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When the truck b_i, which is Newton’s second law of motion, only moves linearly in an absolute reference coordinate system i, the change in momentum L_i with time is the same as equation 5. Here, the momentum is L_i = m_i⋅v_i. When the same truck b_i only rotates in the I-coordinate system, Euler’s Angular momentum theorem is as follows. equations (1) and (2) are applied in Fig. 1 of the system figure, and equations (3) and (4) are the same for truck mass m and yaw mass moment of inertia θ. In other words, if we rearrange the lateral dynamic equation. Therefore, the two degrees of freedom of movement of the four-wheel steering system using the above motion equation, i.e., the sliding angle β and the yaw angular velocity φ˙ of the vehicle body, were summarized in equation (3).

Fig. 1 
Lateral dynamics for truck platooning

In Fig. 2, the trucks are composed of 4 trucks, and in this chapter, we will strategically describe the truck platooning formation. The car located at the top is indicated as T_i. The truck T_i-1 is the truck that follows T_i. D_i denotes the relative distance between T_i and T_i-1 trucks. Based on the platooning algorithm, the required relative distance is D_i1^ref, expressed by equation (7). L_i represents the length of the car. Here, R₀ is the speed necessary for the inter-vehicle distance to converge to zero, H_i is the constant time headway and V_i is the current speed of the trucks.

Fig. 2 
Truck platoon using information from the preceding truck

Also, the actual distance between the preceding trucks D_i1 is expressed as equation (8).

The spacing error between trucks configured with platooning is expressed as equation (9).

The total length of the entire platooning sequence is expressed as equation (10).

This paper designed the simulator architecture of the platooning system as shown in Fig. 4, using the MORAI autonomous driving simulator and the Ubuntu-ROS-based operating system. The MORAI autonomous driving simulator provides a truck model P540 and a Korean-style autonomous driving experimental K-City map. Truck platooning was implemented based on the provided sensor module information used for platooning. First, communication in the V2X sensor module provided by MORAI was used. The vehicle model used in the experiment is a Hyundai P540 truck, and all four are identical. Through this, all four trucks use communication to share messages. Table1 defines the data criteria required for CACC-based longitudinal and lateral integrated controller design using V2X communication.

Fig. 4 
Simulation environment for truck platooning

In this paper, the truck platooning controller is configured, as shown in Fig. 5. The network layer is a layer interlocked with the sensor module. Based on the information provided by V2X, global path information is provided to the truck dynamics layer. Here, the global path is the complete route information for the driving section(map). The Truck dynamics layer represents the status information of the truck. The status information of the car is included in Fig. 4. Local path information is provided to the network layer considering the current location of the car. The local path indicates a waypoint that can be moved from where the current truck is located. Platooning Controller Architecture Configuration.

Fig. 5 
Truck platooning controller layer

Local path information, including the point way, is transmitted back to the network layer. The Network Layer that receives the local path checks the location of each truck and the number of trucks and specifies the size of the platooning queue. To maintain the set platooning queue size, the current speed of each truck is transmitted through the link layer. Link Layer is a feature that combines all information of different trucks. Trucks configured with platooning check the road section at the current location and provide the following trucks with lane change timing and characteristic information for each road section. The Integrated Controller Layer contains the integrated platooning control system. Based on the vehicle distance information between trucks provided from the Link Layer, the Platooning algorithm proposed in this paper is executed. According to each road section required for algorithm execution and the distance to the preceding vehicle, the target velocity is connected with the link layer. Stable truck platooning can be implemented as all layers operate organically. The next chapter 4 describes the truck platooning queue maintenance controller.

V2X-based trucks receive path information, as shown in Fig. 7 The information obtained here is Topological graph generation path information. In this paper, the figure displayed as an HD map is shown in Fig. 6. Data were stored for each node in the HD map. There are two types of stored data for each node. The first is the global path. The global path is the cost-based shortest path of the map that includes between the start point and the endpoint. The second is a local path. The local path is the path where the current truck is located. In this path, the time when lateral control is required can be calculated, and the information is transmitted to the integrated controller of Fig. 3. The line indicates the course requiring lateral control in Fig. 13. The situation in the simulation is shown in Fig. 7. It was applied to the next chapter, the integrated controller system, based on local path information on a road with a sharp curvature.

Fig. 6 
HD map information of K-City

Fig. 7 
Topological graph generation path information

Much research is being done on maintaining a rank in a lateral control situation during platooning consisting of trucks. The platooning currently being studied has difficulty in retaining the platooning positions on roads with sharp curvature. Since truck platooning in this paper acquires data based on V2X communication, it can utilize a more faster and more accurate algorithm application when platooning control. Based on this, we will describe a method that can better cope with the situation of a truck entering the roundabout abruptly in front of it compared to the general environmental sensor based ACC.

Fig. 8 shows the situation of entering a rotary with a sharp curvature of the MORAI simulator. To keep the platooning ranks stable, it is necessary to quickly respond to sudden changes in the driving environment, which is such a situation. The algorithm proposed in this study implements an integrated controller that integrates the CACC algorithm-based longitudinal controller and the Pure-pursuit algorithm-based lateral controller by utilizing the global path and local path. Fig. 9 shows the proposed integrated controller algorithm model. The distance between the vehicle and the front truck suggested in Chapter 2 and the global path and local path received from the link-layer stage indicated in Fig. 5 were used for the values used in this model. The V2X message set signal in Table 1 was used for the values used in the integrated controller. It was judged whether the truck in front was in the same lane as the trucks forming the line, and the logical value was determined based on the local path where the trucks are currently driving and the distance between the trucks in front. In addition, the truck platooning study was conducted under the assumption that the location of trucks constituting the platooning and the coordinates of surrounding vehicles were received using the truck platooning rank maintenance method proposed in Chapter 3 and V2X and Global Path.

Fig. 8 
Trucks performing lateral control

Fig. 9 
Proposed integrated truck platooning controller

Unlike the existing platooning algorithm, the integrated platooning control algorithm proposed in this paper is used to keep vehicles in a lane and drive them in a situation on the road with a sharp curvature. Based on the acceleration, speed, and relative distance to the preceding vehicle obtained through V2X, the controller was designed so that the distance error of the truck queue becomes 0. The longitudinal and lateral control of the car given as an input is implemented. The integrated controller defined that the vehicle in the truck queue is Ego-0, and the number increases by one as it goes backward. To realize the longitudinal and lateral direction integrated controller, the spacing error of the longitudinal control error was first defined as the following equation.

In the above equation, the inter-vehicle distance error Se and V_i represents the speed and acceleration error between the host and preceding vehicles. As shown in this value, it means the cumulative sum of distance errors between cars or trucks that exist in front of the own vehicle. δ₀ is composed of the time gap, the preceding vehicle speed V, and the safe braking distance d_ref as shown in the above equation. According to previous studies, Truck drivers from the general fleet driver population were comfortable using the CACC system in mixed public traffic. They generally tended to prefer the intermediate gap settings over the longest and shortest settings, although there was a significant sub-group that preferred the shortest available setting(0.5 s time gap). When driving platooning with CACC, 0.5 seconds was adopted as the shortest time to reduce fuel consumption as a future study. In the widely-used CACC with a constant time gap(CTG) policy, the prevailing definition of time gap denotes the time it takes the subject vehicle to approach. its predecessor at the current speed. The safe braking distance means the distance from the vehicle in front when stopping, and the inter-vehicle distance was set to 5 m or more by referring to the standard for the ensemble.

The longitudinal control system of truck platooning is composed mainly of upper-level controllers and lower-level controllers. Based on the above, the CACC²⁰⁾ algorithm is executed. The lower-level controller is responsible for the throttle and brakes of the truck. Inter-truck spacing refers to the distance between trucks. Accelerate based on the distance between trucks. The spacing between trucks is described in the next chapter. An upper-level controller is arranged as follows equations 16 and 17. In equation 16, i represents the number of trucks.

The method suggested in the paper of Distributed Consensus Algorithm for the CACC System²¹⁾ was used. where the acceleration of vehicle 1 at time 4 is based on the absolute position difference and the velocity difference between itself with its preceding vehicle j. This algorithm takes the length c_j and braking ability b_i of different vehicles into account. Communication delay τ_ij(t) is also included in the algorithm, making the system more realistic and applicable.

The upper-level controller sends the desired acceleration to the lower controller, and as a variable value to be used in the CACC algorithm, the connected lag is simulated as τ=0.5 s. It is included in the CACC algorithm module in Fig. 9. Inter-Truck Spacing was organized as equations 19, 20, 21, 22, 23 according to the constant spacing policy. The spacing policy is an implementation of the system as a method of keeping the distance between vehicle constant.

Next, the lower-level controller was organized as equations 24 and 25.

The characteristics of the lateral direction controller are pure-pursuit control and control according to the lateral travel estimation method based on global path and local path. In Fig. 10, the positions of the current trucks are represented by the global coordinate system(X_i, Y_i). The global path of the lateral direction is read during truck platooning, and L indicates the constant look-ahead point. It is to find global coordinates X and Y, which are look-ahead points using L. In the lateral direction control method, the point connected to the arc’s center point to be moved from the current truck position is expressed as R. The above algorithm is summarized as equations 26, 27, 28, 29, 30. Next, the lower-level controller was organized as equations 24 and 25.

Fig. 10 
Structure of truck platooning longitudinal control system

Calculate the angle value of the vehicle using the above algorithm. L is the wheelbase. Through the above equation, the desired steering value is shown in equation 33. Look-ahead Point was created on the global path to go with the above algorithm. Look-ahead Point makes 5 Points in advance based on the Local Path marked in red. An arc was drawn based on the created point, and pure-pursuit control was performed to reach the vehicle position on the path. As shown in Fig. 11, the proposed lateral control system that can stably maintain the platooning ranks in a situation where the road’s curvature is sharp is shown.

Fig. 11 
Structure of truck platooning lateral control system

Fig. 12 
Truck platooning lateral path following

Fig. 13 is a map of K-City, a simulation-based Korean autonomous driving test bed that conducted the experiment. First, the platooning driving section was classified into three categories. The blue area is the roundabout path. Here, the lateral control test result is derived. The second section is a straight path section. Run the full speed test―finally, the sharp curve path section. Here, we proceed with the lateral control experiment. All areas are designated as platooning driving routes, and operating results from the driving starting point to the endpoint are derived.

Fig. 13 
K-City map path classification

Fig. 14 shows the implementation speed of platooning for four trucks. It ran on the K-City map for 153 seconds and included straight sections, roundabouts, and roads with sharp curvatures. The experiment was conducted, including the maximum speed of 80 km/h that can be proceeded on the K-City road in the straight section. It shows that the platooning rate can be maintained stably and continuously even on the road with sharp curvature and in the roundabout section. The average speed of 4 trucks is as follows: Truck 1: 53.4 km/h, Truck 2: 52.22 km/h, Truck 3: 51.75 km/h, Truck 4: 51.56 km/h was maintained. Higher speeds also show that continuous platooning can be maintained.

Fig. 14 
Velocity change of truck platooning according to K-City map total driving

The inter-vehicle distance of truck platooning is shown in Fig. 15. The minimum distance while maintaining the truck platooning ranks was 5 m to 10 m. This results from the inter-vehicle distance according to maintaining a stable platooning rank by changing and maintaining the speed suggested by the integrated controller proposed in the longitudinal and lateral directions. The average inter-vehicle distance of Truck 2 is 7.05 m, the average inter-vehicle length of Truck 3 is 7.07 m, and the average inter-vehicle distance of Truck 4 is 7.12. we carried out.

Fig. 15 
Changes in truck inter-vehicle distance according to K-City map total driving

Fig. 16 shows the change in the total train length according to the truck platooning operation. It was confirmed that the ranks were kept stable through the integrated control of truck platooning.

Fig. 16 
Total length change of truck according to K-City map total driving

These are the control precision results for the roundabout path and sharp curve path classified in Fig. 13. Figs. 17, 18, 20, and 21 are shown by converting the driving routes of trucks in the HD map into coordinates. The absolute position coordinates of the HD map and the position of the truck currently located were displayed as two-dimensional points using UTM (Universal Transverse Mercator Coordinate System) coordinate transformation. The value was converted to the UTM-52 zone, which corresponds to K-City in Korea. In Table 2, the distance between the coordinates of the coordinates (X, Y) in the HD map and the coordinates of the current vehicle location (X_i, Y_i) was calculated using the Euclidean distance. In addition, the maximum error was calculated for roads and rotary sections with sharp curvature, and the maximum allowable number of errors was calculated for the case where the error occurred larger than the average error. Roundabout error occurrence section.

Fig. 17 
K-City map roundabout area-1 error comparison

Fig. 18 
K-City map roundabout areas-2 error comparison

Fig. 19 
K-City map sharp curve area-1 error comparison

Fig. 20 
K-City map sharp curve area-2 error comparison

Fig. 21 
K-City map sharp curve area-2 error comparison

Fig. 17 is the error corresponding to the first yellow box in Fig. 13 in the roundabout. Areas with significant errors during lateral control are enlarged and displayed. This is the same as stepping on the lane in Fig. 19.

Fig. 18 is the error corresponding to the second yellow box in Fig. 13 in the roundabout. Areas with significant errors during lateral control are enlarged and displayed. This is the same as stepping on the lane in Fig. 19. The graph is expressed with the coordinates (X, Y) of the HD map and the coordinates of the current truck location (X_i, Y_i). The maximum error shows the lateral position error situation while driving in the rotary section in Fig. 19. That is, such a situation was calculated as the maximum allowable error number.

Fig. 19 is the driving result of the roundabout. For the transverse error, an average value of 0.84 m was derived using the Euclidean distance formula. The maximum error yielded a value of 1.16 m. The maximum error shows the lateral position error situation while driving in the rotary section in Fig. 18. The problem of stepping on the lane was calculated as the maximum allowable error number and indicated in Table 2.

Fig. 20 and Fig. 21 are the error errors corresponding to the gray box in Fig. 13 in the sharp cruise path. Areas with large errors during lateral control are enlarged and displayed. This is the same as stepping on the lane in Fig. 22. The graph is expressed with the coordinates (X, Y) of the HD map and the coordinates of the current truck location (X_i, Y_i). For the transverse error, an average value of 0.88 m was derived using the Euclidean distance. The maximum error was 1.24 m. The maximum error shows the lateral position error situation during sharp cruise path driving in Fig. 22. That is, such a situation was calculated as the maximum allowable error number.

Fig. 22 
Crossing the lane on the K-City map sharp curve

Table 2 classifies the platooning driving section into three categories: a straight line, a road with sharp curvature, and a roundabout. The proposed integrated controller was used to maintain a stable lateral running speed even on roads with sharp curvatures and roundabouts. The corner sections were driven within the following error range. This experiment showed that it continuously maintains a speed higher than the maximum speed of 75 km/h for platooning conducted in the IDIADA experiment, a European ENSEMBLE project.¹⁸⁾

It shows stable platooning even on the road with a sharp curvature that requires lateral control. Also, the average inter-vehicle distance of Truck 2 is 7.05 m, the average inter-vehicle length of Truck 3 is 7.07 m and the average inter-vehicle distance of Truck 4 is 7.12 m. It performed continuous platooning at a narrower interval than the 8 m to 12.5 m distance between platoons tested on the IDIADA road of the European ENSEMBLE project. The experimental environment of the IDIADA project is shown in Fig. 23. The experimental results are shown in Table 3.

Fig. 23 
ENSEMBLE IDIADA project test environment