A continuous Fibonacci model for robotic octopus arm

We introduce a control model for an octopus robot tentacle. The model extends to a continuous setting a class of hyper-redundant planar manipulators characterized by a self-similar structure. The proposed model encompasses manipulators with a links scaling according to Fibonacci sequence. We characterize the class of continuous functions whose graph can be reparametrized as a configuration of the system and we provide an explicit control law. In particular, we give the conditions to prescribe an admissible path for the configurations of the manipulator. The result is an attempt to determine an entire class of admissible paths for the arm deformations