Explicit Nonlinear Control for Optimal Trajectory Tracking of Autonomous Vehicles

Motion control of autonomous vehicles (AVs) that considers nonlinear dynamics and multidimensional motion coupling characteristics represents a critical research direction, particularly for vehicles operating under extreme conditions. However, the nonlinearity of model and the time-varying characteristics of reference states make control law design challenging, often resorting to computationally expensive approaches such as model predictive control (MPC). This paper proposes an explicit nonlinear control design framework for optimal trajectory tracking of AVs. Specifically, taking the three-degree-of-freedom vehicle dynamics model as an example, we first augment the system state to yield an affine representation, followed by input-output feedback linearization. The discrete-time linearized system is then augmented with reference states from the preview horizon, and a linear quadratic regulator is designed to provide an analytical solution for the virtual control inputs. Finally, the original control inputs are computed using the feedback linearization control law. We performed simulations to evaluate the effectiveness of our proposed approach and compared it against MPC. Results indicate that our proposed approach achieves tracking accuracy, smoothness, and robustness comparable to MPC, while significantly reducing computational requirements, with a computing time of nearly 0 ms.