# Evolving the Controller of Automated Steering of a Car in Slippery Road Conditions
## 2 Materials and Methods
### Evolving the Steering Controller via GP  
The third controller we comparatively investigated was a controller utilizing (i) an extended set of parameters (EP) pertinent to the state of the car, and (ii) a relaxed--an arbitrary (rather than additive, as in the PD and PID controllers)--structure of its analytical model (RM) developed heuristically via GP. We denote it the GP-RMEP controller. The rationale of adopting GP is based on our concerns that the above-mentioned PD and PID servo-controllers might not be adequate, because, compared to a car driven on normal, non-slippery roads, the vehicle dynamics model of the skidding, directionally unstable car on a slippery road is rather complex and might involve of additional parameters (beyond the lateral deviations from the desired trajectory) pertinent to the state of the car [13; 26]. Such complexity might not be expressed adequately by the relatively simple, additive PD and PID servo-control models. In addition, due to this complexity, we could not devise an eventual analytical approach to the steering of the car that would effectively counter its directional instability. Moreover, the only parameter pertinent to the state of the car--the lateral deviation \(e\)--used in the SAF, based on the PD and PID servo-control models, might not represent adequately the state of the unstable car on slippery roads. Indeed, even featuring the same lateral deviation, the car may experience different yaw rates and different accelerations of these rates. Depending on how the actual yaw rate differs from the desired one (estimated from the steering angle and the wheelbase of the car according to the bicycle model of a car [3]), the directionally unstable car might suffer either from understeer or oversteer, requiring a different steering input from the controller. On the other hand, increasing the number of state parameters would further complicate the model of the steering controller, which could render the formal, analytical approaches to devise such a controller practically unfeasible. Moreover, even if we assume that it is possible to handcraft the code (applying various top-down, theoretical approaches based on vehicle dynamics [25; 27; 28]) of a more complex, nonlinear PID SAF that controls the steering of an unstable, skidding car in such a way so it regains its stability in a more effective way than the simple PD and PID controllers based on the servo-control model, neither the  
Figure 4: Servo-control model of steering as a proportional-derivative (PD) steering controller. The steering angle function (SAF), defining the steering angle \(\delta\), is implemented as the sum of the proportional (P) and derivative (D) terms of the _error_: the deviation \(e\) from the center of the lane. degree of the optimality of such a code, nor the way to further improve it, would be apparent to the human developer. Therefore, an automated mechanism (i) to evaluate the quality of the coded SAF and (ii) to incrementally improve its intermediate version(s)--e.g., based on models of the natural evolution of species--might be needed. The proposed approach of employing GP implies that the SAF is automatically designed--without an a priori defined structure nor complexity--by a computer system via simulated evolution through selection and survival of the fittest in a way similar to the evolution of species in nature [4; 5; 29]. Adopting GP offers the following advantages:  
* Creative design: GP could evolve the controller's SAF of an arbitrary structure and complexity. Moreover, GP does not require an incorporation of any a priori, domain-specific expert knowledge. This is especially important when such knowledge is mostly empirical, rather than analytical. * Emergent intelligence: Rather than being introduced by the human expert, the task-specific knowledge of how to steer the car on slippery roads might emerge solely from the interaction of the problem solver (the GP) and the steering evaluation (trial) runs of the car [30].