Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse

The paper presents the approximation problem of the inverse kinematics algorithms for the redundant manipulators. We introduce the approximation of the dynamically consistent Jacobian by the extended Jacobian. In order to do that, we formulate the approximation problem and suitably defined approximation error. By the minimization of this error over a certain region we can design an extended Jacobian inverse which will be close to the dynamically consistent Jacobian inverse. To solve the approximation problem we use the Cholesky decomposition and the Ritz method. The computational example illustrates the theory.