Singular perturbation model of robots with elastic joints and elastic links constrained by rigid environment

A robot with distributed flexibility in the links and lumped flexibility in the joints is considered in this paper. First the model of the system in free motion is formulated as a set of ordinary differential equations, adopting a finite number of modes of the link deformation. Then algebraic constraint equations on the generalized coordinates of the system are added, to account for the loss of degrees of freedom due to the contact with rigid environment. A reduced order model, expressed in the residual degrees of freedom is then derived, based on a coordinate partitioning procedure. The singularly perturbed model of the system is finally computed, and the expression of the fast subsystem is given. The special cases of a robot with rigid joints or rigid links are also addressed.