Remarks on robot dynamics: canonical transformations and Riemannian geometry

The author uses tools from Hamiltonian mechanics and Riemannian geometry to illustrate some properties of robot dynamics that are useful both for robot control and for the design of robotic manipulators. 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 particularly simple. In the present work, the author gives necessary and sufficient conditions for the existence of such a factorization and discusses their implications for robot control