A Fibonacci control system with application to hyper-redundant   manipulators
  We study a robot snake model based on a discrete linear control system involving Fibonacci sequence and closely related to the theory of expansions in non-integer bases. The present paper includes an investigation of the reachable workspace, a more general analysis of the control system underlying the model, its reachability and local controllability properties and the relation with expansions in non-integer bases and with iterated function systems. 
Anna Chiara Lai, Paola Loreti and Pierluigi Vellucci
math.OC