**7. Analysis of the Motion of a CT Unit When Avoiding an Obstacle**

At the next step, the CT unit's motion was analyzed with taking into account the temporary decisions made in Section 6. The cosine function was adopted as a basis for the method of planning the vehicle trajectory for the distance travelled by the CT unit when approaching the obstacle; the anticipation radius value was assumed as *La* = 6 m. For such assumptions, recommendations were worked out regarding the clearance margin value *yW* necessary to plan a trajectory that would ensure safe avoidance of the obstacle. The area of searching for the *yW* values is limited by the available space in the carriageway (*Rmax* and *y*0, see Figure 1). In the critical situation under analysis, the *yW* value may be within a range of 0–2 m.

In consideration of the above, model tests were carried out for various values of clearance margin *yW* and CT unit's speed *v*. The results of these tests made a basis for recommending the favorable *yW* values.

### *7.1. Impact of Vehicle Speed on the Obstacle Avoidance Process*

The vehicle speed is an effect of control system's decision made within following the general strategy of CT unit's motion. Figure 18 shows simulation results obtained for *v* = 50 km/h, 60 km/h, and 70 km/h.

The simulation was carried out while observing, in particular, the behavior of the CT unit driven on dry road surface to follow a trajectory *yM*(*x*) calculated for a clearance margin of *yW* = 0.5 m. The applying of rising vehicle speed values as an input caused:


**Figure 18.** Obstacle avoidance simulation results obtained for the cosine method, *La* = 6 m, *yW* = 0.5 m, dry road surface and different driving speeds (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*).

The above shows that the higher vehicle speed, the more attention should be paid to the clearance margin values within *yW* < 0.5 m when searching for the trajectory. If this is done, the trajectory curvature as well as the *ay* values will be reduced. In consequence, the centrifugal force and the angle *ψ<sup>A</sup>* of yaw of the car (and of the trailer, too) in the dangerous direction will decrease (Figure 18A). The risk of unstable trailer's motion resulting from high yaw angle values *ψ<sup>A</sup>* and *ψ<sup>B</sup>* has been confirmed by the research reported in [15]. Therefore, the lowering of the *yW* values when planning the trajectory *yM*(*x*) may produce advantageous solutions.
