Discrete asymptotic reachability via expansions in non-integer bases

Aim of this paper is to show the connection between the theory of expansions in non-integer bases and discrete control systems. This idea is supported by an example of application, in the framework of robotics. We show how a model of multi-phalanx self-similar robot hand may be studied by means of results and techniques coming from non-standard numeration systems and related tools, like Iterated Function Systems (IFS) and, more generally, fractal geometry