**8. Selection of a Clearance Margin** *yW* **for the Obstacle Avoidance Maneuver**

The results of an assessment carried out according to the procedure prepared as described in Section 6 became a basis for selecting temporary parameters, i.e., a method of planning the trajectory *yM*(*x*) and determining the value of *La* for the critical situation under consideration. After the temporary parameters are determined as described above, a trajectory *yM*(*x*) is planned in the control system for a safe vehicle path to be obtained. The course of this path and the behavior of the vehicles moving along this path strongly depend on the dynamic characteristics of the CT unit, including the forces acting on the vehicles. In the critical situation under consideration, it is difficult to predict the values of such forces and the effects of their action (tire sideslip, skidding of wheels of individual axles, vehicles' yaw angles from the carriageway centerline, etc.). In such a situation, it is good to have a set of the *yW* values that would facilitate the planning of a safe trajectory. The description provided in Section 2 and Figure 1 shows that the clearance margin in the critical situation under analysis should be within a range of *yW* ∈ (0, 2 m). Such a margin makes it possible to reserve a corridor for the CT unit's motion, wider than the CT unit width *b*. The said corridor is necessary because the vehicles move in positions yawed by angles *ψ<sup>A</sup>* and *ψ<sup>B</sup>* from the carriageway centreline when they are avoiding the obstacle. This yaw can be seen in Figures 14 and 15.

In the simulation tests carried out, various alternatives of the obstacle avoidance process were analyzed. To assess the alternatives, the distances *yKA* and *yKB* between the edge (corner) of the obstacle and the side of the car and the trailer when passing by the obstacle were taken as a basis. The test result is considered successful if, during the obstacle-avoiding phase of the maneuver, the CT unit safely passed by the obstacle and stayed within the lane planned also just beyond the obstacle, i.e., within the road section *x* ∈ (*x*<sup>0</sup> ; *x*<sup>0</sup> + 10 m (cf. Table 1). When selecting the *yW* (clearance margin) values for the trajectory planning, the following results were considered satisfactory:


If a collision took place between the CT unit and the obstacle contour or the CT unit found itself outside of the road (i.e., outside of the carriageway and the road shoulder) or overturned, such a test result was considered as a "collision with the obstacle" or maneuver failure. The test results have been presented in a synthetic form in Figures 22 and 23 and the clearance margin (*yW*) values used to plan the safe trajectory *yM*(*x*) are specified in Table 3.

**Figure 22.** Area of choosing the *yW* values when planning a vehicle trajectory for safe obstacle avoidance on dry road surface; motorcar and trailer.

**Figure 23.** Area of choosing the *yW* values when planning a vehicle trajectory for safe obstacle avoidance on wet road surface; motorcar and trailer.


**Table 3.** Possibilities of safe avoidance of the obstacle.

The area of acceptable selection of the *yW* values, as plotted in Figure 22, shows that a motorcar in a CT unit moving on dry road surface would be able to avoid the obstacle even if travelling with a speed of up to *v* = 68 km/h, while the trailer towed by it would safely avoid the obstacle only if its speed did not exceed *v* = 62 km/h. If the road surface is wet (see Figure 23), a safe obstacle avoidance would only be possible if the CT unit's speed were limited to *v* = 54 km/h. Assuming the acceptability of using the road shoulder (up to 1 m wide) in the critical situation, the obstacle would be avoided if the vehicle speed were up to 68 km/h on dry road surface and up to 62 km/h on the wet road surface (see Table 3).

The tests described have shown the narrowness of the area of selection of the *yW* values that would enable safe obstacle avoidance in the critical situation under consideration.

### **9. Summary**

This study is dedicated to a critical (pre-accident or causing a collision hazard) road situation where immediate counteraction of the vehicle control system is required in a space that has been only partly defined. The hazards accompanying such a situation arise from the short time available for the reaction and from the complexity of the interactions taking place between the motorcar, trailer, controller, and road surface. The said interactions are strongly non-linear. In the study, an assumption has been made that the information received from the environment perception system will cause the settings of the control system of the CT unit to be re-adjusted as appropriate. The new settings will be introduced temporarily, for the time of passing by the obstacle, and their values will differ from those required at the stable vehicle drive before and after the obstacle avoidance maneuver.

In consideration of the above, the following was worked out:


Based on the above, tests were carried out to select the control system parameters (temporary and variable) that would be appropriate for the specific difficult road situation. The impact of the method of planning the trajectory *yM*(*x*) and the value of the anticipation radius *La* in the control system on the feasibility of safe avoidance of an obstacle having suddenly appeared has been examined. In consideration of high curvatures of the trajectories planned, high vehicle speeds, and dynamic action of the trailer, particular attention was paid to the impact of tire slip and skidding on vehicles' behavior when moving along the curvilinear path.

The research carried out has made it possible to formulate the following findings and conclusions for the CT unit's control system operating in the critical situation under analysis:


Results of the research being carried out support the current trends in the construction of vehicle control algorithms, where the definition of rigid operation rules is being abandoned in favor of immediate and ongoing shaping of the properties and areas of suitable solutions. This is of significant importance for rare critical situations. In such cases, the temporary data obtained from previous computer simulations and stored in the system controller are chiefly used.

**Author Contributions:** Conceptualization, L.P., P.S. and M.Z.; methodology, L.P. and M.Z.; software, P.S.; validation, T.P. and P.S.; formal analysis, L.P., M.Z., P.S.; investigation, L.P., M.Z. and P.S.; resources, T.P.; data curation, P.S.; writing—original draft preparation, L.P.; writing—review and editing, M.Z., P.S., M.G., T.P. and T.L.S.; visualization, M.Z., L.P. and P.S.; supervision, L.P.; project administration, M.Z.; funding acquisition, M.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

