Establish a digital model of the vehicle, which is divided into vehicle kinematics and dynamics models.
Vehicle kinematics model:
The vehicle kinematics model (Kinematic Model) regards the vehicle as a rigid body, mainly considering the relationship between the vehicle's pose (position coordinates, heading angle), speed, front wheel angle, etc., without considering the influence of any force.
1. Assumptions:
- Regardless of the movement in the Z-axis direction, the default movement of the car on the two-dimensional plane
- Steering angle assuming the left and right tires of the car have the same steering speed
- Assuming the vehicle is moving slowly, ignoring the transfer of front and rear axle loads
- Suppose the car is a rigid body motion
- Vehicle motion and steering are assumed to be front-wheel drive
For example, the following picture: the following formula derivation is based on this picture
2. Derivation of vehicle kinematics model
For the above figure, we obtain the corresponding x velocity, y velocity, and heading angular velocity, so that there can be a correspondence for the state quantity = [x, y,
], and the control quantity = [v, δ]:
Taylor series expansion of the above at any reference point r:
Find two of the partial derivatives:
So the variation of the state quantity error is:
Forward Euler discretization of the above formula:
Finally got:
So in this way, we have obtained the relationship between the previous state error and the control error and the latter state error.
That is, the next state quantity error can be predicted by the state quantity error and control quantity error of the current state.
Vehicle Dynamics Model:
The vehicle dynamics model (Dynamic Model) needs to take into account the influence of the force between the vehicle and the ground, including tire lateral deviation.
According to the degree of freedom, the vehicle dynamics model can be divided into:
- Two-degree-of-freedom model: only includes two degrees of freedom of the vehicle lateral and yaw.
- Seven-degree-of-freedom model: including longitudinal displacement, lateral displacement and yaw angular velocity of the body and the rotary motion of the four wheels.
- Eleven degrees of freedom model: including vehicle longitudinal motion, vehicle lateral motion, vehicle yaw, body pitch, rotation of four wheels and front wheel angle.
According to the direction of force, it is divided into transverse dynamics and longitudinal dynamics. Generally, the two are decoupled and studied:
In the longitudinal direction, speed tracking is realized by controlling the rotation speed of the tire;
On the modulus, the path tracking is realized by controlling the front wheel angle.
To sum up, on the basis of small steering angle and tire dynamics, the linear two-degree-of-freedom dynamics model of the vehicle is studied.
The diagram is as follows:
The kinetic equations are derived as follows:
According to the system state equation, the response of the vehicle's lateral displacement, lateral velocity, yaw angle, and yaw rate can be analyzed under a given front wheel angle input, but the purpose of lateral tracking control is to reduce tracking deviation . The required state equation is one that can analyze the vehicle's response to tracking deviations for a given front wheel angle.
