Control mode switching strategy for ACC based on intuitionistic fuzzy set multi-attribute decision making method

Abstract

The control mode switching strategy is a crucial part of the Adaptive Cruise Control (ACC) decision algorithm. A novel switching strategy of control mode is proposed, which is designed using an intuitionistic fuzzy set, multi-attribute decision making method (IFSMADM). At first, three modes of cruising, following and approaching are considered for the control modes of the decision algorithm for the ACC. Then, safety performance, comfort performance and economy performance are treated as the attributes needed to assess alternative sets. Furthermore, the linear weighted average method of IFSMADM is used to achieve control mode switching. Finally, the proposed algorithm is verified based on actual road test data.

Keywords

Adaptive Cruise Control (ACC)switching strategy intuitionistic fuzzy set multi-attribute decision making

1 Introduction

The most popular, recent research on Advanced Driver Assistance Systems (ADAS) has focused upon Adaptive Cruise Control (ACC) systems. Researchers, automakers and consumers across the world are focusing on ACC [8 , 17]. ACC is designed as a comfort-enhancing system and is an extension of conventional Cruise Control (CC). The main functional enhancement of ACC, compared to the standard CC, exists in the ability to sense forward traffic. The algorithm of CC only includes one control mode, because it only needs to control the vehicle’s speed. However, ACC is different from CC, offering more safety and convenience, as well as comprising additional control modes in addition to speed control. Depending on the situation, ACC automatically changes between two basic function modes: speed control and space control [13]. The speed control function is implemented by adjusting the torque of the engine based on the error between the actual speed and the driver-set speed. The space control function intervenes between the engine torque and the brake to keep the ego car a desired distance away from the preceding vehicle [11].

ACC will choose a suitable control mode and implement an appropriate control decision algorithm according to the traffic situation. Generally, two or more control modes are considered in existing works. There are two control modes in Delphi’s ACC decision algorithm: cruise mode and follow mode. BMW’s ACC includes three parts: cruise mode, follow mode and curve mode. The appropriate control mode is selected according to the traffic conditions, and a correction decision will be made under different driving conditions [5, 6]. The ACC decision algorithm in [10] consists of three control modes: (1) the cruise mode when there is no vehicle ahead; (2) the speed control mode; (3) the space control mode when there is a vehicle ahead of the host vehicle.

Most existing works focus on the development of the distance control algorithm and the functional development of the following mode [1 , 12]. With respect to the control mode switching strategies, works in the current literature are rare. Delphi’s ACC uses the distance phase plane and the relative velocity for a mode switching design. There are multiple zones for different control modes in the phase plane. The parameters of each zone should be calibrated, respectively. During the process of mode switching, since it is calculated in different ways in each control mode, large changes in the control input of the decision algorithm will take place. Thus, in designing the ACC’s mode switching strategy, we should consider not only the safety performance, but we also need to consider the smoothness of the control input during the mode switching process. This impacts the driving comfort performance [18]. In order to alleviate the discomfort that results from the changes in the control mode, the weighted average methods have been proposed to solve the problem of target acceleration discontinuities [4 , 14]. In order to smooth the change, the weighted average method uses the weighted average of the former mode and the current mode as the current control input. Since the existing mode switching strategies usually focus on safety performance, the system’s comfort performance is often lacking. In general, two adjacent zones in the phase plane are mixed. That is to say, it is uncertain and ambiguous which control mode will be chosen in the area around the boundaries. As a result, the boundary is not always clear between two control mode zones. From the point of view of mathematics and control, the control mode switching strategy for the ACC is a decision making problem. In order to overcome the shortage of current ACC control mode switching strategies, this paper puts forward a novel method based on the intuitionistic fuzzy set, multi-attribute decision making (IFSMADM). Intuitionistic fuzzy sets are an extension of fuzzy sets. Besides membership, there is hesitancy involved in intuitionistic fuzzy sets when describing the uncertainty, which results in an improved ability of intuitionistic fuzzy sets to process uncertain information [2 , 19]. There are some advantages in adopting a method based on IFSMADM in order to solve the control mode switching problem of ACC: 1) The control mode switching strategy based on IFSMADM is able to implement multi-object, coordinated decision making and automatic mode switching. Thus, the method is not only able to ensure the safety performance of the ACC system, but it is also able to guarantee comfort performance and economy performance. 2) The intuitionistic fuzzy sets provide an effective way to solve the problem that exists in the uncertainty of mode selection, which is helpful for solving the difficulties in determining the boundaries and thresholds of mode switching.

This paper proposes a control mode switching strategy for the ACC system. The remainder of this paper is arranged as follows: in Section 2, the structure and the control modes of the decision algorithm for the ACC are introduced in detail; in Section 3, the control mode switching strategy for the ACC system based on the IFSMADM is proposed; in Section 4, the proposed approach is validated and tested; finally, conclusions are drawn.

2 ACC’s control modes

For ACC’s decision algorithm, three control modes are considered: cruise mode, follow mode and approach mode. A suitable mode is chosen and an appropriate control decision algorithm is implemented based on the actual traffic situation. The decision algorithm of the three modes mentioned above is shown in Fig. 1.

For the cruise mode, a Proportional-Integral controller is utilized using the deviation between the actual velocity and the desired velocity for the target acceleration calculation. Where a_{des_crs} represents the target acceleration of the cruise mode, v_des represents the cruising speed, v_ego denotes the current velocity of the host vehicle, k_p represents the proportional gain and k_i denotes the integral gain.

The objective of the follow mode is to keep the deviations of the velocity and the distance at zero, simultaneously. Thus, a proportion controller is utilized with both deviations of the speed and the distance. Where a_{des_fol} represents the target acceleration and v_p represents the velocity of the preceding vehicle, d is the distance between the host vehicle and the one ahead, d_des represents the target distance, k_v represents the velocity gain and k_d denotes the distance gain.

When the host vehicle is close to the vehicle ahead or the one ahead strongly decelerates, the host vehicle should decelerate using a stable deceleration in order to remain a safe distance away from the preceding vehicle. Where a_{des_app} represents the target acceleration and a_p represents the acceleration of the preceding vehicle.

3 Control mode switching strategy

ACC will change to a suitable control mode and implement an appropriate control decision algorithm according to the traffic situation. Hence, the mode switching strategy acts as an important role in the decision algorithm, directly affecting the control performance of the ACC.

3.1 Intuitionistic fuzzy sets

A novel strategy based on IFSMADM is proposed in this paper. The basic definition of intuitionistic fuzzy sets is as follows:

Definition. Let X be a universe. An intuitionistic fuzzy set A on X can be defined as follows: $A = {< x, μ_{A} (x), υ_{A} (x) > | x \in X}$ where μ_A (x) ∈ [0, 1] and υ_A (x) ∈ [0, 1] such that 0 ≤ μ_A (x) + υ_A (x) ≤1 for any x ∈ X.

Here, μ_A (x) and υ_A (x) are the degree of membership and degree of non-membership of the element x, respectively.

For an intuitionistic fuzzy set, A on X, the function π_A (x) =1 - μ_A (x) - υ_A (x) denotes the hesitation of A. It is obvious that 0 ≤ π_A (x) ≤1 for any x ∈ X.

3.2 Intuitionistic fuzzy set multi-attribute decision making method

The IFSMADM is used to select the best of the solutions by ranking the alternatives using intuitionistic fuzzy sets.

Suppose there exists an alternative set X = {x₁, x₂, …, x_n}, which consists of n decision making alternatives. Each alternative is assessed on m attributes or indexes o_i (i = 1, 2, …, m). Denote the set of all attributes O = {o₁, o₂, …, o_m}. The evaluation of the alternative x_j ∈ X with respect to the attribute o_i ∈ O can be represented by an intuitionistic fuzzy set. This is denoted by F_ij = {(o_i, x_j) , < μ_ij, υ_ij >} (i = 1, 2, …, m ; j = 1, 2, …, n), where μ_ij and υ_ij are the degree of membership and the degree of non-membership of the alternative x_j ∈ X with respect to the attribute o_i ∈ O to the fuzzy concept “excellence,” respectively. The decision matrix of the problem can be constructed as F = (F_ij) _mxn = (< μ_ij, υ_ij >) _mxn,where F_ij (i = 1, 2, …, m ; j = 1, 2, …, n) denot-es the evaluation of the jth alternative on the ith attribute, and F_ij denotes an intuitionistic fuzzy set represented by (< μ_ij, υ_ij >). The importance of the ith attribute is represented by w_i and w = (w₁, w₂ … , w_m) is the weight vector of the attribute set O = {o₁, o₂, …, o_m}.

The procedure of the approach used to rank alternatives in a multi-attribute decision-making method under intuitionistic fuzzy sets can be briefly described as follows:

Step 1. Determine the alternative set X = {x₁, x₂, …, x_n} and the attributes set O = {o₁, o₂, …, o_m}.

Step 2. Create the intuitionistic fuzzy decision matrix F = (F_ij) _mxn = (< μ_ij, υ_ij >) _mxn based on the evaluated values for all of the alternatives on each attribute. Then, calculate the weight vector of the attribute set w = (< p_i, t_j >) _mx1.

Step 3. Calculate the weighted intuitionistic fuzzy decision matrix $\bar{F} = (< {\bar{μ}}_{ij}, {\bar{υ}}_{ij} >)_{mxn}$ $\bar{F} = \begin{matrix} x_{1} \begin{matrix} x_{2} & x_{n} \end{matrix} \\ \begin{matrix} o_{1} \\ o_{2} \\ ⋮ \\ o_{m} \end{matrix} (\begin{matrix} < {\bar{μ}}_{11}, {\bar{υ}}_{11} > & < {\bar{μ}}_{12}, {\bar{υ}}_{12} > & \dots & < {\bar{μ}}_{1 n}, {\bar{υ}}_{1 n} > \\ < {\bar{μ}}_{21}, {\bar{υ}}_{21} > & < {\bar{μ}}_{22}, {\bar{υ}}_{22} > & \dots & < {\bar{μ}}_{2 n}, {\bar{υ}}_{2 n} > \\ ⋮ & ⋮ & ⋮ \\ < {\bar{μ}}_{m 1}, {\bar{υ}}_{m 1} > & < {\bar{μ}}_{m 2}, {\bar{υ}}_{m 2} > & \dots & < {\bar{μ}}_{mn}, {\bar{υ}}_{mn} > \end{matrix}) \end{matrix}$

Step 4. Calculate the evaluating value

$V_{j} = \sum_{i = 1}^{m} < {\bar{μ}}_{ij}, {\bar{υ}}_{ij} >$ of each alternative x_j ∈ X (j = 1, 2 … , n).

Step 5. Rank the evaluating values V_j (j = 1, 2 … , n) of all alternatives. Output the final ranking of all alternatives and select the best one.

3.3 IFSMADM-based mode switching

For the control mode switching of the ACC, the cruising mode, following mode and approaching mode can be treated as the alternatives of the problem. The alternative set can be denoted as X = {x₁, x₂, x₃} = {Cruise Mode, Follow Mode, ApproachMode}. Accordingly, safety performance (o₁), comfort performance (o₂) and economy performance (o₃) are taken into account jointly when evaluating the alternatives, which can be represented as the attribute set O = {o₁, o₂, o₃} = {Safety, Comfort, Economy}.

The evaluation of the alternative x_j ∈ X with respect to attribute o_i ∈ O can be represented by an intuitionistic fuzzy set (< μ_ij, υ_ij >), where μ_ij, υ_ij are the membership degree and the non-membership degree of the alternative x_j ∈ X with respect to the attribute o_i ∈ O of the fuzzy concept “excellence,” respectively. μ_ij and υ_ij can be represented by functions of vehicle motion and the desired acceleration can be determined by the decision algorithm, as shown in Figs. 2 to 4. Moreover, the weight vector of the attribute set w = (< p_i, tj >) _3×1 can be represented by the function of the distance between the host vehicle and the preceding one, as shown in Fig. 5.

The first attribute of the control mode, safety performance (o₁), is represented by the distance between the host vehicle and the preceding one. The longer the distance, the safer is the host vehicle. Therefore, the safety performance can be represented by an intuitionistic fuzzy set, of which the degree of membership and the degree of non-membership are as shown in Fig. 2. In Fig. 2, the horizontal axis is the ratio of d_prd, and d_des, d_prd is the predictive distance between the host vehicle and the preceding one according to the determined acceleration of the ACC. d_des is the desired distance set by the driver. The greater the ratio, the further away is the host vehicle from the preceding vehicle. d_prd can be calculated using formula (1): $d_{prd} = d + v_{p} \cdot t_{T} - v_{h} \cdot t_{T} - 0.5 a_{des} t_{T}^{2}$ (1) where d_prd is the distance between the host vehicle and the preceding one that results from the ACC; d is the actual distance between the host vehicle and the preceding one; v_p is the speed of the preceding vehicle; v_h is the speed of the host vehicle; a_des is the acceleration determined by the ACC’s decision algorithm; t_T is a short period of time used to predict the change in the distance caused by the ACC.

The comfort performance (o₂) of a vehicle equipped with ACC is mainly dependent on the change in the acceleration of the vehicle. Thus, the comfort performance is represented by an intuitionistic fuzzy set, of which the degree of membership and degree of non-membership are represented by a function of the difference between a_des and a_mes. Here a_mes is the actual acceleration of the vehicle, as shown in Fig. 3.

The economy performance (o₃) of the system is mostly influenced by the level of the target acceleration of the system. Thus, the performance is represented by an intuitionistic fuzzy set, of which the degree of membership and degree of non-membership are represented by a function of a_des, as shown in Fig. 4.

For the actual situation, the weight of each attribute (evaluation index) is not fixed. It changes with the actual conditions. When the distance is greater, the system increases the weights of comfort and economy performance. As a result, these performance aspects have more attention paid to them; meanwhile, when the distance is small, the system increases the weight of safety performance in order to guarantee that aspect. Moreover, the weights of the three attributes are vague and determining their values accurately is difficult. In this paper, therefore, the weights of the attributes are also represented by an intuitionistic fuzzy set, of which the degree of membership and the degree of non-membership are represented by a function of the ratio of d_mes to d_des, where d_mes is the distance between the host vehicle and the vehicle ahead and d_des is the desired distance set by the driver, as shown in Fig. 5.

According to the procedure outlined in Section 3.2 above, the intuitionistic fuzzy decision matrix F can be determined based on (1) the membership and non-membership of the intuitionistic fuzzy set of each attribute, (2) the target acceleration determined by the decision algorithm of the ACC, and (3) the motion of the vehicle. The intuitionistic fuzzy set of the weight vector can be determined by the distance between the host vehicle and the preceding one, based on the functions of membership and non-membership. Then, the weighted, intuitionistic fuzzy decision matrix, $\bar{F}$ , can be calculated according to Step 3 given in Section 3.2. The preferred control mode can then be selected by ranking the evaluating values of the three control modes.

4 Verification based on road test data

In this section, the proposed algorithm is verified based on the actual road test data in order to provide useful guidance and prove the quality of the proposal for practical application. The speed data for the preceding vehicles were collected from a test case in a real traffic scenario. The road tests were implemented on a flat, long-straight road. The host vehicle was equipped with a Delphi millimeter wave radar (MMW radar), which was used to measure the motion of the preceding vehicle and the relative distance between it and the host vehicle. In the test, initially, the host vehicle cruised at the desired velocity of 95 km/h while the vehicle ahead drove at a velocity of around 80 km/h. Then, the vehicle ahead accelerated to a speed of 100 km/h. The host vehicle initially decelerated to a speed of 80 km/h in line with the preceding vehicle after the latter was detected. Then, when the preceding vehicle accelerated to a speed of 100 km/h, the host vehicle returned to the cruising velocity once the velocity of the vehicle ahead became greater than the desired cruising speed. The testing scene is shown in Fig. 6.

Details of the speeds in the test case are shown in Fig. 7. The driver’s desired cruising velocity was set to 95 km/h. Firstly, the host vehicle cruised at the desired speed. Then, the host vehicle decelerated to a speed of 80 km/h in line with the former after detecting the preceding car.

In order to prove the advantages of the IFSMADM method, the results are now compared with the traditional mode switching method that has a design based on the relative velocity and the distance. As shown in Fig. 7, in the initial period (about 0 s to 40 s), the host vehicle accelerated from 90 km/h to 95 km/h and maintained cruising speed because the preceding vehicle was far away. When the distance became shorter, the host vehicle switched to the follow mode and decelerated to follow the preceding vehicle. When the preceding vehicle accelerated and moved away, the host vehicle switched backed to cruising mode and accelerated to the desired cruising speed. The results of the IFSMADM method were similar to those under the traditional method. However, they were also an improvement. The desired cruising speed is represented by the dashed line. The measured speed of the preceding vehicle is represented by the dashed-dotted line. The actual speed of the host vehicle that resulted from the method based on IFSMADM is represented by the solid line with squares. The actual velocity of the host vehicle that resulted from the traditional method is represented by the solid line with circles. Figure 8 shows the comparison of the intuitionistic fuzzy decision-making method and the traditional mode switching method. The comparison of the two method results is shown in Table 1.

In the time period from about 20 s to 40 s, the control mode selected by the traditional method is the approach mode, but the control mode selected by the IFSMADM is the cruise mode. In the period from 20 s to 40 s, the relevant velocity is below zero, which meets the control mode switch criteria. Therefore, the traditional method switches the control mode to the approach mode. The IFSMADM selects the cruise mode at this stage. In this period, the host vehicle is far away from the vehicle ahead. Additionally, the safety performance indexes of the approach mode and the cruise mode are the same. However, the comfort performance and economy performance indexes of the cruise mode are higher than those of the approach mode, as was shown in Table 1.

In the second time period from 40 s to 60 s, the control mode selected by the traditional method is the approach mode, while that chosen by the IFSMADM is the follow mode. Here, the relevant velocity is below zero, which meets the control mode switch criteria for the approach mode. Therefore, the traditional method switches to the control mode. The IFSMADM selects the follow mode in this period because the host vehicle is closer to the preceding one. Also, the safety performance index of the follow mode is higher than that of the approach mode. An example is shown in Table 2.

In the period from 70 s to 120 s, the control modes selected by the traditional method are the follow mode and the cruise mode. The control mode switches frequently and repeatedly between the two modes. However, the control mode selected by the IFSMADM is the follow mode without any oscillation. The traditional method is designed based on thresholds. Therefore, any fluctuation of relevant velocity and distance will result in control mode oscillation. The IFSMADM avoids using thresholds. Therefore, it is immune to interference from the motion information noise.

Figure 9 shows the comparison of acceleration between the IFSMADM-based mode switching strategy and the traditional one. The IFSMADM significantly protects the control mode from oscillation. In Fig. 10, the maximum acceleration rate of the IFSMADM switching strategy is 9.531, while the maximum acceleration rate of the traditional strategy is 64.851. This is 6.804 times greater. This proves the performance of the IFSMADM-based strategy is smoother and that the comfort performance is better than those of the traditional switching strategy.

Figures 11 and 12 show the relevant velocity and the distance between the host vehicle and the preceding one, respectively. The relevant velocities that resulted from the two methods are similar, as shown in Fig. 12. Figure 12 also shows that the IFSMADM causes the actual distance to approach the desired distance more quickly. The actual distance is close to the desired distance after 50 s under the IFSMADM. However, the actual distance only becomes close to the desired distance after 70 s under the traditional method. The earlier distance control leads to a safer performance and makes the user experience more satisfactory and comfortable.

5 Conclusions and future work

The existing switching strategies pay particular emphasis to safety performance, ignoring comfort performance during mode switching. Furthermore, since the boundaries between any two modes are uncertain and ambiguous, it is difficult to acquire the exact thresholds of the boundaries of each control mode. To solve the problem mentioned above, an IFSMADM-based mode switching strategy has been developed. The research conclusions are as follows:

The control mode switching strategy realized by the IFSMADM can overcome the difficulties of a design that is based on control-mode boundaries and can also avoid control-mode oscillation.

With the IFSMADM, not only is safety performance taken into account in the control mode switching for ACC, but it also considers comfort performance and economy performance. Moreover, the membership and non-membership of each performance index have been designed in detail. Also, their reasonability and efficiency are proven in this study.

The tests show that the IFSMADM-based mode switching strategy can realize mode switching correctly according to the different traffic scenarios. Moreover, compared with the existing traditional method, as well as the safety performance being guaranteed by the new method, the comfort performance and economy performance of the system have also been improved.

Future research will focus on the on-the-road experiments of the designed algorithm in different operating conditions. Furthermore, future work will focus on the study of the control mode switching strategy satisfying the preferences and attitudes of different drivers and being adaptive to various operating conditions based on online learning.

Footnotes

Acknowledgments

This work is partly supported by National Science Foundation of China (Nos. U1564214, 51675224).

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