On manipulator control by exact linearization

Comments are given on the application to rigid-link manipulators of geometric control theory, resolved acceleration control, operational space control, and nonlinear decoupling theory, and the essential unity of these techniques for externally linearizing and decoupling end-effector dynamics is discussed. Exploiting the fact that the mass matrix of a rigid-link manipulator is positive definite, and the fact that there is an independent input for each degree of freedom, it is shown that a necessary and sufficient condition for a locally externally linearizing and output decoupling feedback law to exist is that the end effector Jacobian matrix be nonsingular.