*6.3. Procedure of Analysing the Calculation Results*

When the best trajectory planning method and the desirable *La* value were selected, individual simulations were treated as successive alternatives of solving the obstacle avoidance problem. The selection was based on an analysis of a set of simulation results, which included numerical values, curves recorded, and logical values.

A procedure was established, which was taken in apart from the AHP (analytic hierarchy process) method [41,42]. In that method, logical values may be used apart from numerical ones, which was of considerable importance in the assessment process. The following steps were adopted in the procedure:


The results of experimental and simulation tests [43] of similar processes have made it possible to formulate the following criteria of recognizing the performance of the obstacle avoidance maneuver (i.e., the criteria and sub-criteria) as correct:


The above was taken into account when the results obtained for individual solutions (i.e., the simulation results for individual alternatives) were assessed. In consequence, the following has been decided:

	- (a) safe vehicle path, i.e., CT unit's motion between lines *Rmin* and *Rmax* (Figure 1) or *yCA*(*x*), *yCB*(*x*) ∈ {0.5*b*; 2*d* − 0.5*b*};
	- (b) vehicle's motion stability maintained, i.e., *ay* < *ayMAX* and Δ*ψ* < Δ*ψMAX*.
	- (a) direct:
		- clearance between the car side and the obstacle when the latter is being passed by (*yKA*);
		- clearance between the trailer side and the obstacle (*yKB*);
	- (b) indirect:
		- car yaw angle relative to the preset vehicle trajectory (Δ*β*);
		- departure of the actual car trajectory from the planned one (|*yM* − *yCA*|);
	- (a) length of the imaginary anticipation radius (*La*) from 4 m to 12 m;
	- (b) methods of calculation of the trajectory planned: with a cosine curve, circular arcs, and parabolas;
	- (c) vehicle speed (*v*) from 40 km/h to 80 km/h on dry and wet road surface.
	- (a) Sub-criteria (Ca)
		- -2.0 m > *yKA* > 0 m;
		- -2.0 m > *yKB*> 0 m;
	- (b) Sub-criteria (Cb)
		- -|*α*| < 16 deg; |Δ*β*| < 90 deg;
		- -|*yM* − *yCA*| < 2 m;
		- -|*yM* − *yCB*| < 2 m;
		- *x*(*yCA* = 3 m) < 25 m.

The most desirable values of the parameters taken as the sub-criteria may be described as follows:


#### *6.4. Results of Applying the Procedure That Has Been Established*

Figure 16 shows example time histories describing the physical quantities that are taken into account in the procedure presented above, i.e., the paths travelled by vehicle mass centers *yCA*(*t*) and *yCB*(*t*), tire sideslip angles *αA*(*t*) and *αB*(*t*), lateral accelerations *ayCA*(*t*) and *ayCB*(*t*), and trailer drawbar turning angle Δ*ψ*(*t*). To facilitate the interpretation of the graphs, curves representing the trajectory planning function *yM*(*t*) and the steering wheel angle *δH*(*t*) have also been plotted.

**Figure 16.** Curves analyzed in the procedure presented above (example obtained for the alternative with *v* = 70 km/h, dry road surface, and cosine method used to plan the trajectory).

To facilitate the inference, pursuant to the procedure presented, the simulation results have been brought together with respect to two points of view:


**Figure 17.** Summarized results of simulations of trailer's motion in a CT unit during an obstacle avoidance maneuver for three trajectory planning methods (explanation in the text above). Vehicle speed values: *v* = 40 km/h, 60 km/h, and 80 km/h; *La* values within a range of 4–12 m; road surface: dry.

Table 1 shows a fragment of a set of results obtained for five obstacle avoidance alternatives. Such summaries of values of the physical and logic quantities determined during individual simulations were used in the procedure described above.

Figure 17 presents an example of the impact of *La* on the results of simulation of the trailer (i.e., vehicle B) motion. In the graphs, the area of acceptable simulation results (according to the sub-criteria adopted) has been marked by double fine lines indicating the upper limit of the said area. A few curves have been plotted in the graphs that represent the functions taken into account in the procedure under consideration. In particular:


• Figure 17C–E show the *yKB*(*La*) curves, representing the clearance between edge *K* and trailer corners (corners *NFRB* and *NRRB*) at the instant when the obstacle is passed by. The safe obstacle avoidance is only possible (i.e., the B criterion, see Table 2, is met) for the alternatives for which the *yKB* values obtained fall between the double fine lines (*yKB* ∈ (0; 2 m)). Such a result was achieved e.g., for *v* = 60 km/h and *La* ≥ 7 m in the cosine method, while in other methods, the *NRRB* corner goes beyond the area of the lane available. For *v* = 80 km/h, the CT unit will hit the obstacle, regardless of the trajectory planning method used.

**Table 2.** Connection between the values given in individual columns of Table 1 and the procedure described above.


The results obtained for individual solution alternatives, exemplified in Table 1 and Figure 17, facilitated the use of the procedure presented. The procedure enabled the following decisions to be effectively made about the temporary solutions implemented in the control system for the distance *x*<sup>0</sup> of the CT unit approaching the obstacle:

