Force measurement of soft actuators has drawn much research interest to realize closed-loop feedback. This work develops an estimation method of contact force of hydraulic soft bending actuators for gripping instead of installing force sensors at interaction position. A simplified analytical model is developed to reveal the relationships among the hydraulic pressure, the bending angle, and the contact force. The method includes the following three steps. Firstly, the bending angle varying with the hydraulic pressure is calibrated when the soft actuators are operated in free space. Secondly, the modulus of elasticity is identified by blocking the soft actuators at initial state. Thirdly, the output force of the soft actuators touching an object is estimated according to the model by measuring the bending angle and the hydraulic pressure through visual and pressure sensors. Experiments on soft actuators with two different structures are implemented to verify the effectiveness of the estimation method. The results show that the estimation method has expected accuracy and robustness. Finally, the estimation method is applied to the closed-loop control of contact force. It is found that good dynamical and steady control performance can be achieved by using the estimated feedback.
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