Adaptive cooperative trajectory tracking control for multi-axle independent steering vehicles considering dynamic load transfer

Multi-axle independent steering vehicles enable axle-wise steering control, improving trajectory tracking in heavy-duty commercial vehicles. However, dynamic load transfer induces substantial variations in axle-level tire cornering stiffness and lateral-force margins. Consequently, fixed inter-axle steering-angle allocation cannot accommodate differences in lateral control capability, compromising tracking accuracy and vehicle stability. To address this issue, this paper proposes a load-transfer-considered adaptive cooperative trajectory-tracking control strategy. First, a linear parameter-varying (LPV) model characterizes the time-varying vehicle dynamics under load transfer, while an axle-level lateral-force margin index derived from tire friction-circle constraints under varying vertical loads quantifies each axle's relative capability to undertake lateral control tasks. On this basis, a cooperative-game-based adaptive distributed model predictive control framework treats each steering axle as a cooperative decision-making player and coordinates their local objectives through a shared global objective function, enabling vehicle-level cooperative optimization of multi-axle steering. Meanwhile, the twin-delayed deep deterministic policy gradient (TD3) algorithm learns the nonlinear mapping from vehicle states and axle-level lateral-force margins to relative inter-axle weights, allowing the players' relative weights to adapt to changes in lateral control capability. This mechanism mitigates the adverse effects of load transfer on tracking accuracy and vehicle stability. Controller-in-the-loop simulation results demonstrate that the proposed method improves trajectory-tracking accuracy and overall vehicle stability under dynamic load transfer.