An Improved Unit Quaternion for Attitude Alignment and Inverse Kinematic Solution of the Robot Arm Wrist

This paper introduces a new method for kinematic modeling of the robot arm by deriving a new elegant mathematical formula based on the axis vector with the tangent of the rotation angle. For this purpose, an innovative analytical quaternion is introduced through integration between Axis-Invariants and unit quaternion features named Ju-Gibbs quaternion, which expresses the body rotation with non-redundant parameters compared with the quaternions in literature. Two theorems based on the new form of the quaternion are developed and proved for the kinematic modeling of the robot arm. The first is attitude alignment, which is essential in multiaxial rotation systems. The second theorem for the wrist inverse kinematic (IK) solution is utilized to obtain the joint variables for the last joints of the end effector. In order to verify the effectiveness and accuracy of the proposed method, a numerical example and simulation of different structural configurations of robot and human arms are intensively studied. The novel quaternion provides a new tool for kinematic analysis and reduces the computational complexity of the kinematic solutions of the Robot-Arms wrist. Furthermore, the method laid a new foundation for the IKs of multi-axis systems based on Axis-Invariant and tangent quaternion.