## 2 Materials and Methods
### Target Quality Function Evaluation  
The target quality function value is intended to estimate the quality of the steering produced by the obtained SAF. We defined the criteria of such a quality from the desired characteristics of the trajectory of the car during the trial. It is simulated on a given test track (as shown in Figure 2) featuring a given friction coefficient \(\mu\), as follows: first, the simulated car is initially positioned at the starting position of the track. Then the car accelerates slowly to a given target speed. In order to render the task of controlling the car challenging, but solvable, the target speed was constant (maintained by simulated cruise control), and equal to 0.85, 0.9, and 0.95 of the critical speed \(V_{CR}\). The critical speed \(V_{CR}\) is the speed at which the car theoretically could pass the turns of the test track with the given coefficient of friction without losing control, running off the track, and eventually crashing. This speed is approximated as the speed at which the centrifugal forces during a steady-state cornering [13] become theoretically equal to the friction force. At the traveling speed of 0.85 of \(V_{CR}\), the car inherently suffers from intermittent instability (due to the yaw inertia both in the entry and exit of corners, and due to dynamic lateral weight transfer in corners [3; 7]) that we intend to counter by the use of the obtained SAF. The car, traveling at \(V_{CR}\) (or above) is theoretically uncontrollable. Consequently, there \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Evolved individuals & SAF \(\delta\) \\ \hline Genetic representation & Parse tree \\ \hline Set of non-terminals (functions) & \{+, -, *, \} \\ \hline \multirow{4}{*}{Set of terminals} & Variables pertinent to the state of the car, and their derivatives: \\  & lateral deviation (\(e\), \(e^{*}\)), speed (\(V\)), steering angle(\(\delta\)), lateral \\  & acceleration (\(a\), \(a^{*}\)) angular deviation (\(\theta\), \(\theta^{*}\)), and a random \\  & constant (C) \\ \hline Population size & 200 individuals \\ \hline Selection & Binary tournament, ratio 0.1 \\ \hline Elitism & Best 4 individuals \\ \hline Crossover & Single point, random, ratio 0.9 \\ \hline Mutation & Single point, random, ratio 0.05 \\ \hline Fitness value & Sum of (i) the area under the trajectory of the car around the \\  & center of the lane and (ii) the average of its lateral velocity. \\ \hline \multirow{2}{*}{Termination criteria} & (\#Generations \(>\) 200) or (no improvement of fitness during 16 \\  & consecutive generations) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of genetic programming (GP). would be no existing SAF that results in a steerable car. Similarly, a car traveling considerably slower than \(V_{CR}\) does not suffer from any instability, and its steering could be accomplished adequately by the canonical servo-control models. The speeds of the car during the trials on the track with different friction coefficients are shown in Table 4.  
The speed of the car is kept constant during the trial by a simple, handcrafted cruise control mechanism that maps the difference between the desired speed (e.g., as shown in Table 4, 13.3 m/s for the trial on a track with friction coefficient \(\mu=0.5\)) and the actual one into an increment (or decrement) of the position of accelerator pedal. As the car reaches the desired speed, the steering of the car is assumed by the obtained SAF. Then, the latter starts to continuously (with a sampling frequency of 40 Hz) produce the desired steering angle \(\delta\) calculated for the currently perceived values of the parameters pertinent to the state of the car. The desired trajectory of the car is the center of the lane. The estimation of the current trajectory obtained via the SAF with new parameters is calculated with the same target quality function as earlier [4] with the purpose of a correct result comparison.