Multi-Head Attention-Based Vertical Tire Force Estimation for Off-Road Vehicles on Boulder Terrain

Driving on boulder field terrain induces severe wheel slip and rapidly varying, highly uneven vertical tire loads, making accurate force estimation essential for maintaining traction and mobility of off-road vehicles. However, direct measurement of tire vertical forces typically requires specialized sensors that are costly and difficult to integrate into practical vehicle systems, while conventional model-based estimation approaches often struggle to capture the complex tire–terrain interactions and nonlinear suspension dynamics encountered in off-road environments. This paper proposes a Pre-Layer-Normalization (Pre-LN) Transformer-based vertical tire force estimation method for off-road vehicles operating on boulder terrain. The proposed approach utilizes five vehicle chassis signals to learn the nonlinear relationship between vehicle motion and tire vertical forces, where a learnable positional encoding is employed to capture the irregular, impulsive temporal dependencies induced by boulder contact. A tire-specific decoupled output architecture with four independent MLP heads is adopted to handle the asymmetric loading conditions characteristic of discontinuous boulder contact, and a tire-weighted MSE loss is employed to promote balanced learning across all four tire force estimators. The proposed estimator is trained and validated using IPG CarMaker simulations with a BMW X5 model traversing boulder terrain at low speed. Simulation results demonstrate that the proposed method achieves an average RMSE of 41.2 N and an average MAPE of 0.76%, reducing the average RMSE by 91.3%, 89.2%, and 86.4% compared to the LSTM, TCN, and DARNN baselines, respectively, and offering accurate and robust vertical tire force estimation for traction management and torque distribution in off-road vehicles.