Practical Algorithm for Solving Real Time Inverse Kinematics of Industrial 7R Robot

Abstract

The practical algorithm solves real time inverse kinematics of industrial 7R Robot. Here D-H method is used to set up a closed-form 4×4 matrix equation of the 7R Robot, and then sine and cosine of joint angles is transformed to complex exponential form, 10 equations in same form are obtained. We extract the coefficient of every term to construct a 16×16 real number matrix. And the inverse kinematics of 7R Robot can be changed into eigenvalues and eigenvectors problem. For the extra revolute joint of the 7R redundant robot, minimize the condition number of all the solutions, the best one can be obtained. A numerical example shows that the program written in C++ language runs fast enough in the real time control of an industrial robot.