**1. Introduction**

Autonomous vehicles are considered as a solution expected to improve the efficiency of transport processes. An important good point of the introduction of autonomous vehicles will be an improvement in road traffic safety. Such an effect, however, will not be produced automatically. It may be achieved through research on vehicle behaviour, including the selection of a vehicle controlling method that would be adequate for difficult road situations. The problem of adapting the vehicle control process to special road situations has been raised, e.g., in [1–7]. A key factor is here the programming of the vehicle control system, in which the algorithms responsible for planning the obstacle-avoiding trajectories are of significant importance. At present, the research works on the control

**Citation:** Prochowski, L.; Ziubi ´nski, M.; Szwajkowski, P.; Gidlewski, M.; Pusty, T.; Sta ´nczyk, T.L. Impact of Control System Model Parameters on the Obstacle Avoidance by an Autonomous Car-Trailer Unit: Research Results. *Energies* **2021**, *14*, 2958. https://doi.org/10.3390/ en14102958

Academic Editor: Islam Safak Bayram

Received: 2 April 2021 Accepted: 17 May 2021 Published: 20 May 2021

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systems are predominantly focused on the planning of vehicle trajectories for lane-change maneuvers (obstacle avoiding, overtaking) [6,8–11].

A lane-change maneuver of this kind is usually planned in advance and performed in predictable conditions, where the restrictions arising from the necessity of avoiding collisions with other vehicles participating in the traffic or from the kinematic and dynamic properties of the vehicle in question can be easily met. In such a situation, a planning stage can be introduced to the control system, at which time the appropriate trajectory would be chosen from a library of solutions pre-programmed in the system controller [12].

The addition of a trailer to the autonomous vehicle will result in better economic and energy efficiency of the transport processes. However, this will also bring about a change in the dynamic properties of the CT unit compared with those of the motor vehicle alone. The presence of a trailer radically affects the dynamics of the towing vehicle and reduces the stability of the vehicle combination as a whole. An extensive review of such research works on CT units has been presented in [13,14]. The attaching of a trailer to a motor vehicle may also cause oscillations of the CT unit in the final phase of the obstacle avoidance process (in the initial phase, the trajectories of both vehicles are almost identical). This can be observed, e.g., in the profile of the trajectory of the CT unit's center of gravity (CG) for rising vehicles' yaw angles from the carriageway centerline [15]. The research on the stability of CT unit's motion, reported in [13,14], has shown that the instabilities occurring in the trailer and vehicle's motion strongly depend on the mass and moment of inertia of the vehicles and on the drawbar length. Experimental research on the stability of a car-trailer unit within a sped range of 48–90 km/h, with a rapid turn of the steering wheel, has confirmed decisive impact of the parameters mentioned above on the behaviour of the vehicle combination [16]. These findings have been taken into account in the modelling described hereafter. The controlling of a motorcar-trailer unit is a far more complex issue in comparison with the controlling of a motor vehicle alone [15]. The values and ranges of the input parameters applied to the control system model must be different as well.

The participation of autonomous motor vehicles in the road traffic may be described with using a few elementary vehicle trajectory models: following of the preceding vehicle, following-up of predesigned reference models, and driving to follow up models that would represent the planned (theoretical) vehicle trajectory [5,6,17]. The design of such models is based on analyses of specific traffic situations and the most frequent drivers' behaviors [18,19]. This is of critical importance for the safe operation of autonomous vehicles in the road traffic where cars driven by human drivers will remain predominate for many upcoming years.

Regardless of the driving model chosen, autonomous vehicles move to follow up a preplanned trajectory. This is also the case when the obstacle avoidance takes place. A critical review of the trajectory planning methods has been presented, e.g., in [1,11]. The trajectory planning is based on determining the curve that describes the lateral displacement of the center of vehicle mass (e.g., when the vehicle changes the lane to the adjacent one) in the form of algebraic equations, which may represent sequences of circular arcs, polynomial splines, clothoid splines, Bézier curves, etc. [1,5,9,20]. When the desired vehicle trajectory is determined, it is important that the basic limitations dictated by the properties of real cars and road surface should be taken into account [21]. As an example, a method of generating the vehicle trajectory has been presented in [8], where the maximum acceptable values of the lateral (centripetal) acceleration of the car were taken into account. In the work reported in [9], the vehicle trajectories and their curvatures were planned taking into account the comfort of vehicle occupants, e.g., a requirement was adopted that the lateral acceleration should not exceed 1.6 m/s2 (the limit for good comfort) or 3.6 m/s2 (the limit for medium occupant's comfort). In the vehicle control system, calculations are carried out to plan the desired vehicle trajectory and to track the actual one. As another option, a controller provided with a library of pre-programmed solutions suitable for plannable situations may be used [12]. An example of planning a trajectory for a safe lane-change and obstacle avoidance maneuver, taking into account the current traffic situation and the

dynamic properties of the CT unit, is shown in [10]. In the vehicle control process, the goal is to minimize the distance between the current position of the center of vehicle mass and the planned vehicle trajectory, and to minimize the difference between the angular positions of the longitudinal vehicle axis and the tangent to the said trajectory [22–24].

In this role, PID (proportional–integral–derivative) controllers and controllers based on fuzzy logic predominate. As an example: in [20,24], the control process is based on the follow-up of the preset vehicle trajectory by a PID controller and the effective use of fuzzy logic in the controllers of mobile robots and vehicles is shown in [18,23,25]. A good result of controlling the drive of mobile platforms in [21] was achieved by using two different control techniques. The controlling of a car with a trailer in typical road situations has been analyzed in [10], where the current obstacle position and the static space limitations posed by the road infrastructure have been taken into account. An interesting method of planning the vehicle trajectory, taking into account the field of "obstacle repulsion" potential during the lane-change maneuver, has been proposed in [6]. In [26], on the other hand, the trajectory was planned based on the preset direction of vehicle movement and the positions of the centers of front and rear axles of an articulated wheel loader relative to the optimum trajectory. The motion of such a machine in a predetermined environment has been described by a trajectory composed of circular arcs and line segments.

At present, the vehicle trajectory is predominantly planned on the grounds of the limitations dictated by the structural vehicle's properties [7,27], and the basic vehicle control methods include the fuzzy logic algorithms [11,27].

Most of the reported methods of generating the desired vehicle trajectory apply to typical maneuvers often performed in road traffic. In contrast, there is a lack of research works and models applicable to the critical situations where autonomous vehicles towing trailers with a high speed would be involved. Particularly dangerous situations take place when the vehicle and the obstacle move along collision paths and in an environment that has been only partly defined.

The study presented includes an analysis of the problem of avoiding an obstacle in a critical road situation that may arise from, e.g., another vehicle driver's failure to yield the right of way on a road intersection. This usually develops into front-to-side collisions of moving vehicles; the percentage of such collisions in the total number of road accidents in Poland shows an upward trend. At present, the said percentage amounts to 32% [28].

It is peculiar to the critical situations that they require difficult defensive (accidentavoiding) maneuvers to be performed, which are often based on very aggressive vehicle control. If this is the case, the vehicle trajectory is planned without being impeded by any limitations related to the possible occurrence of excessive lateral acceleration, tire sideslip, or development of forces exceeding the lateral tire-road adhesion. The analysis applies to a road situation where immediate counteraction is required in a space that has been only partly defined. The autonomous vehicle's control system is expected to plan a safe vehicle trajectory based on information received from an environment perception system. It has been assumed that the algorithm of controlling the vehicle will not change in spite of the occurrence of a critical situation. Nevertheless, the following factors may change according to the information received from the environment perception system:


Therefore, a temporary trajectory is planned in the critical situation under analysis in order to avoid a collision with the obstacle.

The objective of this study is to determine the impact of the trajectory planning method and of the values of some control system parameters on the feasibility of the safe avoidance of an obstacle having suddenly appeared. In this study, the obstacle is a motor vehicle whose driver has violated traffic regulations. The obstacle is moving on a road intersection with poor visibility along a collision path in relation to an autonomous CT unit travelling with a high speed (Figure 1). After hard braking, the said motor vehicle has stopped with blocking one lane for the CT unit. A trajectory planning method and desirable values of the temporary parameters of the control system, which is based on an anticipating model and fuzzy logic, will be shown. The areas of advantageous choice of the temporary parameter values for the critical situation under analysis will be indicated. The problem is explored using computer simulation based on a model of CT unit's dynamics in curvilinear motion. The model was subjected to a validation process, in which results of experimental tests of dynamic lane changing by the CT unit were used.

**Figure 1.** Road situation under analysis.

In this study, a situation is analyzed in which the vehicle's environment perception system has detected an obstacle that suddenly appeared at a distance that may be shorter than the stopping distance of the autonomous vehicle with a trailer. For such a situation, 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 adjusted as appropriate. The new settings will be introduced temporarily (only for the time of avoiding the obstacle) and their values will differ from those required at the stable vehicle drive before and after the obstacle avoidance maneuver. The necessity of local trajectory planning in critical situations has been pointed out, e.g., in [29], where the limitations additionally arising from excessive tire slip and from development of forces exceeding the lateral tire-road adhesion have been highlighted.

In this problem, the control system must cope with a very difficult task. This is not only due to the very short time available for the perception of a specific road situation and for the trajectory planning, but also because of the dilemmas that would arise from the possible lack of any non-collision solution. Such a sudden situation, where only very few of the practicable defensive maneuvers may result in the successful avoidance of a road accident, may be defined as a critical one.

The behavior of a CT unit on the 0–60 m road section under analysis, i.e., before and beyond the obstacle, has been analyzed in [2]. In particular, the trajectory of the center of mass of the vehicle combination has been examined. The analysis presented herein is more detailed and the motion of outermost points on the external edges of the vehicle and trailer has been observed. Simultaneously, the analysis has been reduced to a 0–30 m road section, i.e., to the situation before the point where a collision between the vehicles involved may occur.

#### **2. Scenario of the Road Situation under Analysis**

In this study, the motion of the combination of an autonomous motorcar with a cargo trailer (CT unit) on two lines road with right of way is analyzed. During the motion, the vehicle's perception system has just detected the sudden appearance of another vehicle moving along a collision path (Figure 1). The said other vehicle may be expected to block within a short time the whole width of the lane used by the CT unit and thus to become an obstacle for the latter.

The following notation will be used in this study:

*A*, *B*—autonomous motorcar and trailer, respectively of center of mass *CA*, *CB*;

*Rmin*, *Rmax*—symbols indicating the outermost edges of the lanes involved;

*La*—anticipation radius, used when trajectory *yT*(*x*) is generated;

*yM*(*x*), *yT*(*x*)—planned and preset vehicle trajectory;

*y*0—instantaneous obstacle position in relation to lane edge *Rmin*;

*yCA*(*x*), *yCB*(*x*)—trajectories of the centers of mass of vehicles *A* and *B*;

*K*, *P*—characteristic points: trace of the obstacle edge and target point for the planning of a safe trajectory *yM*(*x*);

*yW*—clearance margin, necessary for safe obstacle avoidance;

*yK*—clearance between the vehicle and the obstacle at the instant when the latter is being passed by;

*b*, *d*—widths of the vehicle combination (CT unit) and the lane;

*δH*, *δ*, *α*, *β*—steering wheel angle, steering angle, tire sideslip angle, and angle of position of the tangent to the planned or preset trajectory of the vehicles;

*R*0, *κ*—radius and curvature of the vehicle trajectory;

*ωu*; *vTu* = *ωurDu*—angular velocity of the *u*th vehicle wheel and circumferential velocity of the tyre;

*rDu*—dynamic tire radius of the *u*th vehicle wheel;

*v*, *vA*—velocity of the center of mass of vehicle *A*;

Δ*ψ* = *ψ<sup>A</sup>* − *ψB*—trailer drawbar turning angle;

*ψA*, *ψB*—yaw angles of the motor vehicle and the trailer;

*FQ*, *ay*—centrifugal inertia force and lateral acceleration of center of mass of the vehicle body.

The *OXY* coordinate system is attached to the *Rmin* lane edge.
