Adaptive Path Following for an Underactuated Nonholonomic Mobile Manipulator

Abstract

We investigate an adaptive path following problem for an underactuated nonholonomic mobile manipulator system and closed planar curves. As opposed to adapting to uncertain or unknown dynamics in the plant, we apply an adaptation approach with respect to an unknown geometric path. First, we present a solution to the non-adaptive path following problem using the concept of a path following output and apply it to circular and elliptical paths. To overcome a drawback associated with our first proposed solution and set the stage for our approach to the adaptive case, we apply an approximation approach based on osculating circles for strictly convex closed curves.

We transition to the adaptive path following case by first presenting an algorithm to estimate unknown path parameters in the case of a circular path. We use our estimation algorithm and our path following solution for circular paths in an indirect adaptive control scheme. Thereafter, again using the osculating circle of a curve and the approximation technique of our second non-adaptive path following solution, we extend our adaptive solution, under some mild assumptions, for unknown strictly convex closed curves in the plane.