# Design of a Reinforcement Learning-Based Lane Keeping Planning Agent for Automated Vehicles
## 2 Environment
### Vehicle Model  
The last sensitive aspect of the environment is the choice of the vehicle model, thanks to the controversy between maneuver accuracy and computational requirements. Choosing the appropriate complexity for a vehicle model is always a challenge because two different goals have to be reached at the same time. On the one hand, the vehicle model should be as realistic as possible to cover all possible driving situations, while on the other hand, the computational need of the model has to be scaled back as much as possible to decrease the runtime of the final simulation [28]. The used vehicle model is a nonlinear single track model complemented with a dynamic wheel model. This vehicle model represents an excellent trade-off between computational efficiency and vehicle dynamics because it provides fundamental dynamics for a wide variety of maneuvers. Figure 3 shows the multi-body model of the vehicle; it also shows that the main parts of the model are the vehicle chassis and two rigidly attached wheels that also symbolize the axles of the front and the rear. The model has several parameters; thus to provide a transparent description, all the influential parameters are detailed in Table 2. \begin{table}
\begin{tabular}{c l} \hline \hline
**Parameter** & **Meaning** \\ \hline \(m\) & Mass \\ \(\theta\) & The inertia of the chassis. \\ \(l_{f}\) & The horizontal distance between the center of the front wheel and the vehicle’s center of gravity. \\ \(l_{r}\) & The horizontal distance between the center of the rear wheel and the vehicle’s center of gravity. \\ \(h\) & The height of the vehicle’s center of gravity. \\ \(\theta_{f/r}\) & The moments of inertia of the front and rear wheel. \\ \(r_{f/r}\) & The radius of the front and rear wheel. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the vehicle model. Figure 3: Sideview and top view of the single track nonlinear model [29]. It is also necessary to introduce the influential parameters of the wheel model, which are the Magic formula's \(C_{[f/r],[x/y]}\),\(B_{[f/r],[x/y]}\),\(E_{[f/r],[x/y]}\) parameters, which are fitting constants of a specific wheel-ground contact pair. These determine how much force can be transmitted between the tire and the road surface [30] based on the slip value. Moreover, the friction coefficient also has to be mentioned as a relevant parameter of the wheel model. The model has three inputs, which are the breaking \(M_{b}\) and driving \(M_{d}\) torques applied at the wheels, and the third is the steering angle \(\delta\) of the front wheel. The distribution of the brake torque \(M_{[f/r],b}\) is ideal for providing equal brake slips, while the driving torque \(M_{[f/r],d}\) is distributed between the front and rear with a time-dependent distribution factor \(\xi_{M}\). In the following model description, the variables without a subscription have to be considered in a ground-fixed coordinate system, while the variables with subscription \(W\) have to be considered in the wheel-fixed coordinate system and variables with subscription \(V\) have to be considered in a vehicle-fixed coordinate system, and the dot notation represents time derivatives. The possible direction of movements of the chassis is the movement along the \(x\) longitudinal axis, the \(y\) lateral axis, and the rotation around the chassis \(\Psi\) vertical axis, while the wheels are only able to rotate around their horizontal axes \(\phi_{[f/r]}\), and the lateral and longitudinal slips modeled in a dynamical manner \(s_{[f,r],[x,y]}\).