*Article* **3D Model Identification of a Soft Robotic Neck**

**Fernando Quevedo \*, Jorge Muñoz, Juan Alejandro Castano Pena and Concepción A. Monje**

RoboticsLab, University Carlos III of Madrid, Avenida Universidad 30, 28911 Madrid, Spain; jmyanezb@ing.uc3m.es (J.M.); jucastan@ing.uc3m.es (J.A.C.P.); cmonje@ing.uc3m.es (C.A.M.) **\*** Correspondence: fquevedo@ing.uc3m.es

**Abstract:** Soft robotics is becoming an emerging solution to many of the problems in robotics, such as weight, cost and human interaction. In order to overcome such problems, bio-inspired designs have introduced new actuators, links and architectures. However, the complexity of the required models for control has increased dramatically and geometrical model approaches, widely used to model rigid dynamics, are not enough to model these new hardware types. In this paper, different linear and non-linear models will be used to model a soft neck consisting of a central soft link actuated by three motor-driven tendons. By combining the force on the different tendons, the neck is able to perform a motion similar to that of a human neck. In order to simplify the modeling, first a system input–output redefinition is proposed, considering the neck pitch and roll angles as outputs and the tendon lengths as inputs. Later, two identification strategies are selected and adapted to our case: set membership, a data-driven, nonlinear and non-parametric identification strategy which needs no input redefinition; and Recursive least-squares (RLS), a widely recognized identification technique. The first method offers the possibility of modeling complex dynamics without specific knowledge of its mathematical representation. The selection of this method was done considering its possible extension to more complex dynamics and the fact that its impact in soft robotics is yet to be studied according to the current literature. On the other hand, RLS shows the implication of using a parametric and linear identification in a nonlinear plant, and also helps to evaluate the degree of nonlinearity of the system by comparing the different performances. In addition to these methods, a neural network identification is used for comparison purposes. The obtained results validate the modeling approaches proposed.

**Keywords:** mathematical modeling of complex systems; non-linear models; soft robotics; soft robotic neck; tendon-driven actuators
