Adaptive Cruise Control System Using Model Predictive Control

The Adaptive Cruise Control (ACC) system is a control system that modifies the speed of the ego car in response to conditions on the road. As in regular cruise control, the driver sets a desired speed for the car; in addition, the ACC system can slow the ego car down if there is another car moving slower in the lane in front of it.

A vehicle (ego car) equipped with ACC has a sensor, such as radar, that measures the relative distance to the preceding car in the same lane (lead car), D_rel. The sensor also measures the relative velocity of the lead car, V_rel. The ACC system operates in the following two modes:

Speed control: The ego car travels at a driver-set speed as shown in Figure 1.
Distance control: The ego car maintains a safe distance from the lead car as shown in Figure 2.

The ACC system decides which mode to use based on real-time radar measurements. For example, if the lead car is too close, the ACC system switches from speed control to distance control. Similarly, if the lead car is further away, the ACC system switches from distance control to speed control. In other words, the ACC system makes the ego car travel at a driver-set speed if it maintains a safe distance.

Figure 1: Speed Control

Figure 2: Distance Control

The following rules are used to determine the ACC system operating mode:

If $D_{rel} ≥ D_{safe}$, then speed control mode is active. The control goal is to track the driver-set velocity, $V_{set}$.

If $D_{rel} < D_{safe}$, then distance control mode is active. The control goal is to maintain the safe distance, $D_{safe}$.

Simulink Model for Lead Car and Ego Car

The dynamics for lead car and ego car are modeled in Simulink as shown below:

Figure 3: Simulink Model for the Lead Car and Ego Car

To approximate a realistic driving environment, the acceleration of the lead car varies according to a sine wave during the simulation. The Adaptive Cruise Control System block outputs an acceleration control signal for the ego car as shown in Figure 3.

Define the sample time, Ts, and simulation duration, T, in seconds. Ts = 0.1; T = 80;

For both the ego vehicle and the lead vehicle, the dynamics between acceleration and velocity are modeled as:

$G(s) = \frac{1}{s(0.5s+1)}$

which approximates the dynamics of the throttle body and vehicle inertia.

The Simulink model for the ego and lead cars is shown in Figure 4.

Figure 4: The Simulink model for the ego and lead cars

Specify the linear model for ego car.

G_ego = tf(1,[0.5,1,0]);

Specify the initial position and velocity for the two vehicles.

x0_lead = 50;   % initial position for lead car (m)
v0_lead = 25;   % initial velocity for lead car (m/s)
x0_ego = 10;   % initial position for ego car (m)
v0_ego = 20;   % initial velocity for ego car (m/s)

Configuration of Adaptive Cruise Control System Block

The ACC system is modeled using the Adaptive Cruise Control System Block in Simulink. The inputs to the ACC system block are:

Driver-set velocity V_set Time gap T_gap Velocity of the ego car V_ego Relative distance to the lead car D_rel (from radar) Relative velocity to the lead car V_rel (from radar)

The output for the ACC system is the acceleration of the ego car. The safe distance between the lead car and the ego car is a function of the ego car velocity, V_ego:

$D_{safe} = D_{default} + T_{gap} \times V_{ego}$

where D_default is the standstill default distance and T_gap is the time gap between the vehicles.

Specify values for D_default , in meters, and T_gap, in seconds.

t_gap = 1.4;
D_default = 10;

Specify the driver-set velocity in m/s.

v_set = 30;

Considering the physical limitations of the vehicle dynamics, the acceleration is constrained to the range [-3,2] ((m)⁄(s^2)).

amin_ego = -3;
amax_ego = 2;

For this example, the default parameters of the Adaptive Cruise Control System block match the simulation parameters. If your simulation parameters differ from the default values, then update the block parameters accordingly.

Simulation and Results

Figure 5: Acceleration, Speed, Distance between two cars

Conclusions

1. In the first 3 seconds, to reach the driver-set velocity, the ego car accelerates at full throttle.
2. From 3 to 13 seconds, the lead car accelerates slowly. As a result, to maintain a safe distance to the lead car, the ego car accelerates with a slower rate.
3. From 13 to 25 seconds, the ego car maintains the driver-set velocity, as shown in the Velocity plot. However, as the lead car reduces speed, the distance error starts approaching 0 after 20 seconds.
4. From 25 to 45 seconds, the lead car slows down and then accelerates again. The ego car maintains a safe distance from the lead car by adjusting its speed, as shown in the Distance plots.
5. From 45 to 56 seconds, the distance error is above 0. Therefore, the ego car achieves the driver-set velocity again.
6. From 56 to 76 seconds, the deceleration/acceleration sequence from the 25 to 45 second interval is repeated.
7. Throughout the simulation, the controller ensures that the actual distance between the two vehicles is greater than the set safe distance. When the actual distance is sufficiently large, then the controller ensures that the ego vehicle follows the driver-set velocity.

References

[1] https://www.mathworks.com/help/driving/examples/adaptive-cruise-control-with-sensor-fusion.html

[2] https://www.mathworks.com/help/mpc/ug/adaptive-cruise-control-using-model-predictive-controller.html

[3] Mehrdad Moradi, Bentley James Oakes, Mustafa Saraoğlu, Joachim Denil (2020) “Exploring Fault Parameter Space Using Reinforcement Learning-based Fault Injection”, 2020 50th Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W)

[4] https://scholarworks.calstate.edu/concern/projects/cf95jh631