The control problem for robot manipulators with flexible joints is considered. The results are based on a recently developed singular perturbation formulation of the manipulator equations of motion where the singular perturbation parameter µ is the inverse of the joint stiffness. For this class of systems it is known that the reduced-order model corresponding to the mechanical system under the assumption of perfect rigidity is globally linearizable via nonlinear static-state feedback, but that the full-order flexible system is not, in general, linearizable in this manner. The concept of integral manifold is utilized to represent the dynamics of the slow subsystem. The slow subsystem reduces to the rigid model as the perturbation parameter µ tends to zero. It is shown that linearizability of the rigid model implies linearizability of the flexible system restricted to the integral manifold. Based on a power series expansion of the integral manifold around µ = 0, it is shown how to approximate the feedback linearizing control to any order in µ. The result is then an approximate feedback linearization which, assuming stability of the fast variables, linearizes the system for all practical purposes.

If nonlinear subsystems with continuous equilibria are weakly connected, their local behavior is fast compared with the system-wide behavior caused by the connections. The slow behavior is described by an aggregate model which appears as a slow subsystem in the singular perturbation form of the model. In this way earlier linear aggregation results by Simon et al in economics and slow coherency results in power systems are extended to nonlinear systems and related to singular perturbations.