A path following algorithm for manipulator inverse kinematics

An algorithm for the continuous iterative solution of the inverse kinematics problem for six-degree-of-freedom manipulators of arbitrary structure is presented. The algorithm is based on path following from a known solution by the predictor-corrector method using: a new second-order predictor, a first-order Newton-method corrector, and the idea of including the end effector´s position (along its trajectory) as a variable in the formulation. The importance of the proposed approach is that it follows for the rapid generation of joint trajectories that include regular positions as well as singular positions. The algorithms for both the predictor and the corrector are derived from Taylor series expansion of the matrix equation of closure and require only the solution of linear systems of equations. The approach is illustrated with examples for the Puma manipulator and a general manipulator