The concept of dynamic isotropy and its applications to inverse kinematics and trajectory planning

The concept of dynamic isotropy, a measure of the dynamic performance of manipulators, is presented. An associated index, the dynamic conditioning index, is defined to describe this concept quantitatively. This index measures the dynamical coupling and numerical stability of the generalized inertia matrix of a manipulator in its dynamics model. Reduction of this index weakens the dynamic coupling while increasing the numerical stability of the dynamics model, which leads in turn to an improvement of the robot performance for simulation and control under dynamical conditions. The concept can be used as a criterion for manipulator performance and design optimization. The application of this concept to inverse kinematics of redundant manipulators and to the optimum trajectory planning of nonredundant manipulators is illustrated with two examples