*7.2. Impact of the Clearance Margin yW on the Safety of Obstacle Avoidance*

The simulation results presented in Figures 19–21 have been obtained for clearance margin values *yW* = 0–2.0 m and for the CT unit being driven on dry and wet road surface with a speed of *v* = 40–90 km/h. This has made it possible to formulate a more detailed recommendation for the selection of *yW*.

**Figure 19.** Curves representing selected physical quantities for the cosine trajectory planning method, *La* = 6 m, *v* = 60 km/h, dry road surface, and three clearance margin values *yW* (individual columns): (**A**) CT unit's motion animation; (**B**) path planning trajectory *yM*(*x*) and vehicles center of mass trajectory *yCs*(*x*); (**C**) steering wheel angle *δH*(*x*), yaw angle *ψA*(*x*), trailer drawbar turning angle Δ*ψ*(*x*); (**D**) tire sideslip angles for the rear axle of vehicles *αs*(*x*); (**E**) lateral acceleration of vehicles center of mass *ayCs*(*x*).

**Figure 20.** Distance *yK* between the front corner of the car and trailer (*NFRA*, *NFRB* ) and the obstacle when the latter was passed by wet road surface, *yW* = 0.0–2.0 m.

**Figure 21.** Extreme values of the steering wheel angle (the first extremum of the *δH*(*x*) curve) vs. the clearance margin *yW* for vehicle speeds of *v* = 40–90 km/h.

Figure 19 presents the process of obstacle avoidance by a CT unit moving with a speed of *v* = 60 km/h, with the trajectory *yM*(*x*) having been calculated for *yW* = 0.2 m, 0.5 m, and 1.0 m. The results of these simulations provide grounds for a statement that when the clearance margin value *yW* was reduced from 1.0 m to 0.2 m, then:


It should be added here that when the clearance margin value was raised within the range *yW* > 0.5 m in the vehicle driving conditions under analysis, then:

• at the instant when the obstacle was being passed by, the tire sideslip angle of the motorcar rear axle wheels rose from 10.0 deg to 13.8 deg, i.e., it reached values that made it difficult to control the vehicle movement (cf. the *Fy*(*α*) curve in Figure 8);

• the differences between the trajectories (*yCB*(*x*) − *yCA*(*x*)) and the yaw angles (*ψB*(*x*) − *ψA*(*x*)) of the trailer and the car increased as well, which may result in the instability of the CT unit's motion on the road section just beyond the obstacle.

The tests represented in Figure 19 have confirmed that the applying of low *yW* values when planning the obstacle-avoiding trajectory would be well justified, but within a limited range of vehicle speeds (especially on wet road surface). This information was gained after the tests were extended to a vehicle speed range of *v* = 40–90 km/h.

In Figure 20, simulation results have been presented in the form of curves *yK* = *f*(*yW*) plotted for the obstacle avoidance on wet road surface. When analyzing these results, it should be taken into account that the *yK* values should be higher than zero, preferably within the range of 0–2 m, for the obstacle avoidance to be safe. The course of the green curve in Figure 20 confirms the conclusions drawn from the tests presented in Figure 19 for *v* = 60 km/h. For such a vehicle speed, the *yW* values may be chosen from a wide range; previously, the recommendable value was specified as *yW* ∼= 0.2 m for dry road surface.

The angle *δH*(*t*) corresponds to a signal generated by the control system (Figure 3). Its values at the first extremum have been shown in Figure 21. During the initial part of the obstacle avoidance maneuver (*x* ∈ (0; 0.5*x*<sup>0</sup> >), they should steeply rise so that the CT unit would be able to follow the path with the curvature as planned. Such an effect may be obtained if a big distance margin *yW* is adopted. With this objective in view, high clearance margin values should be used when planning the trajectory *yM*(*x*). However, it is not easy to make the CT unit avoid the obstacle this way at as low speeds as *v* > 60 km/h because of high values of lateral acceleration *ay*, lateral force *FQ*, and tire sideslip (Figures 18D and 19D), which increase the distances between the vehicle paths (*yCA*(*x*) and *yCB*(*x*)) and the trajectory planned (*yM*(*x*)) (Figure 21B for *v* = 70 km/h). This highlights one more of the dilemmas to be resolved when selecting the *yW* values.

A synthetic summary of the simulation results presented in Figures 19–21 has made it possible to formulate some recommendations for the selection of *yW*; simultaneously, it has highlighted the following dilemmas:


The very diverse impact of *yW* on the obstacle avoidance by a CT unit will be made use of to build a set of clearance margin values recommendable for the planning of an obstacle-avoiding trajectory *yM*(*x*).
