Parameter identification and experimental study of robot foot-terrain constitutive model on rheological surfaces

Accurate identification of foot-terrain constitutive model parameters for field rheological terrain is critical for robotic foot force perception, motion control stability, and adaptive capabilities. Traditional methods such as multiple linear regression (MLR), constrained by inherent linear model limitations, fail to characterize the complex nonlinear mechanical behavior arising from coupled multi-phase soil components. To address this, the present study investigates parameter identification and experimental validation of robot foot-terrain constitutive models, using the Loess Plateau rheological terrain as a case study. An experimental platform for foot-terrain constitutive parameter identification was established, and simulated soil samples were prepared following a Box-Behnken design to acquire foot-terrain interaction mechanical data. Four methods were then systematically compared: multiple linear regression, response surface methodology, kernel functions, and support vector regression with fused kernel functions. An empirical force prediction model based on end-to-end direct mapping was established as the foot-terrain mechanical constitutive model, enabling efficient prediction from soil composition to foot forces for robots operating on rheological terrain in outdoor environments. Results demonstrate that the support vector regression model with fused Gaussian kernel functions outperforms the MLR model in both prediction accuracy (MRE = 15.91%) and stability (RMSE = 2093.22), validating the effectiveness of the proposed method for nonlinear mechanical identification problems.