A Fast Algorithm and System for the Inverse Kinematics of GeneralSerial

We present fast and robust algorithms for the inverse kinematics of serial manipulators consisting of six or fewer joints. When stated mathematically, the problem of inverse kinematics reduces to simultaneously solving a system of algebraic equations. In this paper, we use a series of algebraic and numeric transformations to reduce the problem to computing the eigenstructure of a matrix pencil. To eeciently compute the eigenstructure, we make use of the symbolic formulation of the matrix and use a number of techniques from linear algebra and matrix computations. The resulting algorithm computes all the solution of a serial manipulator with six or fewer joints in the order of tens of milliseconds on the current workstations. It has been implemented as part of a generic package, KINEM, for the inverse kinematics of serial manipulators.