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.

软执行器的力测量引起了很多研究兴趣，以实现闭环反馈。这项工作开发了一种用于夹持的液压软弯曲执行器的接触力的估计方法，而不是在交互位置安装力传感器。开发了一个简化的分析模型来揭示液压、弯曲角度和接触力之间的关系。该方法包括以下三个步骤。首先，当软执行器在自由空间中运行时，随液压变化的弯曲角度被校准。其次，通过在初始状态阻止软致动器来识别弹性模量。第三，通过视觉和压力传感器测量弯曲角度和液压，根据模型估计软执行器接触物体的输出力。对具有两种不同结构的软执行器进行了实验，以验证估计方法的有效性。结果表明，该估计方法具有预期的准确性和鲁棒性。最后，将该估计方法应用于接触力的闭环控制。发现通过使用估计反馈可以实现良好的动态和稳定控制性能。该估计方法应用于接触力的闭环控制。发现通过使用估计反馈可以实现良好的动态和稳定控制性能。该估计方法应用于接触力的闭环控制。发现通过使用估计反馈可以实现良好的动态和稳定控制性能。