Vehicle Lateral Control

vehicle lateral model with state variables as position error and Orientation Error

The model illustrates the two-degrees-of-freedom "bicycle" model of the car under consideration. The vehicle's lateral position, y and yaw angle, 𝜓 serve to represent the two degrees of freedom.The vehicle's lateral position is determined by measuring from the point O, the vehicle's rotational center, along the lateral axis of the vehicle. The yaw angle of the car is measured with relation to the equatorial plane, i.e the X-axis. The vehicle's longitudinal speed at center of gravity is represented by the symbol Vx. 𝜓ⅆ𝑒𝑠 is the desired yaw rate of the vehicle and 𝜓 is the actual yaw rate of the vehicle.

Where:

e1 = Position error = 𝒚 − 𝑦ⅆ𝑒𝑠

𝑒2 = Orientation error = 𝜓 − 𝜓ⅆ𝑒𝑠

𝑦ⅆ𝑒𝑠 = desired vehicle’s lateral position

𝒚 = vehicle’s lateral position

𝜓 = yaw rate/ vehicle’s orientation

𝜓ⅆ𝑒𝑠 = desired yaw rate/ desired vehicle’s orientation

𝑥1 = 𝑒1

𝑥2 = d/dt(e1) = d/dt(x1)

d/dt(x2) = dd/dtt(e1)

𝑥3 = 𝑒2

𝑥4 = 𝑒2̇ = 𝑥3̇

𝑥4̇ = 𝑒2̈

𝛿 = input vector = steering angle = 𝑢1