## 2 Materials and Methods
### Adaptive Co-Pilot--Arbitration  
Once the main controller has a configurable authority that assures performance and stability, the next step is to design the decision logic that finds the appropriate value of \(\lambda_{\text{dim}}\), to distribute the control authority between driver and automation. For this purpose, an FIS is designed to perform the arbitration process. FIS algorithms have offered a solution for including human knowledge in the design of automated driving functions [26], including applications for shared control [39]. This method uses a set of MFs and linguistic IF-THEN rules that defines the output of the decision logic. Figure 4: Stability test with variable damping (\(b_{\lambda}\)). The arbitration module proposed in this section is developed specifically for the use case of assistance for a distracted driver (described in Section 3.1). Similar work on shared control for inattentive drivers [22] proposed a strategy where the authority of the controller increased proportionally to the distraction level. In addition to this consideration, our decision logic also considers the deviation from the lane center as a second condition that helps to calculate the appropriate authority (this will be important in design principle (1)). To summarize, the fuzzy logic system is composed of two inputs (lateral error and level of driver distraction) and one output (level of authority \(\lambda_{\text{dim}}\)), as described in Table 5. The two inputs are chosen as variables that represent the driver and the automated system. Concerning the design of the MFs, the values for each label are representative rather than exact values (this is one of the advantages of FIS algorithms, as it resembles how humans define variables). In terms of lateral error, 1.5 m (HIGH) is the distance when the vehicle is at the lane border, while 0.3 m (NONE-LOW) was selected to give the driver some freedom to deviate from the lane center without experiencing intervention by the automated system. On the other hand, the MFs for driver distraction were selected by observing the raw distraction signal of different drivers. With respect to the output (\(\lambda_{\text{dim}}\)), 15 Nm (HIGH) is the maximum steering motor torque, while the other values were selected experimentally based on subjective driver feeling on the steering: (a) MED, strong but possible to override (10 Nm), (b) MED-LOW, strong guidance with some driver freedom to move (6 Nm), and c) LOW-MAN, soft guidance barely felt at the steering (2 Nm). Additionally, the design of this arbitration module considers the following two principles: (1) minimal intervention and (2) safety over comfort. 1. The minimal intervention principle follows the idea that drivers only need assistance under specific circumstances; on the contrary, automation could create unnecessary conflicts that will produce a feeling for the driver of being controlled all the time, and decrease the driver acceptance rate. Additionally, not intervening when drivers are in suitable conditions to drive aims to increase the sense of responsibility for the driving task, in order to avoid over-trust in automation. Moreover, the inclusion of the lateral error in the logic is part of this principle, as assistance should not be given to the driver only considering the distraction level (as the driver could maintain a