A Study on the Establishment of a Variable Stiffness Physical Model of Abdominal Soft Tissue and an Interactive Massage Force Prediction Algorithm

This research focuses on the crucial issue of ascertaining safe and suitable massage forces for abdominal massage robots. It does so by constructing variable stiffness soft tissue physical models and devising a machine learning-based prediction algorithm. Twelve healthy volunteers with diverse body types (underweight, standard, overweight) were enlisted. A self-developed experimental platform was utilized to gather high-precision mechanical data. Two physical models were formulated to depict the nonlinear force-displacement relationship of abdominal soft tissues. Model 1 was based on an exponential function, and Model 2 was based on a power function. Model 1 showed greater accuracy for standard body types (R2 > 0.95 at 72.22% of data points) and underweight body types (R2 > 0.95 at 100% of data points). In contrast, Model 2 was a better fit for overweight individuals (R2 > 0.95 at 47.06% of data points). Furthermore, a transformer-based machine learning algorithm was developed. This algorithm predicts interaction forces using anthropometric and physiological characteristics. It achieved an accuracy of 92.60% within a pressing depth of 0–15 mm. In most situations, especially in full-range predictions (with an accuracy of 58.60%), the algorithm outperformed both physical models. This study presents a dual framework that combines biomechanical modeling and data-driven algorithms. It lays the theoretical and practical groundwork for safe and adaptable force control in abdominal massage robotics.