FEEDBACK LINEARIZATION OF ROBOT MANIPULATORS AND RIEMANNIAN CURVATURE

Several authors have noted that if the robot inertia matrix D(q) can be 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 which the robot dynamics are linear except for gravity terms. In this article, we show that necessary and sufficient condition for the existence of such a factorization is that the Riemannian curvature of the robot inertia matrix D(q) vanish identically. We use this result to generate feedback linearization and approximate feedback linearization control laws that require fewer calculations than the usual method of computed torque. (C) 1995 John Wiley & Sons, Inc.