Invariant manifolds and their application to robot manipulators with flexible joints

In this paper we examine a recently developed singular perturbation formulation of the equations of motion for a robot manipulator with flexible joints, where the fast variables are the elastic forces at the joints and their time derivatives. The concept of an invariant manifold is utilized to represent the dynamics of the slow subsystem. The dynamics of the system restricted to this manifold reduce to the usual rigid body dynamics as the perturbation parameter ε tends to zero. Based on a power series expansion of the exact manifold around ε = 0, higher order corrections of the manifold are obtained. This leads to reduced order models of the full system which may prove more useful for control system design than either the full model or the rigid model. The case of a single link with joint flexibility is worked out in detail.