Jin-xi ZHANG, Shuang-bao LUO, Bang-yi XU, Tai-xu ZHANG, Xiong XIAO

(College of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, China)

Abstract: With an increasing growth of the automobile industry and the Internet, it has become a new trend to replace manual driving with intelligent driving relying on computer system. Although the ACC adaptive cruise technology still requires manual driving, the electronic control program can be used to maintain a reasonable following distance in the traffic flow. Based on unmanned driving and adaptive cruise control theory, this paper proposes a driving mode between these two, i.e., when two cars are driving in the same direction, the front car drives manually and the rear car will follow automatically. Moreover, Solidworks is adopted for vehicle 3D modeling. The motion simulation plug-in is used to simulate the state of the acceleration, deceleration, uniform straight line and corner steering motion for the front vehicle, and then observe the following vehicle following situation，obtaining the corresponding vehicle following dynamics simulation results.

Key words: Motion simulation, Unmanned, ACC adaptive cruise, Automatic follow

Adaptive Cruise Control System (ACC), regarded as the “second driver” of automobile, can improve driving comfort effectively, reduce the occurrence of traffic accidents caused by fatigue driving [1]. However, ACC has some limitations, such as the vehicle cannot trigger adaptive cruise control system at a low speed, vehicle cannot avoid the emergency collision owing to the comfort requirements, and vehicle cannot guarantee the absolute safety. Consequently, it must be controlled by a driver [2].

Auto-driving vehicle can complete automatic planning of vehicle route, speed regulation and auto-steering without driver-operation, maintaining stable driving state in traffic flow and avoiding obstacles automatically, etc.[3]. But the autopilot technology is not fully mature and cannot completely substitute the driver’s driving in the short term [4]. For example, special vehicles and dedicated lane must be used when driving. In addition，due to the constraint of expenses, multi-vehicle formation and automatic driving with mixed traffic flow are difficult to be realized in real vehicles and actual roads.

In this paper, a kind of vehicle auto-following mode between auto-driving and ACC adaptive cruise is proposed. The simulation is carried out driven by SolidWorks interpolated dynamic simulation software Motion, namely, the front car drives with a driver while the rear is not. Although much progress on the research of vehicle ACC system has been made, it is still a semi-finished product for automatic driving technology. From ACC system to automatic driving, automatic following mode is of great practical value.

1 Safety distance

Safe vehicle distance, an important part of the vehicle automatic following system, determines the distance between the front car and the next rear car in the course of driving. In the auto-following system of vehicles, the event-based motion is used to control the rear-car servo motor to realize the adaptive adjustment of the expected speed and distance. It’s extremely easy to cause the traffic accidents with too short safety distance; while too long safety distance will not only lose the traffic capacity of the road, but also easily result in vehicle lane change insertion in adjacent lanes, thus it will influence the efficiency of car-following and reducing the usage rate of automatic vehicle-following system. Therefore, the effect and efficiency of the safety distance control strategy depends on whether it can adapt to the changeable driving environment, and whether it can balance the safety, vehicle-following ability and road capacity effectively in the driving process.

A variable safety distance model is put forward to simulate driver behavior in the literature [5].

vc=a1t+v

(1)

(2)

Where,srefers to the safety distance,vcstands for the speed of the rear car,v?involves with the speed of the front car,Thstands for the reaction time of the driver and the car, a refers to the braking deceleration, Δxstands for the minimum safety distance that the two cars should keep when parking,a1involves with the acceleration of the car,vstands for the initial speed of the car,trefers to the time.

For a car,Th,aand Δxare the fixed values. In this paper,Thtakes 0.8 s, takes 2 m/s, and Δxtakes 4.3 (the length of a body). When the front car arrives at the destination, the front car will stop, i.e. the speed of the front car will change to 0 m/s, so that the in the Eq. (2) is also 0 m/s. The Eq. (3) can be rewritten as follows:

(3)

Assume that the vehicle brakes at the speed of 7.96 km/h (i.e., 2.21 m/s),s≈7.28 m, the minimum distance of simulation is 6.6 m and the maximum distance is 8.49 m. Therefore, Eq. (3) can meet the design requirements.

2 Establishment of motion simulationmodel

2.1 Simulation model

The simulation model in this paper consists of two cars and the highway. The car model is composed of trapezoidal steering mechanism [6], body, wheel and the rear axle. The model is shown in Fig.1, and Fig.2 builds a road model and draws a line on the road. Use the path coordination to let the front car follow this line[7]. The establishment of this model is shown in Fig.3.

Fig.1 Automobile trapezoidal steering mechanism

Fig.2 Whole model of the rear vehicle

Fig.3 Establishment of road model

2.2 Front and rear motor settings

2.2.1Changeoffrontvehiclespeedandacceleration

From the speed of the front car in Fig.4 and the acceleration of the front car in Fig.5, one could see that the forward motor of the front car adopts data point motor. From 0 s to 3 s, the front car moves at a uniform speed of 390 degrees/s; then from 3 s to 6 s, the front car moves at a uniform acceleration speed from 390 degrees/s to 480 degrees/s; from 6 s to 9 s, the front car moves at a uniform speed of 480 degrees/s; from 9 s to 12 s, the front car moves at a uniform deceleration speed from 480 degrees/s to 390 degrees/s; from 12 s to 15 s, the front car moves at a uniform speed of 390 degrees/s. The servo speed motor and the servo displacement motor are used in the simulation of the rear vehicle. The servo speed motor adjusts the speed according to the changes of speed of the front vehicle when driving in a straight line, and the servo displacement motor turns according to the distance from the front vehicle when it is driving in a curve.

Fig.4 Speed of the vehicle ahead

Fig.5 Acceleration of the vehicle ahead

2.3 Sensor setup and installation

In Solidworks Motion, approaching sensor 2, approaching sensor 3 and approaching sensor 4 are established, respectively. The sensor 2 is used for the vehicle distance, and the sensors 3 and 4 are used to control the left and right steering of the rear vehicle. As shown in Fig.6, when the infrared ray of sensor 4 senses the front car, the rear car turns left; when the infrared ray of sensor 3 senses the front car, the rear car turns right; and when the infrared ray of sensor 2 senses the front car, the rear car slows down. In order to make the servo motor more closely connected with the approaching sensor, the event-based motion is also established in this model.

Fig.6 Setting of following sensors

In SolidWorks Motion simulation, physical contact is added to the vehicle tire and ground [8]. Steel (dry) is the material for road and rubber (dry) is for tire. For the model loading gravity, theYdirection is used, and the size is 9 806.65 mm/s2[9].

3 The analysis of simulation results

The simulation time is 15 seconds.

According to the track of the front and rear vehicles in Fig.7, one can see that the track of the rear vehicle can basically coincide with that of the front vehicle, which can meet the requirements of automatic following.

Fig.7 The track of the car ahead and the car behind

As can be seen from Fig.8, there is always a distance between the rear car and the front car no matter how the speed of the front car changes, because the front car has a process of acceleration and deceleration. The minimum distance is 7.02 m, so the occurrence of the rear-end collision is impossible. The maximum safety distance between the front and the rear vehicle is 8.04 m. In the process of auto following, the distance will be changed as well, so it is impossible for another car to be inserted between the front and the rear car.

Fig.8 Relative displacement of the car ahead and the car behind

In Fig.9, the blue line represents the front car. From the blue line’s curve, it can be seen that the front car has a process of acceleration, uniform speed and deceleration. The unit of data point motor is degree/s, which can be changed into mm/s according to Eq. (4), in which D represents the diameter of tire. Originally, the initial speed of the front car is 390 degrees/s, but in fact, the speed of the car needs a process from 0 mm/s to 2 395 mm/s, so there is a uniform acceleration line when the car starts. The red line means that the rear car has uniform acceleration movement until 3s to catch up with the front car. From 3 s to 5.2 s, uniform motion is performed. In Fig.8, the distance between the front car and the rear car reaches the minimum at the time of 5.2 s. Infrared light of sensor 2 senses the front car. Under the action of event-based motion, the rear car decelerates. Then, due to the distance between the front and rear cars is too large, approaching sensor 2 does not sense the front car, and the rear car accelerates under the action of event-based motion. At 6.53 s, the rear car decelerates under the action of event-based motion due to the reason of approaching sensor 2. Then, because the front car pulls away from the rear car, approaching sensor 2 does not sense the front car. Under the action of event-based motion, the rear car accelerates. From 7.15 s to 10.96 s, the rear speed is basically the same as the front speed. From 10.96 s to 11.48 s, the rear car decelerates. Due to the reason of approaching sensor 2, the rear car decelerates under the action of event-based motion. From 11.48 s to 15 s, the rear and front cars basically do uniform motion.

As shown in Fig.10, the blue line represents the front car and the red line refers to the rear car. Because of the contact mode between the tire and the road, the contact material and the shake when the engine starts, the curve is not smooth when the car starts to run. The car starts to turn at 2.01 s. When the infrared ray of the rear car approach sensor 3 senses the front car at 5.62 s, the rear car starts to turn right. The angle of the displacement servo motor applied to the steering wheel is 27 deg. The tire begins to turn back at 6.62 s, and the first turn is not completed until 8.07 s. The front car begins to turn into the second turning at 4.94 s. The infrared ray of the rear car approaching sensor 4 senses the front car at 7.67 s. The rear car starts to turn left. The turning angle of the displacement servo motor applied to the steering wheel is -70deg. The tire begins to turn back at 10.87 s, and the second turning is completed at 12.88 s.

Fig.9 Speeds of the front and the rear

Fig.10 Angular velocity of the car ahead and the car behind

Through this simulation experiment about one car with a driver while the other is not, as we can see from Fig.7, when the two cars are driving in the same direction, the movement trajectories of the two cars are basically similar; from Fig.8 and Fig.9 whenever the speed of the front car is accelerating, decelerating and uniform, the rear car will follow the front car and keep a certain distance to prevent rear-end collision. From the Fig.10, when the front car turns, the rear car also turns and the direction is the same. Therefore, when the current car starts to move, whether the front car is accelerating, decelerating, uniform speed and turning at the same time, the rear car can realize the acceleration, deceleration, uniform speed and simultaneous steering in the case of unmanned driving, which basically conforms to the actual road condition.

4 Concluding remarks

In this paper, through the dynamic simulation of the vehicle’s automatic following performance, sets the motion state of the front car in advance in terms of the acceleration, deceleration, uniform speed and curve steering, discovering that the rear car can follow the steering in time, nearly have the same motion path as the front car and keep the safe target distance for avoiding the rear-end collision. Moreover, it helps provide reference and implication for the real motion state of the vehicle in this similar condition.