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In the paper a hierarchical overtaking strategy, which is a driver assistance function or rather an autonomous function in electric/autonomous vehicles, is proposed. The solution uses speed and acceleration signals from the surrounding vehicles. These signals are processed with clustering methods in order to achieve probability density functions and predict their expected motion. The strategy includes several additional layers, such as decision making concerning the maneuver, the computation of the required trajectory, and the tracking control of the vehicle. Trajectory generation is formed as an optimization task, which is able to include the prediction model of the surrounding vehicles in the constraints. A robust Linear Parameter Varying (LPV) control design method is proposed to guarantee the tracking of the computed reference. The proposed strategy is able to guarantee the safe motion of the vehicles and handle the interactions with the other traffic participants.

Overtaking and lane changing maneuvers are critical on roads due to various types of human errors. The necessary distance required by the maneuver must be estimated accurately and the vehicle should return to the lane as fast as possible and the maneuver must be safe regarding the other participants in the traffic.

The appropriate handling of overtaking maneuvers is also difficult for several reasons:

The motion of the vehicle ahead must be monitored and predicted

The motions of vehicles in the environment, especially vehicles coming from the opposite lane and traveling in the return lane, must be monitored and predicted

The overtaking maneuver must be designed

Before the maneuver the decision concerning the necessary overtaking must be made

Several factors, such as lateral/longitudinal acceleration and jerks in relation to comfort, must be considered

steering, braking, and driving must be coordinated

Several different control approaches in the field of overtaking maneuvers of vehicles have been developed. An optimal control design of the overtaking trajectory using polynomial equations to minimize the lateral jerk was proposed by [

The prediction of vehicle motions is strongly linked to the overtaking in the field of autonomous vehicles; see, e.g., [

In this paper an overtaking strategy of our own vehicle is developed. In the following our vehicle will be referred to as ego vehicle. The overtaking strategy is formed in a hierarchical structure with different layers. The core of the autonomous strategy is the motion prediction of the preceding vehicle and surrounding vehicles (e.g., in the opposite lane). Speed and acceleration signals are used to generate probability density functions, which are built in a constrained optimization structure of the trajectory generation. The result of the calculation is a clothoid trajectory, which enhances smooth driving and traveling comfort. Moreover, the paper proposes a strategy, with which further vehicle motions can be considered, e.g., following and overtaking the preceding vehicles. The tracking of the designed trajectory is based on the robust LPV vehicle control, which has the important role in guaranteeing safety in all scenarios, such as overtaking, lane changing, and following the preceding vehicle.

The overtaking control has been composed of a hierarchical architecture with three different layers, as found in Figure

Architecture of the control system.

(a) The inputs of the surrounding vehicle estimation block are the longitudinal velocity and the acceleration signals of the ego and the surrounding vehicles, while the outputs are the lateral constraints in the vehicle motion

(b) Based on the constraints the actual reference signals

(c) Finally, the robust vehicle control computes the actual steering angle

In the rest of the paper the layers of the automated overtaking strategy are presented. The estimation of the surrounding, especially the preceding vehicle motion, which includes the processing of vehicle data and the prediction of its position, is presented in Section

Safe overtaking and lane changing maneuvers require information about the motion of the preceding vehicle. In this paper its motion is estimated using the current longitudinal velocity

The proposed estimation has two main steps. First, the preceding vehicle signals are processed through a clustering procedure and the probability density function is generated. Second, the future position of the vehicle is predicted based on the calculated density functions.

The preceding vehicle is considered to be driven by a human, whose velocity selection is determined by a reference velocity

Data on preceding vehicle.

The generation of probability density functions requires the clustering of data. In this vehicle dynamic examination clustering means that the collected data are ordered in groups, depending on their locations in the plane

The purpose of the algorithm is to minimize the Euclidean distance between the objects and the centre of the selected cluster, such as

In the estimation process the number of the clusters significantly influences the results. Several methods have been developed for the determination of the cluster number; see, e.g., [

Selection of cluster number.

Clustered data on preceding vehicle.

Results of the clustering show that the

Probability density function of preceding vehicle.

Based on the proposed algorithm the preceding vehicle data are transformed into a probability density function, which depends on both

The future position of the vehicle is predicted based on the longitudinal kinematic equations

Slices of probability density function at different velocities.

The computations of

Due to

Illustration of the

In the prediction of the vehicle position the probability density function has fundamental importance. The probability

Finally, it is necessary to mention that the proposed estimation method is also used for the estimation of the motions of the vehicles in the opposite lane. If the data

In the overtaking and lane changing strategy the result of the estimation is used for the computation of the vehicle trajectory. In the design two criteria are considered. First, the results of the estimation must be incorporated in the trajectory design to guarantee safe cruising. Second, the generated trajectory must guarantee a comfortable maneuver. It means that the motion of the vehicle must be smooth, which is achieved by applying a clothoid trajectory. The advantages of the clothoid trajectory were presented in [

The lateral motion of the vehicle is formulated based on the kinematic model of the vehicle, such as

To guarantee a smooth trajectory for the vehicle, the curvature

Piecewise linear formulation of the curvature.

The motion equations (

Using (

In the trajectory design the lateral position of the vehicle

The trajectory design of the overtaking maneuver is formed in a finite horizon length

Through the minimization of the cost function

Determination of

Finally, from (

The overtaking and lane changing strategy is based on the constrained trajectory optimization method (

Before the maneuver the ego vehicle reaches a preceding vehicle which is traveling at a slower speed. The vehicle must follow the preceding vehicle. If the preceding vehicle accelerates or decelerates the ego vehicle must strictly track the velocity within the speed limit. Meanwhile, it calculates a safe trajectory for the overtaking and lane changing. The optimization method (

However, if there is a follower vehicle in the inner lane which is traveling at a higher velocity, a conflict with the ego vehicle may occur during the overtaking maneuver. Moreover, if there is a vehicle in the opposite lane, a conflict with the ego vehicle in the maneuver may also occur. These maneuvers are considered unfeasible. Infeasibility means that it is impossible to find an appropriate trajectory which guarantees both the minimization (

When the traffic situation changes and the optimization becomes feasible, the overtaking maneuver can be performed. The maneuver is realized through the actuation of steering and driving/braking systems; see, e.g., [

Note that the proposed method can be used not only for overtaking, but also for simple lane changing maneuvers, e.g., changing the route in a highway intersection. In this scenario the reference signal of the road

The goal of the robust LPV control is to guarantee the tracking of the trajectory, which has been generated by optimization (

After the computation of the reference signals the tracking performances together with the control performance are defined as

The model of the vehicle is described by the dynamical bicycle model; see [

The control design is based on a weighting strategy, which is formulated through a closed-loop interconnection structure; see Figure

Closed-loop interconnection structure.

The design of the control is based on robust LPV methods. The advantage of these methods is that the controller meets stability and performance demands by using affine parameterized Lyapunov functions in the entire operational interval, since the controller is able to adapt to the current operational conditions; see [

To illustrate the efficiency of the proposed method a complex simulation scenario is presented. The traffic scenario contains four vehicles, such as the ego vehicle, two preceding vehicles, and another vehicle in the opposite lane. In the setting of the optimal trajectory computation the sample time is set at

The simulation is illustrated in Figure

Simulation scenario.

Start of overtaking

End of overtaking

Approaching the preceding vehicle

Tracking the preceding vehicle

Change of lane

Cruising with its own reference velocity

The numerical values of the lateral position and the velocity are illustrated in Figure

Simulation results.

Trajectory of the vehicle

Velocity profile

In the paper an overtaking and a lane changing strategy have been proposed. The expected motion of the preceding vehicle is predicted by using clustering methods and probability density functions. The trajectory design is formed as a constrained optimization problem, in which the traffic in the lanes of the road is considered. In the decision making concerning overtaking the motions of the surrounding vehicles such as the follower vehicle with higher velocity and vehicles in the opposite lane is also incorporated. The robust parameter varying tracking control design of the lateral dynamics has been presented. The proposed strategy is able to guarantee the safe motion of the vehicles and handle the interactions with the other traffic participants. The results have been illustrated through simulation examples.

No data were used to support this study.

The authors declare that they have no conflicts of interest.

The research reported in this paper was supported by the Higher Education Excellence Program of the Ministry of Human Capacities within the frame of Artificial Intelligence research area of Budapest University of Technology and Economics (BME FIKPMI/FM). The research was supported by the Hungarian Government and cofinanced by the European Social Fund through the project "Talent Management in Autonomous Vehicle Control Technologies" (EFOP-3.6.3-VEKOP-16-2017-00001). The work of Balázs Németh was partially supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences and the ÚNKP-18-4 New National Excellence Program of the Ministry of Human Capacities.

_{2}-norm control for LPV systems with bounded parameter variation rates

_{∞}control with parametric Lyapunov functions