Path tracking with dynamic bicycle models
Implementation of path tracking with a linear/non-linear bicycle model. We use the PID and standley controllers to control the longitudinal and lateral movements, respectively. We use the key idea of ref.[1], while replacing the vehicle dynamics in Carla simulator with linear/non-linear bicycle models.
We use the kinematic and dynamic bicycle models as mentioned in ref.6.
Fig.1 Kinematic Bicycle Model
The control inputs are [throttle, steering].
Given the current speed v(t) we minimize the error term e = v_desired − v_current using a PID controller for the throttle value. The range for the throttle values is [-1, 1]. The formula is
Where KP, KI and KD are proportional, integral and derivative parameters, respectively.
For lateral control, we adapt the standley control(To learn more about the Stanley Control, check out ref.5). There are two error metrics: the distance to centerline d(t) and the relative angle ψ(t). The control law to calculate the steering angle δ_{SC}(t) at the current vehicle speed v(t) is given by
where k is a gain parameter.
We test vehicle models with PID and standley controllers.
Fig.2 Speed tracking of linear vehicle model
Fig.3 Path tracking of linear vehicle model
The testing results on non-linear bicycle models.
Fig.4 Speed tracking of non-linear vehicle model
Fig.5 Path tracking of non-linear vehicle model
Here we enlarge the throttle by 5 times for better visualization.
Path tracking simulation with Stanley steering control and PID speed control.
[Kong, Jason, et al. "Kinematic and dynamic vehicle models for autonomous driving control design." 2015 IEEE Intelligent Vehicles Symposium (IV). IEEE, 2015.] (https://borrelli.me.berkeley.edu/pdfpub/IV_KinematicMPC_jason.pdf)