization of manipulators with extra degrees of freedom. Mech. Mach. Theory . 19(3):325-330.

32.

Zhou, J. , and Mayne, R.W. 1985. Monotonicity analysis and recursive quadratic programming in constrained optimization Trans. ASME J. Mech. Trans. Automat. Design 107:459-462.