MATLAB Implementation of Four-Wheel Steering Vehicles

MATLAB implementation of four-wheel steering vehicles can be achieved through various methods, each differing in modeling accuracy and complexity. Below are three common implementation approaches suitable for MATLAB 6.5 version. ### 1. Simple Implementation Based on Kinematic Model The simplest approach uses a kinematic model that assumes low-speed vehicle operation while ignoring lateral tire forces and inertial effects. In this method, vehicle sideslip angle (β) and yaw rate (ψ_dot) can be directly calculated through geometric relationships. The inputs are front wheel steering angle (δ_f) and rear wheel steering angle (δ_r). Code implementation typically involves basic trigonometric calculations and coordinate transformations using MATLAB's built-in mathematical functions. ### 2. Implementation Based on Linear 2-DOF Model This method employs the classical two-degree-of-freedom vehicle dynamics model, suitable for medium-speed driving conditions. The model considers tire cornering characteristics and calculates vehicle sideslip angle and yaw rate through linearization. Inputs remain the front and rear wheel angles, but the model incorporates parameters like vehicle mass, wheelbase, and front/rear tire cornering stiffness. Code implementation requires solving linear differential equations using MATLAB's ODE solvers (e.g., ode45) and matrix operations for state-space representation. ### 3. Implementation Based on Nonlinear Multi-DOF Model For higher simulation accuracy, a multi-degree-of-freedom nonlinear model can be adopted, considering suspension movement, nonlinear tire characteristics, and longitudinal-lateral coupling effects. This approach involves significant computational load but provides more realistic simulation of four-wheel steering vehicle dynamics. Implementation typically requires advanced MATLAB features like S-function programming, nonlinear equation solvers, and possibly Simulink integration for complex system modeling. All three methods are compatible with MATLAB 6.5, where the first approach suits rapid prototyping, the second is ideal for control algorithm development, and the third serves high-precision vehicle dynamics research applications.