Adaptive Control of Singularly Perturbed Worm-Like Locomotion Systems

Abstract

We consider a certain type of a worm-like locomotion system: a three mass point system. We assume that this worm is towing a payload, so the masses differ extremely, and we have to deal with a singularly perturbed system. The dynamics equations are coupled via a small parameter \({{\varepsilon}}\) , which is typical for singularly perturbed systems. In order to apply simple adaptive feedback mechanisms (to approach desired properties of the worm motion) we have to guarantee the minimum-phase property (among others) of such systems. We show that such properties are preserved under singular perturbation. This is done within a general system class via construction of a normal form to gain deeper insight and to analyze such systems. We present the general case and apply the basic transformations to the worm equations. We point out that we are able to classify all required assumptions and properties by system qualities as, e.g., zeros of the reduced model or boundary-layer system. This is in contrast to other authors.