High-Precision Dynamic Control of Soft Robots With the Physics-Learning Hybrid Modeling Approach

The continuum deformation and nonlinear mechanical behaviors of soft materials make it challenging to develop an accurate and computationally efficient dynamic model for soft robots intended for real-time control purposes. In this article, we present a physics-learning hybrid modeling approach based on absolute nodal coordinate formulation (ANCF) and the multilayer neural network (MLNN), achieving both real-time simulation and high-precision dynamic control for a class of soft parallel robots. In the proposed modeling approach, the ANCF-based model physically characterizes the quasi-static motions of the soft robot, while the MLNN further describes the nonlinear dynamic behavior of soft materials and the hysteresis of pneumatic actuation. This way, the developed hybrid dynamic model can accurately predict the robot's motions under different speed conditions, with the average calculation time in each step being less than 3 ms. Furthermore, we demonstrate that the developed hybrid dynamic model is also efficiently invertible, making it feasible for real-time controller designs using both feedforward and feedback-linearization control strategies. Finally, we perform various trajectory tracking tests at different speeds to verify the effectiveness of the developed hybrid dynamic model and the model-based controllers. The experimental results demonstrate that the tracking errors of the hybrid model-based feedforward controller are reduced by 53%-67% compared to the purely physics-based feedforward controller. In addition, the hybrid model-based feedback-linearization controller further attenuates tracking errors to an impressive range of 0.4-1.1 mm with the speed spanning from 5 to 80 mm/s.