Adaptive cruise control system based on improved variable time headway spacing strategy

Abstract

In the following process, in order to improve the driving safety and road utilization of the adaptive cruise control (ACC) system, a variable time headway spacing strategy was studied. In view of the fact that the variable spacing strategy cannot adapt to the complex and variable deceleration conditions, an improved variable time headway strategy is proposed, which changes with the deceleration time and deceleration of the preceding vehicle. Based on this, the upper controller of adaptive cruise control based on model predictive control is designed, and numerical simulation of the variable time headway spacing strategy is performed, which verifies the effectiveness of the improved variable time headway strategy. The results show that the spacing strategy proposed in this paper can more smoothly keep up with the preceding vehicle, and improve driving safety, comfort and road utilization.

Keywords

Adaptive cruise control variable time headway spacing strategy model predictive control

1 Introduction

The adaptive cruise control (ACC) system is one of the advanced driver assistance systems (ADAS) systems. It can detect the position and speed of the preceding vehicle through various on-board sensors, and then automatically adjust the vehicle speed to keep a proper safety distance from the vehicle in front through control strategies [1, 2].

Spacing strategy selection is one of the important components of the ACC system, whether its design is reasonable will directly affect the safety of vehicles and road utilization [3]. Too small a distance can easily lead to rear-end collisions, while too large will not only reduce road capacity, but also cause vehicles to be inserted from adjacent lanes. Spacing strategies are mainly divided into two categories: constant spacing (CS) strategies [4] and variable spacing (VS) strategies [5]. Because the constant-pitch strategy cannot balance multiple control targets and adapt to a complex and changing driving environment [6], a variable spacing strategy is produced.

Among the variable spacing strategies, the current mainstream is the spacing strategy based on the time headway, which is divided into a constant time headway (CTH) [7] and a variable time headway (VTH) [8] according to whether it changes. Xu [9] obtained a variable spacing strategy by experimenting with curve fitting of human driver behavior provided by vehicle manufacturers. In the case of front lane change, the relative distance between two vehicles is changed linearly to the desired distance. Loannou [10] studied adaptive cruise control and proposed a safety distance model based on a constant time headway distance to improve road utilization and driving safety. In the VTH strategy designed for the intelligent cruise control system, the time headway is directly proportional to the speed of the vehicle [11]. Yi [12] designed a variable spacing strategy that takes into account the effects of tire road friction on vehicle braking distance and driver driving mode. Yanakiev [13, 14] studied the longitudinal control of automatic heavy trucks and designed a real-time VTH strategy combining relative speed. This strategy reduces transient errors and allows the fleet to maintain a smaller spacing. Luo [15] proposed a multi-objective ACC algorithm based on model predictive control, and designed a VTH strategy, in which the acceleration of the preceding vehicle was introduced to simulate the future trend of the speed of the preceding vehicle. Wang [16, 17] proposed a spacing strategy based on the Macroscopic traffic flow theory, which believed that the time headway was related to the road’s congestion density and free flow speed. Chen [18] proposed an improved variable time headway spacing strategy, which considers macroscopic traffic flow theory, relative speed, and front vehicle acceleration. Compared with CTH and VTH strategies, it has certain applicability and advantages. Jiang [19] proposed a variable time headway strategy with a non-linear change in relative speed and a proportional increase in acceleration, which improved the stability and safety of the variable spacing strategy.

This article is aimed at the existing spacing strategy can not adapt to the driving environment when the front vehicle decelerates. Based on the existing distance strategy, a variable time headway strategy is proposed that varies with the deceleration and deceleration time of the preceding vehicle. The model predictive control theory is used as the upper layer of adaptive cruise control to simulate and compare it.

2 Spacing strategy design

As the variable spacing strategy can adapt to more complex traffic environments, this article adopts the following spacing strategy, $d_{des} = t_{h} v_{f} + d_{0}$ (1)

Where d_des is the expected distance,t_h is the time headway, v_f is the speed of the vehicle, and d₀ is the minimum safe distance.

2.1 VTH strategy

Yanakiev [13] and other researchers studied the longitudinal control of automatic heavy trucks, and designed a real-time VTH strategy that combined the relative speed (v_ref = v_p - v_f) and the variable time headway distance decreased as the relative speed increased: $t_{h} = t_{0} - c_{v} v_{ref}$ (2)

Where t₀ is the parameter greater than zero, c_v is the weight coefficient of relative velocity.

In order to improve the dynamic performance of ACC control, Luo [15] proposed to consider the trend of the speed of the preceding vehicle in the distance strategy, that is: $t_{h} = t_{0} - c_{v} v_{ref} - c_{a} a_{p}$ (3)

Where c_a is the weight coefficient of the acceleration of the front vehicle, and a_p is the acceleration of the front vehicle.

Considering that the time headway is non-negative, and too large will cause waste of traffic flow, literatures [13] and [15] and so on all use saturation functions to limit the time headway is too large or too small: $t_{h} = {\begin{matrix} t_{h m a x} t_{h} > t_{h m a x} \\ t_{h} t_{h m i n} < t_{h} \leq t_{h m a x} \\ t_{hmin} t_{h} \leq t_{h m i n} \end{matrix}$ (4)

Where t_hmax and t_hmin are the upper and lower limits of t_h, respectively.

This article mainly studies the characteristics of Yanakiev and Luo’s VTH strategy, improves Luo’s VTH strategy, and analyzes its inability to adapt to the complex and variable deceleration environment of the front vehicle. It improves the safety, comfort and road utilization when the speed of the preceding vehicle is too large or sudden changes. Finally, the MPC algorithm is used as the upper control algorithm of the ACC system, and the simulation is performed to compare the differences between Yanakiev, Luo, and the improved VTH strategy in the three following scenarios. The results prove the effectiveness of the improved strategy.

2.2 Improve VTH strategy

Based on the algorithm in [15], this paper finds that c_a is a fixed value under the condition of deceleration of the preceding vehicle and cannot meet the following behavior of ACC vehicles. When the front vehicle deceleration reaches a certain value, there is a danger of rear-end collision. And the vehicle can’t guarantee its safety under the condition of continuous deceleration at a deceleration.

Therefore, when the current vehicle continues to decelerate uniformly, in order to ensure its safety, the time headway of the vehicle should change as the deceleration time of the preceding vehicle changes, that is: $t_{h} = t_{0} - c_{v} v_{ref} - c_{a} k_{t} a_{p}$ (5)

Where k_t is the duration of the deceleration of the front vehicle.

Considering that the time headway is non-negative, and too large will cause waste of traffic flow, this paper divides the time headway into front vehicle acceleration and front vehicle deceleration sections. This article is consistent with the literature [15] when the front vehicle accelerates or runs at a uniform speed.

When the preceding vehicle decelerates, its value changes with the duration of the acceleration. In the case of the preceding vehicle decelerating, the safety issue should be considered first. Therefore, this article adopts a lower limit without an upper limit: $t_{h} = {\begin{matrix} t_{h} t_{h} > t_{h m i n} \\ t_{hmin} t_{h} \leq t_{h m i n} \end{matrix}$ (6)

3 ACC upper control algorithm

In this paper, a multi-target adaptive cruise control algorithm based on model predictive control theory is used. According to the longitudinal kinematic relationship between the ACC vehicle and the target vehicle [20], let x(k)=[Δd, v_f, v_ref, a_f, j] T be the state vector, and y(k)=[Δd,v_ref,a_f, j] T be the optimized performance index vector. Where, Δd=actual spacing(d) - expected spacing (d_safe), d_safe = v_ft_h + d₀,v_f is the vehicle speed, d₀ is the minimum safety distance, relative velocity v_ref = v_l - v_f and j are the acceleration and acceleration change rate of ACC vehicle speed, and the longitudinal kinematic state equation of ACC vehicle is: $x (k + 1 | k) = Ax (k) + Bu (k) + Gw (k)$ (7) $y (k) = Cx (k)$ (8)

Where x (k + 1|k) is the predicted value of k + 1 under the condition of k, u (k) is the control variable of k, w (k) = a_l (k) is the acceleration disturbance of the target vehicle at k, and A, B, C and G are the coefficient matrix.

Rolling optimization is a major feature of model predictive control. It can perform finite time domain optimization in an infinite time domain.

In order to meet the desired response to the control goals of safety, car following, comfort, and fuel economy during driving, the objective function is summed up: $J = {(Y_{P} - Y_{r})}^{T} Q (Y_{P} - Y_{r}) + U_{N}^{T} {RU}_{N} + ɛ^{T} ρ ɛ$ (9)

Where Y_P,Y_r, U_N and ɛ are the matrices of performance index vector, reference trajectory and control variable in time domain P respectively, Q, R and ρ are weight matrices, which meet the requirements of Q = Q^T ⩾ 0, R = R^T ⩾ 0, ρ = ρ^T ⩾ 0. ɛ is the relaxation factor vector.

Considering the safety of the vehicle, fuel economy, self and traffic laws and regulations, the relative distance, own vehicle speed, acceleration, acceleration change rate and control variables are limited to a certain range. And for the case where there is no solution under the hard constraints during the MPC rolling optimization process, this article uses the method in [21] to distinguish the constraints that need to be widened, so the constraints are relaxed: ${\begin{matrix} Δ d ⩾ 0 + ɛ_{1} v_{\max}^{Δ d} \\ v_{fmin} + ɛ_{2} v_{\min}^{v_{f}} ⩽ v (k) ⩽ v_{fmax} + ɛ_{2} v_{\max}^{v_{f}} \\ a_{fmin} + ɛ_{3} v_{\min}^{a_{f}} ⩽ a (k) ⩽ a_{fmax} + ɛ_{3} v_{\max}^{a_{f}} \\ j_{\min} + ɛ_{4} v_{\min}^{j} ⩽ j (k) ⩽ j_{\max} + ɛ_{4} v_{\max}^{j} \\ u_{\min} + ɛ_{5} v_{\min}^{u} ⩽ u (k) ⩽ u_{\max} + ɛ_{5} v_{\max}^{u} \end{matrix}$ (10)

Where ɛ_i ⩾ 0 (i = 1 ∼5) is the relaxation factor, $v_{\max}^{Δ d}, v_{\max}^{v_{f}}, v_{\max}^{a_{f}}, v_{\max}^{j}, v_{\max}^{u} ⩾ 0$ is the relaxation factor of the upper bound of the hard constraint, and $v_{\min}^{Δ d}, v_{\min}^{v_{f}}, v_{\min}^{a_{f}}, v_{\min}^{j}, v_{\min}^{u} ⩾ 0$ is the relaxation factor of the lower bound of the hard constraint.

4 Simulation

The numerical simulation analysis platform is MATLAB R2018a version under Microsoft Windows 10 64bit. The simulation parameters are shown in Table 1. Simulation experiments are carried out on the spacing strategy proposed in this paper. The calculation process does not consider factors such as road and vehicle diversity.

Table 1
Simulation parameters

parameter value parameter value

P 10 N 4

Q diag(1,1,1,1) T_S 0.2

R 1 τ 0.4

d₀ 5 t₀ 1.5

$V_{\max}^{Y}$ (3;0.9;0.01;0.05) M (0, 50,2.5,2.5)

$V_{\min}^{Y}$ (–3;0;–0.1;–0.05) N (NaN,0,–5.5,–2.5)

$v_{\max}^{u}$ 0.01 c _v 0.05

$v_{\min}^{u}$ –0.1 th_max 2.2

th_min 0.2

parameter	value	parameter	value
P	10	N	4
Q	diag(1,1,1,1)	T_S	0.2
R	1	τ	0.4
d₀	5	t₀	1.5
$V_{\max}^{Y}$	(3;0.9;0.01;0.05)	M	(0, 50,2.5,2.5)
$V_{\min}^{Y}$	(–3;0;–0.1;–0.05)	N	(NaN,0,–5.5,–2.5)
$v_{\max}^{u}$	0.01	c _v	0.05
$v_{\min}^{u}$	–0.1	th_max	2.2
		th_min	0.2

Where $V_{\max}^{Y} = [v_{\max}^{Δ d}, v_{\max}^{v_{f}}, v_{\max}^{a_{f}}, v_{\max}^{j}]$ , $V_{\min}^{Y} = [v_{\min}^{Δ d}, v_{\min}^{v_{f}}, v_{\min}^{a_{f}}, v_{\min}^{j}]$ , M=[0, v_fmin, a_fmin, j_min], N=[NaN,v_fmax, a_fmax, j_max].

4.1 The relationship between c_a and a_p

This article assumes that when the ACC vehicle and the preceding vehicle are following normally, the preceding vehicle continues to decelerate at a certain deceleration until the preceding vehicle stops. By adjusting the value of the weighting coefficient c_a to obtain the value of c_a that meets the following conditions, under different deceleration conditions, Scatter plots of the weighting coefficients c_a corresponding to different decelerations are obtained (c_a selection principle: the relative distance is not greater than the initial vehicle distance and the minimum relative distance is greater than zero).

Figure 1(a). shows the scatter diagram of all the c_a values that meet the selection conditions under each deceleration condition. In order to better get the relationship between c_a and a_p, the scatter diagram as shown in Fig. 1(b). is obtained by selecting the intermediate values that meet the conditions of each deceleration segment, and the relationship between c_a and a_p is found by 1stOpt software.

Fig. 1

The relationship between c_a and a_p.

$c_{a} = f (a_{p}) = \frac{1}{p_{1} + \frac{p_{2}}{a_{p}} + \frac{p_{3}}{a_{p}^{2}}}$ (11)

Where p₁, p₂ and p₃ are constant coefficients.

By adjusting the value of c_a under different deceleration conditions, it can be known that its size changes with the change in acceleration. From the above simulation, the time headway t_h is obtained as: $t_{h} = t_{0} - c_{v} v_{ref} - f (a_{p}) k_{t} a_{p}$ (12)

4.2 Simulation verification

This article focuses on the deceleration conditions of the front vehicle, which are divided into normal acceleration and deceleration conditions of the front vehicle (2m/s²,–2m/s²), high deceleration following conditions [–2m/s²,–4m/s²), emergency deceleration stop conditions [–4m/s², –6m/s²). The simulation parameters in this article are based on Table 1. The simulation parameters of other strategies are adjustable. The improved variable time headway(IVTH) strategy will be improved, which is proposed by this paper to change with the deceleration duration and deceleration of the preceding vehicle, and the variable time headway by Luo strategy (LVTH) [14] and the variable time headway by Yanakiev [12] strategy (YVTH) for simulation comparison.

4.2.1 Normal acceleration and deceleration of the front vehicle

Assuming that the initial speed of ACC vehicle and target vehicle is the same, both are 30m/s, and the relative distance is 50m, the front vehicle accelerates at an acceleration of 1m/s² in the first 4s, and decelerates at a deceleration of –1m/s² for 6s in the 10th s, the results are as shown in the figure.

Under normal acceleration and deceleration conditions, before 10s, the front vehicle accelerates and the host vehicle follows the front vehicle. IVTH and LVTH follow the same situation. While the current vehicle decelerates and the own vehicle decelerates to follow the preceding vehicle phase. As shown in Fig. 2(a), during the deceleration phase of the preceding vehicle, the minimum value of the relative distance between the two vehicles of IVTH is greater than LVTH and YVTH, which improves a certain driving safety and reduces the risk of rear-end collision when the front vehicle decelerates. As shown in Fig. 2(b), the speed change during the deceleration phase is smoother and it follows the speed of the preceding vehicle faster than other strategies. As shown in Fig. 2(c), the amplitude of the acceleration change is smaller than the other two. As shown in Fig. 2(d), the acceleration change rate changes positively at 16s. Since the front vehicle keeps a uniform speed after 16s. IVTH, LVTH and YVTH are the same strategies. They are only related to the relative speed, and the relative speed of IVTH is the smallest, so its deceleration gradually becomes smaller, that is, the acceleration change rate changes positively in advance.

Fig. 2

Comparison diagram of normal acceleration and deceleration conditions of front vehicle.

4.2.2 Rapid deceleration following working conditions

Under this working condition, it is assumed that the front vehicle continuously decelerates to stop at a certain time, assuming that the initial speed of ACC vehicle is the same as that of the target vehicle, both of which are 30m/s, and the relative distance is 50m, and the front vehicle runs at a deceleration of –3m/s² in the first 5 seconds, the results are as shown in the figure.

Following the rapid deceleration following conditions of the preceding vehicle, it can be seen from Fig. 3(a) that the minimum value of the relative distance between the two vehicles of the IVTH is greater than the other two, reducing the risk of rear-end collision when the preceding vehicle decelerates at a large deceleration. As can be seen from Fig. 3(b), the speed of the host vehicle changes smoothly, and it more quickly follows the speed of the preceding vehicle. As shown in Fig. 3(c), the maximum value of the deceleration of the own vehicle is at the 2.5s of the deceleration of the preceding vehicle, while the other two reach the maximum deceleration at the 6s, which improves the response time of the deceleration. It can be seen from Fig. 3(d), due to the rapid response of IVTH, the amplitude of the acceleration change rate is higher than that of LVTH within the first 5s. At 5s, the speed of the IVTH is closer to the speed of the preceding vehicle, so the deceleration is gradually reduced, the acceleration change rate is positive and the amplitude is small, and the other two speeds are much greater than the speed of the preceding vehicle, so the time is short. Within this time, the deceleration gradually increases, the acceleration change rate changes abruptly and the amplitude is large.

Fig. 3

Rapid deceleration following working condition comparison chart.

4.2.3 Emergency deceleration and stopping conditions of the preceding vehicle

Assuming that the initial speed of ACC vehicle and target vehicle is the same, both are 30 m/s, and the relative distance is 50m, the vehicle decelerates to stop at a deceleration of –5m/s² before the fifth second.

This case mainly verifies the performance of the spacing strategy in emergency situations. When the deceleration of the preceding vehicle reaches –5m/s², as shown in Fig. 4(a), near 5s, the LVTH and YVTH strategies have rear-ended with the preceding vehicle. It can be seen from Fig. 4 that under emergency conditions, IVTH can ensure stable following of the preceding vehicle. Compared with the other two spacing strategies, the adaptability of the spacing strategy is improved. Under the sudden deceleration condition of the preceding vehicle, a certain following distance can be guaranteed to avoid rear-end collision with the preceding vehicle.

Fig. 4

Comparison of emergency decelerating and stopping conditions of front vehicles.

4.3 Joint simulation verification

In order to make the algorithm closer to the actual situation, MATLAB/Simulink and CarSim for joint simulation was shown in Fig. 5. Build vehicle models and environmental information at CarSim. Build the lower controller model, braking pressure controller model and throttle opening controller model in Simulink. The lower controller adopts feedback PID control (Target speed setting cycle conditions). As shown in Fig. 7, the actual relative distance always remains in the range greater than 0 and the minimum value is greater than 2m throughout the cycle. It shows the safety of the algorithm in the co-simulation process and can maintain the desired safe distance from the vehicle in front.

Fig. 5

ACC system model.

Fig. 6

Cycle conditions.

Fig. 7

Distance comparison.

As shown in Fig. 8, the vehicle speed can effectively track the speed of the vehicle ahead in the cycle. And the maximum value of the relative speed of the two vehicles does not exceed 10km/h, which ensures the following performance of the vehicle under cycling conditions.

Fig. 8

Speed comparison.

5 Conclusion

In order to improve the adaptability of the spacing strategy, especially when the front vehicle is decelerating, an improper strategy may lead to a rear-end collision. Under the variable time headway strategy of relative speed and acceleration of the front vehicle. In the case of acceleration and uniform speed of the preceding vehicle, the spacing strategy adopts a variable time headway strategy with upper and lower limits. In the case of deceleration of the preceding vehicle, a variable time headway strategy is proposed that varies with the deceleration duration and deceleration of the preceding vehicle, with a lower limit and no upper limit. Numerical simulations show that the improved variable time headway strategy proposed in this paper can continue to maintain a good following effect when the front vehicle accelerates. And in the case of deceleration of the preceding vehicle, the spacing strategy proposed in this paper has more stable following speed and acceleration, which further improves driving safety and road utilization. Finally, the effectiveness of the algorithm is verified by the joint simulation of MATLAB/Simulink and CarSim.

Footnotes

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 61701397 and Grant 51705419, and in part by the China Postdoctoral Science Foundation under Grant 2019M653702.

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Adaptive cruise control system based on improved variable time headway spacing strategy

Abstract

Keywords

1 Introduction

2 Spacing strategy design

Table 1 Simulation parameters parameter value parameter value P 10 N 4 Q diag(1,1,1,1) TS 0.2 R 1 τ 0.4 d0 5 t0 1.5 V max Y (3;0.9;0.01;0.05) M (0, 50,2.5,2.5) V min Y (–3;0;–0.1;–0.05) N (NaN,0,–5.5,–2.5) v max u 0.01 c v 0.05 v min u –0.1 thmax 2.2 thmin 0.2

4.2.1 Normal acceleration and deceleration of the front vehicle

Footnotes

Acknowledgments

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