# Evolving the Controller of Automated Steering of a Car in Slippery Road Conditions
## 1 Introduction
This model mimics well the steering behavior of a human driver and, similarly to such a driver, provides a good quality of steering on dry, non-slippery roads. With an appropriate tuning of the relevant gain coefficients (depending on the specific features of the physical model of the particular car), on dry roads the servo-control could achieve a steering behavior that is very similar to that of a human driver in adequate cognitive condition [12]. However, to the best of our knowledge, there is no documented research on the applicability of the PD servo-control model for automated control of the car under more challenging--_slippery_ (e.g., wet, snowy, or icy)--road conditions. We speculate that PD servo-control might not be adequate in such conditions because the vehicle dynamics model of a directionally unstable (e.g., understeering or oversteering) car on slippery roads is more complex and involves additional variables (beyond the lateral and angular deviations from the desired trajectory) pertinent to the state of the car than are involved in a car driven on normal, non-slippery roads [13]. Such complexity might not be expressed adequately by the relatively simple PD servo-control. Moreover, in an eventual case of unacceptability of the PD servo-control as a steering model in such slippery conditions, which alternative model would be more appropriate, and how to develop it, would be open questions too. These two concerns--the eventual inapplicability of the PD servo-control model and the lack of understanding of its alternative(s) for the steering of a car on slippery roads--motivated our research. Our _objectives_ were (i) to examine the applicability of PD servo-control as an auto-steering model of a car on slippery roads, and (ii) to investigate the feasibility to develop heuristically the optimal (possibly nonlinear) steering model in such road conditions by means of simulated evolution via genetic programming (GP). Our work is additionally motivated by the fact that despite the significant body of research on computational intelligence in The Open Racing Car Simulator (TORCS) [14; 15], we are not aware of any implementation of SAF of the car on slippery roads in this simulation environment. Rather, the focus of such research is on the automated development (via either a simulated evolution or machine learning) of racing agents aimed at attending (and, ultimately, winning) simulated car races. The eventual incorporation of SAF on slippery roads would be seen as unneeded as the races are usually held on dry, grippy tracks where the cars seldom experience any significant directional instability. On the other hand, the inspiration for the proposed heuristic development of SAF via GP is that, to the best of our knowledge, there are no documented attempts to automatically develop the SAF on slippery roads via evolutionary computing and GP in particular. The related work includes the seminal work of [PERSON] et al. (2018), who have demonstrated that GP--as an unsupervised machine learning approach--could be successfully applied to heuristically develop from scratch a PD controller that stabilizes a car on slippery roads by eliciting precisely quantified asymmetric brake forces on its wheels. The control of the steering, however, has not been subjected to any optimization for the given slippery road conditions, but rather implemented as a generic, handcrafted PD servo-control that has performed well on dry, grippy roads. Similarily to GP, end-to-end reinforcement learning (e.g., of deep neural networks) does not require an explicit modularization of the controller ([PERSON] et al., 2016; [PERSON] et al., 2017). Instead, the internal structure of the controller is automatically developed by the learning framework. The advantage of his approach is that it could discover and utilize the unusual features of the environment and develop sophisticated controllers that could solve the tasks for given (generic) environmental conditions.