A comparative study of four Jacobian matrix derivation methods for quadruped robot

The Jacobian matrix is one of the important parameters for locomotion control of the quadruped robot. Based on the homogenous transformation matrix of the robot, Four Jacobian matrices of the quadruped robot are deduced based on the methods of forward kinematics, differential transformation, vector product and transformation of link velocity. Then, the basic four derivation approaches of the Jacobian matrix are compared and the equivalence relation between the vector product and the differential transformation is also discussed based on the coordinates of the quadruped robot. The difference of the vector product, the forward kinematics and the transformation of link velocity is also introduced in this paper, which can help the researcher deeply understand the derivation methods of the Jacobian matrix for the quadruped robot.