Kinematics of the center of mass for robotic mechanisms based on lie group theory

This paper presents the kinematics about the center of mass (CoM) for robotic mechanisms based on Lie Group theory because the movements of CoM is very important for mobile manipulating robots. Different from general kinematics, the CoM kinematics relates the position of the CoM to the joint angles and the pose of the robot. The concept of the homogeneous coordinates of mass points is define as the product of the mass and the general homogeneous coordinates. Then, the mass translation matrix is introduced to derive the formula of the product of exponentials and Jacobian matrix for CoM (COM-POE). The COM-POE has the same form as the standard POE formula used to model the kinematics of serial manipulators. Hence the traditional methods to deal with kinematic problems can be adopted directly. Two application instances based on the CoM-POE have been presented. The first one is a mobile platform with a redundant serial manipulator and the second one is a quadruped robot. The simulation results show that the CoM kinematics is very useful in motion planning to guarantee the stability of mobile manipulating robots.