FEEDBACK LINEARIZATION OF ROBOT MANIPULATORS AND RIEMANNIAN CURVATURE

Several authors have noted that if the robot inertia matrix D(q) can b e factored as N-T(q)N(q) where N(q) is the Jacobian of a function Q(q) , then Q and P = N(q)q define a canonical transformation relative to w hich the robot dynamics are linear except for gravity terms. In this a rticle, we show that necessary and sufficient condition for the existe nce of such a factorization is that the Riemannian curvature of the ro bot inertia matrix D(q) vanish identically. We use this result to gene rate feedback linearization and approximate feedback linearization con trol laws that require fewer calculations than the usual method of com puted torque. (C) 1995 John Wiley & Sons, Inc.