Comprehensive Theory of Differential Kinematics and Dynamics for Motion Optimization

This paper presents a novel unified theoretical framework for differential kinematics and dynamics for complex robot motion optimization. By introducing 18 times 18 comprehensive motion transformation matrix (CMTM), forward differential kinematics and dynamics including velocity and acceleration can be written in a simple chain products like ordinary rotational matrix. This formulation enables analytical computation of derivative of various physical quantities including joint force or torques with respect to joint coordinate variables and their derivatives for a robot trajectory in an efficient manner (O(Nj), where Nj is the number of the robot's DOF), which is useful for motion optimization.