A general framework for the analytical inverse kinematics solution of industrial robots

Inverse Kinematics of robots is a fundamental problem in robotics that involves calculating the joint angles of a robot to achieve a desired end-effector position and orientation. Analytical solutions are generally used when the robots' configurations are consistent. However, in practical applications, different manufacturers may have varying base coordinates, robot end coordinates, and axis rotation directions, which limits the generality of the analytical solutions. This paper introduces a general framework for solving the inverse analytical solution of robots with the same configuration. The framework exclusively relies on the Denavit-Hartenberg (D-H) parameters of the robots. The proposed framework requires the specification of a D-H parameters template for robots with the same configuration. It derives closure equations for the inverse kinematics using traditional geometric and algebraic methods based on the D-H parameters of the template. The proposed framework also provides a method for converting arbitrary D-H parameters of robots with the same configuration to the D-H parameters template. In demonstrating the effectiveness and generality of the proposed framework, it was applied to five robots with the same configuration from different manufacturers. The results demonstrate that the framework can effectively and accurately solve the analytical inverse kinematics problem for these robots.