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A Lane-Changing Decision-Making Method for Intelligent Vehicle Based on Acceleration Field.


Recently, intelligent vehicle technology has widely attracted attention in both military and civilian fields, and some entrepreneurs have begun researching and testing [1]. However, most intelligent vehicles can only travel under limited conditions, and there are still many issues that need to be solved. Among these problems, lane-changing decision-making is a critical section for an intelligent vehicle to perform as well as or even better than a human driver. Defined as a part of intelligent vehicle system's upper control module, lane-changing decision-making and subsequent trajectory planning can significantly affect traffic efficiency, driving safety and ride comfort.

In order to determine the factors that influence a driver's decision on lane-changing, Gipps P. G. proposed the Gipps model, which assumes that the driver's behavior is rational, and decision-making depends on safety, feasibility, obstacles' location and advantage in relative speed in target lane [2]. MITSIM model and the CORSIM model are used more frequently. In MITSIM model, the process of a lane change is divided into three steps: judgement for the necessity of a lane change, detection of the gap between traffic vehicles, and implementation of a lane change. This model puts forward two concepts: tolerance factor and speed difference factor, which are used to judge the necessity of a change; once given the target speed, traffic signal and vehicle position information, the model will judge feasibility; when both necessity and feasibility satisfy requirements, a lane-changing behavior will be excuted [3]. The CORSIM model makes decisions by motivation, benefits and urgency [4]. Jongsang Seo designed a decision-making algorithm, which consists of vehicle location index module, mode selection module and direction selection module. The vehicle location index module is responsible for receiving external environment information, the mode selection module is used to judge whether a collision will happen and the direction selection module is used to select the proper target lane [5]. These approaches offer much reference on lane-changing decision-making method. However, they consider only few elements involved. Drivers' habits, uncertainty of traffic vehicles' motion, and road adhesion condition can all have effects on the method. To make further exploration, Xuemei Chen used rough set theory to extract lane-changing rules from data obtained from a driving simulator. She divided the lane-changing process into two phases: intention generation phase and implementation phase. Analysis results demonstrate that during intention generation phase, decisions almost depend on only two factors: relative distance and relative velocity between host vehicle and preceding vehicle. During the implementation phase, if relative velocity is large, then relative distance has little effect on the decision; when relative distance is small, relative velocity would impose a great effect on the decision [6]. Jieyun Ding came up with the notion of Comprehensive Decision Index, which was designed with fuzzy method to estimate surrounding traffic vehicles' effect on decision-making [7]. Ding Zhao proposed a rapid evaluation method for intelligent vehicle, which was based on data collected under cut-in scenarios [8]. These methods built on pattern recognition require a large amount of experimental data to fit different driving habits. But without a model with clear physical meaning, some of those outputs can hardly be predictable and their accuracy needs to be further improved.

In fact, a complete lane-changing process involves trajectory planning as well, which entails an optimal start position and an initial velocity. Traditional artificial potential field methods are suitable for decision-making and trajectory planning under a static environment, but they come with defects of falling into the local minimum and can lead to jittering when a vehicle is close to an obstacle [9], which makes them unable to adapt to a complex traffic environment. One way to skip the trap of local minimum in trajectory planning is to use rapid-exploring random tree algorithm, or RRT algorithm. It was proposed by LaValle S. M. to search for an accessible path [10]. The method is characterized by simplicity and efficiency. In order to overcome certain disadvantages of the algorithm itself [11, 12], Qingkun Jiang proposed an improved RRT algorithm with B spline curve to make the planned trajectory smooth and executable [13]; Song J. Z. put forward an improved algorithm of bidirectional extend RRT, which was designed for practical application on intelligent vehicles [14]; adopting a goal-biased sampling strategy and a reasonable metric function, Mingbo Du presented a continuous-curvature RRT algorithm to reduce the waste of computing resource and accelerate planning process [15].

Although artificial potential field method has the advantage of continuity and the RRT method has the advantage of efficiency, neither of them is suitable for trajectory planning under urban environment, since the former is bound to produce a shaking trajectory and the latter lacks stability. After comparison and analysis, this article adopts the polynomial trajectory planning method to match the proposed decisionmaking method and ensure trajectory curve's continuity at the same time.

In this article, we proposed a lane-changing decisionmaking method. Compared with other methods mentioned above, this method is more concise, and physical meaning is clear. Besides, the result is predictable, which is crucial for intelligent vehicles. Its innovation lies in the introduction of continuous acceleration field to provide guidance for personalized lane-changing decision-makings. Taking factors like safety, comfort, traffic efficiency and personality into consideration, the decision-making method can be more practical and reliable.

Remaining parts are arranged as follows: In Section II, based on analysis of braking process, an artificial acceleration field related to relative velocity and relative distance is set up. Section III takes advantage of the field and proposes a lane-changing decision-making method. In section IV, velocity regulation is taken into consideration. In section V, the lane-changing decision-making method and the polynomial trajectory planning method are linked together, and simulations based on Matlab/Simulink are conducted to verify its effectiveness.

Acceleration Field

Generally, two periods will be experienced successively within the process of confirming a lane-changing decision: intention generation and feasibility judgment. Based on existing research, we can find out factors that prompt a driver to change lane, such as relative velocity and relative distance. These parameters both have something to do with braking safety. Therefore, in order to predict lane-changing intention quantitatively, we extend emergency braking safety distance model first, and then establish an acceleration field.

Braking Safety Distance Model

Braking safety distance refers to the distance between host vehicle and the traffic vehicle ahead from which time the host vehicle start to brake and can finally maintain the same speed as preceding vehicle without collision. In braking safety distance model, assumptions are as follow:

1. Host vehicle and preceding vehicle are in the same urban straight lane.

2. Preceding vehicle keeps driving at constant but lower speed than host vehicle's initial speed.

3. Time for braking reaction will not be taken into consideration.

Then host vehicle's braking process can be divided into three stages: elimination of brake clearance, rise in braking pressure, and constant deceleration braking. The curve of acceleration-time is shown in Figure 1. Note that there is no necessity to keep on braking when velocity of host vehicle is reduced to the same value as front vehicle, so the braking process ends at that moment.

[t.sub.b1] in the figure represents time span to eliminate brake clearance plus latency of signal processing, during which time the acceleration is zero, and distance traveled by the host vehicle can be expressed as

[S.sub.b1] = [v.sub.h][t.sub.b1] Eq. (1)

where [v.sub.h] is the velocity of host vehicle.

[t.sub.b2] in the figure represents the time for increasing braking pressure. In this period, acceleration is reducing with the slope of k, and the distance traveled by host vehicle can be expressed with [S.sub.b2]:

k = [a.sub.bmax]/[t.sub.b2max] Eq. (2)

[mathematical expression not reproducible] Eq. (3)

where [a.sub.bmax] is the minimum acceleration accessible, which is negative, [] is the target acceleration during the braking process, which can be set as any value within [a.sub.bmax] at will.

[t.sub.b3] in the figure represents the time for uniform acceleration braking. During [t.sub.b3], braking deceleration remains constant until the host vehicle's speed is down to the same value as the front vehicle's. The distance traveled by the host vehicle can be expressed as

[mathematical expression not reproducible] Eq. (4)

where [v.sub.t] is the velocity of preceding vehicle.

During the whole braking process, the traveling distance of preceding vehicle is

[mathematical expression not reproducible] Eq. (5)

In order to ensure safety, a certain margin [] should be kept between these two vehicles in the final state, as shown in Figure 2. And the braking safety distance can be deducted as in formula (6):

[mathematical expression not reproducible] Eq. (6)

[] = [S.sub.b1] + [S.sub.b2] + [S.sub.b3] Eq. (7)

[[DELTA].sub.v] = [v.sub.t] - [v.sub.h] Eq. (8)

Given a target deceleration, the formula (6) can calculate the corresponding safety distance according to the current speed difference. The relationship between deceleration, speed difference and safety distance can also be expressed as in Figure 3.

Acceleration Field for Intention Generating

In an emergency braking condition, target braking deceleration is expected to be the maximum that can be reached under a certain road condition. In fact, if we adjust the target braking acceleration to a different value, we can acquire a different braking safety distance, which can be regarded as an emergency braking safety distance model under a specific road condition, or as a non-emergency braking safety distance model on a better road. Thus, we are inspired to take different target braking accelerations to represent degrees of safety on a satisfactory pavement and as a parameter that drives the driver to generate the intention of making a lane change.

In formula (6), if we take [] and [DELTA]v as independent variables, [] as dependent variable, then we can derive the value of [] as [] and [DELTA]v change within the range, thus an acceleration field is formed, as in Figure 4(a). Figure 4(b) is the 2-D projection with contours of this field, which shows that with larger speed gap or smaller relative distance, situation gets more emergent.

Generally, when preceding vehicle on the same lane runs faster than host vehicle does, a driver can hardly be in want of a lane change. And when preceding vehicle's speed is lower than that of the host vehicle, with relative distance continuing to reduce along with the influence of velocity difference, there is an increasing likelihood for a driver to produce the intention to change lane. Now we use [] to denote the current relative distance between host vehicle and preceding vehicle, Av to denote the velocity difference, then substitute them into the numerical relationship, the calculation result [] can represent magnitude of a driver s desire to switch lane: stronger desire comes with greater value of |[]|. Note that parameter [] now indicates the target braking acceleration to be applied if the braking is taken at the moment and then achieve a critical state where collision happens to be avoided. This method of measuring a driver's degree of willingness to change lane is consistent with life experience from the view of ensuring safety, reducing speed loss, along with improving traffic efficiency.

Acceleration Field for Feasibility Judgment

As mentioned above, when the way forward is 'blocked' by the vehicle ahead, a driver will naturally think of a lane change. Thus the second step of confirming a lane-changing decision needs to be performed, which aims at determining whether a lane change is feasible.

For front vehicle on the side lane, we can take it as on the same lane with the host vehicle and then compute [] by relationship expressed in formula (6), which is adopted as the indicator of lane-changing feasibility.

For rear vehicle on the side lane, if it runs slower than the host vehicle and keeps a certain distance away, a lane change will be feasible; if it runs faster than the host vehicle, the feasibility of a lane change will require a further judgment. In the lane-changing process, it is of higher priority for the passing of vehicle on the adjacent lane, and it is reasonable to assume the velocity of rear vehicle on the side lane as constant. In order to avoid collision, the host vehicle should be affected like an electrically charged particle when another particle with same electrical property comes near, and the force of repulsion can result in a forward acceleration motion. Therefore, we can derive the driving safety distance model with reference to the braking safety distance model, then substitute current relative distance and relative velocity into the model, the acceleration calculated in reverse can be used to quantitatively describe the strength of this effect.

Similarly, we analyze the process of driving and get the driving safety distance model as expression (9).

[mathematical expression not reproducible] Eq. (9)

where [S.sub.dw] is the driving safety distance, [S.sub.dt] is the distance traveled by rear vehicle during the host vehicle's accelerating process, [S.sub.dh] is the distance traveled by the host vehicle in the process, [S.sub.ds] is the margin that should be kept in the end of the process, [a.sub.dg] is the target acceleration during the driving process, [t.sub.d1] is the time for eliminating acceleration clearance, and [k.sub.d] is the growth rate of acceleration.

Complete Acceleration Field

Combining the braking and driving conditions, we can obtain the whole acceleration field as in Figure 5. A positive [S.sub.w] stands for the relative distance between preceding vehicle and host vehicle, and a negative [S.sub.w] represents the relative distance between the rear vehicle and host vehicle. When a traffic vehicle is running at a higher speed than host vehicle, [DELTA]v is a negative number. Otherwise, it is zero or a positive number. Figure 5(a) is the 3-D diagram of the acceleration field, which covers the entire domain of definitions. Figure 5(b) is the projection with contours of Figure5(a), which shows that dangerous situations are all embodied in the second and fourth quadrants: the blue part of the upper left corner indicates the need for braking, and the red part of the lower right corner calls for acceleration.

Now, by calculating the acceleration [a.sub.g] needed for not to collide with preceding vehicle on the same lane, we can roughly predict the likelihood of generating a lane-changing intention. Then, by calculating the acceleration needed for front side traffic vehicle and rear side traffic vehicle respectively, we can make further studies so as to judge the feasibility of that lane change.

Basic Lane-Changing Decision-Making Method

A narrow gap, along with a velocity larger than that of preceding vehicle, can prompt the host vehicle to slow down or change lane. However, before deciding whether to make a lane change or not, the feasibility of a lane change will be kept unknown until a refined calculation is conducted, so it's necessary to define a critical state, where worse situations can be regarded as dangerous and thus unacceptable. In doing so, we build a braking decision-making model and take the deceleration acquired as the safety base line.

Braking Decision-Making Method

One thing to reaffirm is that the acceleration (a negative number) obtained in the acceleration field represents the least braking intensity needed to ensure safety. Therefore, this acceleration field can be taken as the basic safety model. It means that before a lane change is confirmed feasible, host vehicle is supposed to drive at a deceleration no less than the value calculated in the field.

On this foundation, we have established two decision reference lines and a warning line in a relative distance-relative velocity state plane, as in Figure 6.

Line B1: primary lane-changing intention reference line. It is a contour in the braking acceleration field. We assume the driver of host vehicle is rational, and the existence of lane-changing intention depends on safety index, which can be quantified in acceleration field. In this case, it's reasonable to set a specific reference acceleration value and extract the corresponding line B1 from the field. When acceleration calculated with actual traffic environment information reach this reference line, a human driver is highly likely to start to plan a lane change. It should be noted that the reference acceleration value is personalized and can be adjusted to adapt to different types of drivers.

Line B2:brake starting reference line. This is also a contour of a certain acceleration value in the braking acceleration field. According to driving experience, in a relatively safe condition, a driver will usually not brake to reach the same speed as preceding vehicle, in which process there will be a loss of traffic efficiency. Besides, it does nothing good to improve ride comfort. So we set an acceleration threshold, when required braking intensity reaches the corresponding line B2, the driver would begin to consider braking. Similarly, this acceleration threshold can be adjusted to be personalized as well.

Line B3: emergency braking warning line. This line is calculated with the maximum braking deceleration the road surface can provide. When the state point in the plane corresponds to actual traffic environment is below the line B3, the host vehicle can only brake with the maximum deceleration accessible, even if a collision is inevitable.

With these definitions, braking decisions can now be illustrated with Figure 6. Suppose there is a vehicle in front of the lane, and the relative speed and relative distance between preceding vehicle and host vehicle can be represented by point A on the state plane. Since we have already assumed the velocity of the traffic vehicle is invariant, if host vehicle doesn't take any action, velocity difference between them will stay the same, but relative distance will gradually decrease over time. During this process the state point will move from point A to point B, C and D successively, and the deceleration required by the field will increase. Therefore we suggest the host vehicle not to take any action when state point is above the line Bl, but to make judgments all the time after reaching that point, which means the driver may have already sensed the potential danger. And then do as follows:

1. If driving risk can be reduced by an available lane change, then make it immediately (it will be elaborated in detail later).

2. If it's unfeasible to make a lane change at the time and the state point is on the line segment BC, since it hasn't reached brake starting line B2, there isn't necessity to brake. In this case, the host vehicle should keep on driving without taking extra operation.

3. If it's unfeasible to make a lane change at the time and the state point is below point C, the host vehicle is expected to brake at the deceleration calculated in the field to ensure safety.

For extreme conditions corresponding to state point D or below, if a lane change is still unpractical, a collision is bound to occur and what host vehicle can do is to brake at maximum deceleration to reduce loss as much as possible.

Basic Lane-Changing Decision-Making Method

Lane-Changing Assumptions and Simplifications After setting up a braking decision-making method that guarantees safety, we need to judge the feasibility of a potential lane change when there has already been a lane-changing intention. Therefore, we make reasonable assumptions and simplifications of a lane-changing process:

1. Speeds of both host and traffic vehicles remain unchanged;

2. To make it conservative, host vehicle is seen as in both starting lane and target lane during the process.

3. On the premise of ensuring safety, a lane change is supposed to give priority to velocity loss. Therefore, only when velocity of front side vehicle is lower than that of host vehicle, but larger than that of preceding vehicle on the same lane with host vehicle, in which process the host vehicle has to finally keep the same speed as the vehicle in front of it, a lane change can be considered beneficial to efficiency and then carried out.

4. As a simplified case, we will temporarily not consider host vehicle's speed regulation before a lane change, which means the host vehicle can only adjust to the velocity of preceding vehicle on the target lane after the completion of that change.

Analysis of Lane-Changing Process In the process of planning, the system should generate a series of trajectories [16], which include an optimal trajectory and a worst one within the limit of tolerance. Assumed invariant during the lane-changing process, for each driving velocity, there is an optimal and a threshold lane-changing duration. According to these two time points, we obtain the corresponding distance required to complete the lane change under different relative velocities, as shown in reference line LC1 and line LC2 in Figure 7.

Tine LC1: optimum lane-changing reference line. When state point is on or above line LC1, host vehicle can take the optimal time length to change lane. After getting line LC1, we take the larger value between line LC1 and the primary lane-changing intention reference line B1 (in Figure 6) to form a new lane-changing intention reference line, so as to ensure enough space for a lane change when intention is generated.

Tine LC2: lane-changing emergency warning line. When the state point is between line LC1 and line LC2, duration of an expected lane change should be shorter than the optimum value and longer than the lower limit, and it can be proportionally derived from the state point's position on the plane. When state point is below line LC2 and host vehicle is assumed to be driving at a constant speed during the lane-changing process, a lane change can no longer avoid conflict with front car; then braking is the only way to mitigate collision loss.

A typical lane-changing process can be shown in Figure 8. When host vehicle has the idea of changing lane, it will have to make judgment on feasibility. We use semitransparent icons in the graph to indicate relative position between vehicles at the time. At the beginning of decision-making, we denote the relative distance between host vehicle and traffic vehicle 1 as [S.sub.A], and distance between host vehicle and traffic vehicle 2 as [S.sub.B]. They are marked by point A and point B on the state plane, respectively. As the point A is above point [A.sub._LC1] on line LC1, host vehicle is supposed to change lane with the optimum lane-changing time. Then relative distances after the completion of a lane change can be recorded by [S.sup.'.sub.A] and [S.sup.'.sub.B], which are corresponding to point A' and B'. Since we assume the host vehicle is on both original and target lane for the duration, the process can be reflected by state trajectories on state plane as line AA' and BB'.

For line AA', the final sate point A' is above the line where DeltaS = 0, which means the relative distance is larger than 0; thus safety condition meet our requirement. For line BB, there's necessity to calculate the deceleration needed on the final state point B' in acceleration field to estimate the risk from traffic vehicle 2. If the brake intensity calculated is lower than a permissible value, the process can be finally evaluated as safe and feasible. Otherwise, the plan of a lane change at that moment should be cancelled.

Decision-Making Method According to analysis of braking and lane-changing process, we can summarize a lane-changing decision-making method as in Figure 9.

In each decision-making cycle, host vehicle should first use on-board sensors to perceive surrounding environment information, including relative distance and relative velocity between host vehicle and traffic vehicles nearby. Then determine if there is a lane-changing intention: without an intention, it should drive in a straight line as instructed by the braking decision-making method; otherwise, it's necessary to judge the feasibility of a lane change by lane-changing decision-making method. As simplified in this section, we ignore velocity regulation, and choose "brake", "change lane" or "maintain the status quo" directly. When practicable, change lane at once, otherwise, host vehicle is supposed to run in the braking mode within current decision-making cycle.

Extended Lane-Changing Decision-Making Method

In this section, we will extend the basic lane-changing decision-making method in two aspects:

1. Consider the impact from rear side traffic vehicle.

2. Consider velocity regulation before it starts to change lane.

Inspection on Rear Side Traffic Vehicle

In the basic lane-changing decision-making method, we have considered potential risks from preceding vehicles. Moreover, it's meaningful to judge the feasibility from rear side traffic vehicle's perspective.

According to traffic rules and driving experience, a lane change usually has no effect on the vehicle ahead. And a vehicle can only change lane when it poses no danger to rear vehicle on the side lane. For rear vehicle, it has to adjust speed to adapt to real-time dynamic traffic environment. This process involves interaction between two vehicles; thus we take two parameters to judge the feasibility of a possible lane change. The first one is the acceleration acquired from the acceleration field for host vehicle, which is exerted by rear vehicle on the side lane. The second one is the deceleration acquired for rear vehicle, which assumes that host vehicle will keep a constant speed. These two parameters represent the urgency imposed on two vehicles separately, and any of them exceeding an acceptable range will reject the claim for a lane change.

Extended Method with Velocity Regulation

In Section II, we allow the braking process to be executed only after the completion of a lane change. In fact, host vehicle can certainly brake before changing lane, which will gain flexibility at the expense of part of safety. The process of velocity regulation can be illustrated with Figure 10. Relationship with preceding vehicle and anterolateral vehicle can be represented by point A and B respectively. When planning a lane change, host vehicle needs to determine the feasible region for velocity regulation.

Since the host vehicle will eventually run at the same speed with front vehicle in the target lane, and speed difference between host vehicle and the two vehicles ahead during the process of deceleration is reduced synchronously, we stipulate that the maximum range of velocity regulation for host vehicle equals the initial speed difference between the host vehicle and the target front vehicle. Besides, to make it safe, starting position of a lane change on state plane shall not be lower than the lane-changing emergency warning line. Then we can determine a feasible regulation region, which consists of a speed regulation range and a distance regulation range, shown as the red frame in Figure 10. Legends LC1 and LC2 are the ones appeared in Figure 7, for LC1 is the optimum lane-changing reference line and LC2 is the lane-changing emergency warning line.

In an attempt to find the optimal initial state of lane change, we select a series of acceptable acceleration and then calculate the state points at a certain time interval, which are represented by black dots and taken as possible initial states of a lane change. Next, screen out those feasible with the method presented in Section II. After that, make a comprehensive evaluation of each plan by function designed as expression (10).

[mathematical expression not reproducible] Eq. (10)

where J is the evaluating indicator, [a.sub.limit] is the maximum braking deceleration that is acceptable, [a.sub.bef] is the deceleration selected before the lane change, [a.sub.aft] is the deceleration acquired in the acceleration field to ensure safety after the lane change, [L.sub.p] is the longitudinal distance required for the lane change, [L.sub.opt] is the temporary optimal longitudinal distance for the lane change given by trajectory planning method, [L.sub.limit] is the shortest longitudinal distance needed but still within the limit of tolerance. [w.sub.1] and [w.sub.2] are weight coefficients responsible for measuring the importance of comfort in the braking process before and after a lane change, and [w.sub.3] is the weight coefficient measuring handling stability and comfort of the lane-changing process.

By calculating the evaluation value while giving priority to the span of a lane change, we can reach the best lane-changing scheme overall, which includes the braking deceleration and the time needed before the lane change, together with the longitudinal distance required by that lane change. When the optimal scheme is to change lane immediately, decisionmaking module sends the termination of that lane change to trajectory planning module and then makes the change. When the better initial state for changing lane can be achieved by a period of braking, then prepare for the upcoming lane change by driving in the origin lane as instructed. The whole decisionmaking process can still be shown as in Figure 9.

Simulation with Polynomial Trajectory Planning

High-order polynomials have properties of at least the two-order continuity. Taking advantage of this strength, polynomial trajectory planning methods obtain smooth trajectories while considering constraints of both start and end states. Instead of emphasizing the innovation of trajectory planning methods, this article hopes that by choosing a stable and reliable planning method to cooperate with the proposed lane changing decision-making method, a complete decisionmaking and planning system can be formed, in which a vehicle can determine the timing of a lane change and obtain a feasible trajectory. Therefore, this article only adopts the five order polynomial trajectory planning method to generate feasible trajectory clusters and extract the temporary optimum trajectory and the shortest trajectory within comfort limit. This information will be delivered to decision-making modules to make a further decision. Afterwards, the overall optimum lane-changing state will be fed back to the trajectory planning method, then the ideal trajectory can be produced directly. After being processed by trajectory following module, this lane-changing trajectory can be finally achieved with actuators.

To verify the decision-making method proposed, a typical scenario shown in Table 1 is simulated. Simulation results are expressed in Figures 11-13, and decision-making parameters shown in Figure 11 are explained in Table 2.

In Figures 11 and 12, we can see that at the beginning of simulation, host vehicle is in the lane 1 (Lane = 1), acceleration calculated in the acceleration field approximately equals 0, and the room for a possible lane change is rather ample, so there's no intention to change lane (LC_intention = 0), and no necessity to judge the feasibility for a lane change (LC_feasibility = -1). Therefore, the decision-making module gives the instruction to maintain the original state (Decision = 0).

When t = 2.197 s, distance to preceding vehicle hits the lane-changing intention reference line. Since velocity of front vehicle in the same lane is lower than that of host vehicle, and velocity of anterolateral vehicle is also higher than that, it's reasonable to generate the intention of changing lane (LC_intention = 1). When feasibility is checked and confirmed (LC_feasibility = 1), decision-making module gives the instruction to change lane (Decision = 3). From then on, the host vehicle is seen as in both original and target lane at the same time (Lane = 12).

The whole lane-change process lasts for 5.22 s, during which the host vehicle's trajectory, lateral acceleration, and steering wheel angle are shown in Figure 13. Figure 14 is the local enlarged drawing of the trajectory graph in Figure 13. It is the superposition of a series of local planning trajectory, which do update over time with only the beginning part of each executed. Finally, the track left by host vehicle is showed as the red line in Figure 13. As the results show, time for change is abundant, and the trajectory planned is quite smooth, which meets basic requirement of a lane change. Besides, in this case, the velocity of front vehicle is larger than that of host vehicle, so acceleration field gives the value of 0, which means there's no need to decelerate or accelerate. This is also in line with lane-changing rules.

On the whole, the decision-making method proposed in this article achieves the goal of making a safe and comfortable lane change. With safety as first priority, the method is proposed based on extended safety distance model, and the risks of collision with preceding vehicle, anterolateral vehicle and posterolateral vehicle are fully considered in the process of making braking or lane-changing decision. From Figure 12, we can see the distance between host vehicle and preceding vehicle is over zero during the process, which approves the safety of that lane change. Moreover, to reduce the discomfort caused by braking or steering during the lane-changing process, the method imposes restrictions on deceleration in the braking and longitudinal distance for the lane change while evaluating the lane-changing-plans feasibility. As revealed in Figure 13, lateral acceleration keeps lower than 1.3 m/[s.sup.2] during the process, which guarantees a comfortable lane change. Furthermore, to avoid an over huge gap that a traffic vehicle in adjacent lane may cut in, we proposed the primary lane-changing intention reference line and the brake starting reference line, where only the relative state reaches one of them will an operation of braking or a lane change be triggered, and that promises the traffic efficiency. Finally, different reference lines correspond to different drivers. As intention reference line, brake starting reference line and optimum lane-changing reference line can be adjusted to adapt to different perceptual and driving habits, this method can be personalized.


This article proposed a new lane-changing decision-making method with consideration of safety, comfort, traffic efficiency and personality. The innovation lies in the proposal of acceleration field and the personalized lane-changing decision-making method, which can adapt to multi-vehicle traffic environment and cater to different drivers' preference at the same time. First, we analyzed the process of braking and extended the emergency braking safety distance model to set up a braking acceleration field, then added the driving part to form a complete acceleration field that covers the common traffic environment. Second, we made a basic lane-changing decision-making model on the basis of acceleration field and some rules, which also caters for driver's habits, traffic efficiency and safety. Third, we extended the basic method and then velocity regulation was taken into consideration, which largely improve its flexibility. Finally, simulations with polynomial trajectory planning method were conducted to verify its effectiveness. As simulation results showed, the method presented in this article can provide safety evaluation and give an optimum driving state on a structured straight road. For next step, we are positively making preparation for experiment, hoping to verify and improve the method further by acquired real vehicle data.

Contact Information

Dr. Bing Zhu is currently a professor at College of Automotive Engineering and State Key Laboratory of Automotive Simulation and Control, Jilin University, China.

Dr. Jian Zhao, corresponding author, is currently a professor at College of Automotive Engineering and State Key Laboratory of Automotive Simulation and Control, Jilin University, China.


This work is partially supported by National Key R&D Program of China (2018YFB0105103, 2016YFB0100904), National Natural Science Foundation of China (51775235, 51575225).
Symbols and Abbreviations

Item           Meaning

[a.sub.aft]    Deceleration acquired in the acceleration field
               after lane change
[a.sub.bef]    Selected deceleration for lane change
[]     Target acceleration(minus) during
               braking process
[a.sub.bmax]   Accessible minimum acceleration(minus)
[a.sub.dg]     Target acceleration during
               accelerating process
[a.sub.limit]  Maximum braking deceleration that is acceptable
               for driver
J              Evaluating indicator
k              Average acceleration rate during t[b.sub.2]
[k.sub.d]      Average acceleration rate while acceleration
               is increasing
[L.sub.limit]  Shortest longitudinal distance for lane change
               that within tolerance
[L.sub.opt]    Optimal longitudinal distance for lane change
[L.sub.p]      Longitudinal distance required for lane change
[S.sub.b1]     Traveling distance of host vehicle during [t.sub.b1]
[S.sub.b2]     Traveling distance of host vehicle during [t.sub.b2]
[S.sub.b3]     Traveling distance of host vehicle during [t.sub.b3]
[]     Traveling distance of host vehicle during the
               whole braking process
[]     Safety margin between host vehicle and
               preceding vehicle for deceleration
[]     Traveling distance of preceding vehicle during
               the whole braking process
[]     Safety braking distance
[S.sub.dh]     Traveling distance of host vehicle during its
               accelerating process
[S.sub.ds]     Safety margin between host vehicle and
               preceding vehicle for acceleration
[S.sub.dt]     Traveling distance of rear vehicle during host
               vehicle's accelerating process
[S.sub.dw]     Safety driving distance for acceleration
[t.sub.b1]     Time span to eliminate brake clearance plus
               latency of signal processing
[t.sub.b2]     Time for increasing braking pressure
[t.sub.b3]     Time for uniform acceleration (minus) braking
[t.sub.d1]     Time span to eliminate acceleration clearance
               plus latency of signal processing
[v.sub.h]      Velocity of host vehicle
[v.sub.t]      Velocity of target traffic vehicle
[w.sub.1]      Coefficient to weigh the importance of comfort
               before lane change
[w.sub.2]      Coefficient to weigh the importance of comfort
               after lane change
[w.sub.3]      Coefficient to weigh the importance of handling
               stability and comfort during lane change
[DELTA]v       Relative velocity, equals to [v.sub.t] - [v.sub.h]
Line B1        Primary lane-changing intention reference line
Line B2        Brake starting reference line
Line B3        Emergency braking warning line
Line LC1       Optimum lane-changing reference line
Line LC2       Lane-changing emergency warning line


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Bing Zhu, Shuai Liu, and Man Zhao, Jilin University, China


Received: 26 Apr 2018

Revised: 05 Dec 2018

Accepted: 05 Mar 2019

e-Available: 29 Apr 2019

TABLE 1 Simulation scenario.

Parameter                                               Value

Initial velocity of the host vehicle                    40 km/h
Initial velocity of the front vehicle in the same lane  35 km/h
Initial distance to the front vehicle in the same lane  10 m
Initial velocity of the front vehicle in adjacent lane  45 km/h
Initial distance to the front vehicle in adjacent lane   5 m
Initial velocity of the rear vehicle in adjacent lane   45 km/h
Initial distance to the rear vehicle in adjacent lane   20 m

TABLE 2 Decision-making parameters in simulation.

Parameter    Meaning       Description

Lane         Lane that     1: Host vehicle is on the original lane
             host vehicle  2: Host vehicle is on the adjacent lane
             is on         12: Host vehicle is changing lane
LC_          Lane-         0: Without intention to change lane
intention    changing      1: With intention to change lane
LC_feasible  Feasibility   -1: There's no need to judge feasibility
             of a lane     0: Unfeasible to change lane
             change        1: Feasible to change lane
Decision     Measure       0: Keep the state unchanged
             decided to    1: Brake
             take          2: Prepare for a lane change
                           3: Change lane
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Author:Zhu, Bing; Liu, Shuai; Zhao, Man
Publication:SAE International Journal of Passenger Cars - Electronic and Electrical Systems
Date:Aug 1, 2018
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