A Method to Pass Through the Singularity by Changing the Solution Type of Inverse Kinematics for Machining with an Industrial Robot

This paper proposes an algorithm that interpolates joint angles using polynomial equations after changing the IK (inverse kinematics) solution type for a 6-DOF manipulator, enabling smooth motion through the vicinity of the singularity. When passing through the singularity and its vicinity, some joints rotate rapidly. To suppress such rapid rotations, the algorithm switches between different IK solution types in the singularity. However, in the vicinity of the singularity, switching between different discontinuous IK solutions can still cause rapid joint rotations. To address this, the proposed algorithm interpolates joint angles using polynomial equations, thereby reducing rapid motion. In particular, quintic polynomials are used to ensure smooth angular acceleration. Although polynomial interpolation introduces position and posture errors at the end-effector, these errors are compensated using a numerical approach based on the jacobian matrix. As a result, all joint rotations remain below the maximum rotational speed of the servomotors, allowing stable passage through the singularity and its vicinity. This algorithm was verified on a large 6-DOF industrial robot. As a practical application, singularity machining was demonstrated using a robotic machining system equipped with a spindle motor attached to the end-effector. By applying the proposed algorithm, machining over a wide area including singularity and its vicinity was successfully achieved.