Modeling and application for pneumatic soft actuators based on a novel deep neural network

Soft robots, with the characteristics of lightweight, compliance and safety compared to rigid robots, have drawn the attention of many researchers. However, the current limitations in operational speed and the inherent nonlinearity of soft robots pose challenges in mathematical modeling and control accuracy. This paper presents a four-wheeled rigid-flexible coupled robot with a cylindrical pneumatic soft actuator for unknown domain exploration, which has the property of a higher movement speed. A deep neural network (DNN) is applied to model the dynamics of the actuator which describes the relationship between air pressure and bending angle. The proposed DNN integrates a multilayer perceptron (MLP) with a residual neural network (Res-Net), with the final output derived from weighted summation of both networks’ outputs, adjusted for varying environmental conditions. Experiments demonstrate that the learning-based modeling method outperforms traditional model-based methods in describing the relationship between air pressure and bending angle of the soft actuator, while also significantly reducing development time. The maximum value of the MAE of the DNN during prediction is 0.5733°, which is 67.37% smaller than the error of the model-based method. This method enables immediate training upon acquiring real-world data without the need for preliminary model accuracy verification. Additionally, it captures the dynamic response of the system effectively. When the actuator’s operational environment changes, the method rapidly adapts to new dynamics. After adjusting the experimental environment, the maximum MAE predicted by the DNN trained with the new data was only 0.3365°. The result provides ideas for future modeling and control of soft robots.