Modeling closed kinematic chains via singular perturbations

Abstract

Closed kinematic chains (CKC) are constrained multibody systems the dynamics of which are characterized by differential-algebraic equations. In this paper we present a novel approach to modeling CKC that supports model-based control. The approach is based on a singular perturbation formulation with attractive properties including (i) the number of slow second-order differential equations is the same as the number of degrees of freedom of the system, (ii) the domain of definition of the singularly perturbed system is the entire singularity-free workspace of the CKC. We illustrate the effectiveness of our approach by simulating the dynamics of the parallel Rice Planar Delta Robot.