Error Manifold-Based LTV-MPC for Mitigating Tracking Dynamic Response Lag in Two-Wheeled Differential Platforms

Vision-guided two-wheeled differential platforms often exhibit transient response lag during low-speed terminal tracking with small errors. This issue mainly arises from sensitivity degradation in linear time-varying model predictive control (LTV-MPC) during model linearization. Near the equilibrium point, conventional historical-input linearization causes key coupling terms in the state Jacobian to vanish, disrupting the gradient transmission channel in the quadratic programming (QP) optimization and leading to conservative control responses. To address this problem, an improved LTV-MPC method based on error-manifold-driven gradient reconstruction is proposed. The method maps the current error state to a virtual reference input, restoring prediction model sensitivity and preserving an effective, coupling-dependent QP descent direction in small-error regions without modifying the optimization objective or constraints. Experimental results show that the proposed method mitigates terminal response lag, reducing the average rise time by 30%–40% under typical conditions. Parameter sensitivity analysis indicates that the mapping parameter regulates transient dynamics while preserving the steady-state optimal solution, demonstrating structural decoupling between the prediction model and optimization layers and independence from conventional MPC tuning parameters.