Electroactive polymers (EAPs) generate highly non-linear deflections when they are used as actuators, which are known as artificial muscles. Though several modelling methods have been proposed before to understand their mechanical, chemical, electrical behaviours or 'electro-chemo-mechanical' behaviour, estimating the whole shape deflection of the EAP actuators has not been studied yet. Therefore, we report on (i) an effective methodology to estimate these actuators' whole shape deflection by employing a soft robotic actuator/manipulator approach and (ii) an angle optimization method, which we call AngleOPT, to accurately solve the EAP actuators' inverse kinematic problem. Laminated polypyrrole (PPy) EAP actuators are employed to validate the soft robotic kinematic model which has more degrees of freedom than its input. This follows that we have reduced a difficult problem to an easy-to solve inverse kinematic problem (easier to solve) of a hyper-redundant soft robotic system. A parametric estimation model is also proposed to predict the tip coordinates of the actuators for a given voltage. The experimental and numerical results are presented to demonstrate the efficacy of the methodology for estimating the EAP actuators' highly non-linear bending behaviour from the inverse kinematic model. The proposed methodology can be extended to other type of smart structures with a similar topology. © 2013 Elsevier Ltd.