Real time inverse kinematics for general 6R manipulators

D. Manocha, J.F. Canny
Proceedings 1992 IEEE International Conference on Robotics and Automation  
The inverse kinematics of serial manipulators is a central problem in the automatic control of robot manipulators. The main interest has been in inverse kinematics of a six revolute jointed manipulator with arbitrary geometry. It has been recently shown that the joints of a general 6R manipulator can orient themselves in 16 di erent con gurations (at most), for a given pose of the end{e ector. However, there are no good practical solutions available, which g i v e a l e v el of performance
more » ... of performance expected of industrial manipulators. In this paper, we present an algorithm and implementation for real time inverse kinematics for a general 6R manipulator. When stated mathematically, the problem reduces to solving a system of multivariate equations. We m a k e use of the algebraic properties of the system and the techniques used for reducing the problem to solving a univariate polynomial. However, the polynomial is expressed as a matrix determinant and its roots are computed by reducing to an eigenvalue problem. The other roots of the multivariate system are obtained by computing eigenvectors and substitution. The algorithm involves symbolic preprocessing, matrix computations and a variety of other numerical techniques. The numerical accuracy of these operations is well understood and for most cases we are able to compute accurate solutions using double precision arithmetic. The average running time of the algorithm, for most cases, is 11 milliseconds on an IBM RS/6000 workstation. This approach is applicable to inverse kinematics of all serial manipulators.
doi:10.1109/robot.1992.220309 dblp:conf/icra/ManochaC92 fatcat:qvrcagvav5blzouynsu3wy2wye