Kinematics Solution Analysis of 6R Robot Based on Spinor Exponential Product

In the kinematics research of multi-degree-of-freedom robots, D-H(Denavit-Hartenber) parametric modeling is the most commonly used. However, the D-H parameter method needs to establish a complex coordinate system relationship, and it is difficult to avoid singular solutions. To solve these problems, a new forward and inverse motion solution method based on the exponential product form of the spinor theory is proposed. In the model, the rigid body motion equation based on the spinor theory is described based on the Plücker coordinate system. And a mathematical model for the robot's forward kinematics that is based the product of the spinor and the exponential is proposed. Based on the mathematical model of positive kinematics, the derivation operation is used to construct the inverse kinematics equation of the robot, and solve the complex multivariate equation system expanded by inverse kinematics. The mathematical symbolic operation method combined with MAPLE and MATLAB is used to solve the complex multivariate equations in inverse kinematics, and avoid the complexity of the Paden-Kahan subproblem process used in inverse kinematics based on spinor theory. The kinematics analysis and solution of the KUKA-KR5 arc 6R robot are carried out by the proposed method of rotational volume exponential product modeling. Through example calculation, the correctness and effectiveness of the proposed forward and inverse kinematics solution algorithm are verified.