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Electroactive polymer (EAP) actuators have been attracting the attention of researchers due to their muscle-like behaviour and unusual properties. Several modelling methods have been proposed to understand their mechanical, chemical, electrical behaviours or `electro-chemo-mechanical' behaviour. However, estimating the whole shape or configuration of the EAP actuators has always been challenging due to their highly non-linear bending behaviour. This paper reports on an effective method to estimate the whole shape deflection of the EAP actuators by employing a so-called backbone approach. Tri-layer configured polypyrrole (PPy) based EAP actuators were used as a soft and smart structure with more degrees of freedom than its input. After deriving the inverse kinematic model of the actuator, its complete shape is estimated by solving the inverse kinematic model with an angle optimization (AngleOPT) method. The experimental results and numerical results have demonstrated the effectiveness of the method in estimating the highly non-linear bending behaviour of the PPy actuators and applicability of this modelling approach to other EAP actuators.