Iterative Kinematic Inversion of General Five-Axis Robot Manipulators

Abstract

A kinematic model is derived that allows the computation of the joint coordinates and their time rates, given the Cartesian coordinates, velocities, and accelerations of five-axis manipu lators of arbitrary architecture. The model leads to a for mally overdetermined nonlinear algebraic system of six equations in five unknowns. Its least-squares approximation produces the desired joint coordinates. Joint rates are com puted as the least-squares approximation of a formally over determined linear algebraic system of six equations in five unknowns, relating the desired rates with the Cartesian ve locities. The time derivatives of the joint rates are computed similarly, but from Cartesian accelerations. The procedure is illustrated with two fully solved examples.

Get full access to this article

View all access options for this article.

References

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

Angeles, J. , and A. Rojas. 1984. On the use of condition-number minimization and continuation in the iterative kinematic analysis of robot manipulators . Proc. Fifth IASTED Symposium Robotics and Automation , New Or-leans.

Featherstone, R. 1983. Position and velocity transformations between robot end-effector coordinates and joint angles. Int. J. Robotics Res. 2(2):35-45.

Golub, G.H. , and C. van Loan. 1983. Matrix Computations. Baltimore: Johns Hopkins University Press.

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

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

Paul, R.P. , B. Shimano , and G.E. Mayer. 1981. Kinematic control equations for simple manipulators. IEEE Trans. Systems, Man and Cybernetics SMC -11(16):449-455.

Sugimoto, K. , and J. Duffy. 1983. Analysis of five-degree-of freedom robot arms. J. Mechanisms, Transmissions, and Automation in Design: Trans. ASME. 105:23-27.

Tsai, L.-W. , and B. Roth. 1972. Incompletely specified displacements: Geometry and spatial linkage synthesis. ASME Paper 72-Mech-13, ASME Mechanisms Conference, San Francisco.

10.

Tsai, L.-W. , and A.P. Morgan. 1984. Solving the kinematics of the most general six- and five-degree-of-freedom manipulators by continuation methods . ASME Paper 84-DET-20. ASME Design Engineering Technical Conference. Cambridge, Mass.

11.

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