Vector model for solving the inverse kinematics problem in the system of external adaptive control of robotic manipulators

Abstract

A new approach that allows to solve the problems of forward and inverse kinematics for robotic manipulators is proposed by the authors. The approach is to represent the kinematic model of a robotic arm with six rotational joints in the form of a vector model. The first 4 vectors make their movements and turn in the same plane, because of the geometric features of the robot. Thus, on the basis of a vector equation, a system of nonlinear algebraic equations was formed, which were solved by the numerical Newton method, at each iteration of which a system of linear algebraic equations was solved by the Seidel method. The algorithm was tested on a trajectory set in the form of an Archimedean spiral approximated by straight line segments. Trajectory was checked by a real robot KUKA KR6 R900 and it was shown that deviation between calculated and real position of flange point was less than 0.005 mm. It is shown that in comparison with the common Denavit–Hartenberg method the method proposed by the authors has an order of magnitude fewer mathematical operations (790 versus 52).