Automatic control of the traffic flow

Aurel Vlaicu University of Arad, Romania, Aurel Vlaicu University of Arad, Romania, e-mail: balas@e-mail: balas@drbalasdrbalas.ro.ro

Valentina E.Valentina E. Balas Balas

CONTENT1. INTRODUCTION. THE ADAPTIVE CRUISE CONTROL

2. TRAFFIC INDICATORS

3. THE CONSTANT TIME TO COLLISION CRITERION

4. THE PD FUZZY-INTERPOLATIVE CRUISE CONTROLLER

5. CONSTANT TIME TO COLLISION PLATOONS

6. CONCLUDING REMARKS

1. Introduction. The Adaptive Cruise Control

Logistics is the management of the flow of goods, information and other resources, including energy and people, between the point of origin and the point of consumption, in order to meet the requirements of consumers. Logistics involves the integration of information, transportation, material-handling, and packaging.

This lecture is dealing with a new method for the management of the traffic flow on highways.

The Intelligent Transportation Systems allow cars to “think.” A set of facilities with different degrees of implication in the driving action is proposed by the Advance Driver Assistance Systems (ADAS), etc.

ADAS are systems to help the driver in its driving process. When designed with a safe Human-Machine Interface it should increase car safety and road safety.

• Adaptive cruise control (ACC) or the Intelligent Cruise Control (ICC) uses either a radar or laser setup to allow the vehicle to slow when approaching another vehicle and accelerate again to the preset speed when traffic allows.

• Collision warning system, a system of sensors that is warning the driver of any dangers that may lie ahead on the road. Some of the dangers that these sensors can pick up on include how close the car is to other cars surrounding it, how much its speed needs to be reduced while going around a curve, and how close the car is to going off the road.

Following ACC cars on highway

• Intelligent speed adaptation or intelligent speed ad-vice (ISA) are systems that constantly monitor the local speed limit and the vehicle speed and imple-ments an advice or an action when the vehicle is found to be exceeding the speed limit.

• In-vehicle navigation systems with GPS and TMC (Traffic Message Channel) for providing up-to-date traffic information.

• Lane/road departure detection/warning system • Lane change assistance • Night vision • Adaptive light control

• Pedestrian protection system • Automatic parking • Traffic sign recognition • Blind spot detection • Driver drowsiness detection • Car to car communication • Hill descent control • etc.

ACC (Adaptive Cruise Control) signal processing architecture

Despite the safety benefits: enhanced driving performance and minimization of crash risks, reduced driver stress and fatigue, reduced conflicts and vari-ance in behavior, etc. the effective put in practice of these developments will have to wait. The causes are economic, but also technical.

Automate driving is likely to produce at its turn safety risks by the driver distraction and reduced situation awareness, causing in time the reducing of the driving skill. But above all, any automate inter-vention into the car’s operation can cause instinctive and inopportune reactions of the driver.

ACC (Adaptice Cruise Control) human-machine interface

2. Traffic Indicators

In the car following case, several indicators were introduced in order to measure the characteristics of the traffic flow:

•the time-to-collision (TTC) •the time-to-accident (TTA)•the post-encroachment-time (PET)•the deceleration-to-safety-time (DTS)•the number of shock waves, etc.

The Time-to-Collision (TTC) is the time that it takes before Car2 collide with Car1, assuming unchanged speeds of both vehicles during this approach:

(1) Negative TTC imply that Car1 drives faster, i.e. there is no danger. Positive TTC express a certain unsafe approach. TTC is linked to the longitudinal driving task and supports a set of safety techniques as the Intelligent Speed Adapter (ISA) limiting the speed to the prevailing speed limit of the current road section.

The Time to Collision indicatorThe Time to Collision indicator

12 vv

dTTC

The Inverse Time to CollisionThe Inverse Time to Collision

Due to the annulations of its denominator when vDue to the annulations of its denominator when v22 = v = v11, ,

TTC is presenting frequent commutations between ±TTC is presenting frequent commutations between ±. That is . That is why TTC is often replaced by the d(vwhy TTC is often replaced by the d(v11 - v - v22) trajectory.) trajectory.

However d(vHowever d(v11 - v - v22) is not very suggesting when evalu-) is not very suggesting when evalu-

ating the collision risk. That is why in a previous paper we ating the collision risk. That is why in a previous paper we introduced the introduced the Inverse Time to CollisionInverse Time to Collision TTC-1, which is pro-portional to the collision risk :

(2)

d

vvTTC 121-

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V1

& V

2

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t [s]

d [m

]V1

V2

A simulation scenario

-8 -6 -4 -2 0 2 40

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V2-V1 [km/h]

d [m

]

A d(v2-v1) diagram

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-10

-5

0

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time [s]

TTC

[s] &

30/

TTC

[1/s

]

TTC

1/TTC

Fig . 10. The evolutions of TTC and TTC-1

The evolutions of TTC and TTC-1

Fig. 2.A TTC-1(v2 – v1) trajectory and a corresponding fuzzy partition assisting the driver

Among other specifications referring to speed, acceleration and deceleration limitations, AICC (Adaptive Intelligent Cruise Control) is introducing a particular di(v2) law: di(v2) = z0 + z1 · v2 + z2 · v2

2 = 3 + z1 · v2 + 0.01 · v22 (3)

Several settings are recommended, for example z1 = 0.8s or z1 = 0.6s. Two objections can be drawn against (3):- no adaptation to the traffic intensity is provided: if (3) is tuned for the highest possible traffic, when the traffic is de-creasing, the following cars will continue to maintain the same short distance-gaps between them; - z1 and z2 are artificially introduced parameters, a polynomial design has no significance for humans.

3. The Constant Time to Collision criterion

We will replace (3) by an optimal di(v2) issued by a particular criterion: the Constant Time To Collision (CTTC).

Since the on-line control of TTC is impossible because of the evolution of v2 – v1, CTTC must be implemented off-line, with the help of the di(v2) mappings.

The initial assumption: a distance gap planner build with TTC will produce CTTC.

The method can be applied by computer simulations. Accurate knowledge about the parameters of each specific car (traction, brakes, weight, aerodynamic coefficient, etc.) can be such way taken into account, which is not possible to the simplified and leveling analytic representation (3).

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V2 [km/h]

d [m

]

TTC=10s

TTC=4s

TTC=7s

The di(v2) mappings for three different TTC

The SIMULINK-MATLAB model of the tandem Car1-Car2

d

v2-v1

TTC control loop

0

Xo2

50

Xo1

200

Vo2

200

Vo1

TTC

PID PID Controller

1200

M2

1200

M1

7

ImposedTTC

Driver

F2 [kN]

M2 [kg]

Vo2 [km/h]

Xo2 [m]

x2 [m]

v2 [km/h]

a2 [m/s2]

Car 2

Ftr1 [kN]

M1 [kg]

Vo1 [km/h]

Xo1 [m]

x1 [m]

v1 [km/h]

a1 [m/s2]

Car 1

1/u

1/d

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d [m

]

CTTC

Polynomial di(v2)

A comparison between imposed distances generated by the polynomial model (1) and by CTTC

Applying CTTC brings two obvious advantages:•- a constant collision risk for each vehicle;•- the possibility to control the traffic flow on

extended road sections, if each vehicle will apply the same TTC that is currently recommended by the Traffic Management Center: a long TTC means low traffic flow and higher safety while a short TTC means high traffic flow and higher risk.

4. The planned fuzzy-interpolative distance controller4. The planned fuzzy-interpolative distance controller

The planned distance-gap controller consists of:The planned distance-gap controller consists of:

a)a) A PD distance controllerA PD distance controller The input variables are the distance-gap error The input variables are the distance-gap error εε = d = dii – d, – d, between the imposed and the realized distance between the between the imposed and the realized distance between the cars, and its derivate cars, and its derivate εε’’.. The output variable is the force F, The output variable is the force F, positive for traction and negative for brakingpositive for traction and negative for braking

b) b) A dA dii(v(v22) mapping) mapping that is adapting the imposed distance d that is adapting the imposed distance dii to the current velocity of the following car vto the current velocity of the following car v22..

We are using a specific tool: the Fuzzy-Interpolative Con-troller (FIC). A FIC is a fuzzy controller that can be equaled with an interpolative network with linear interpolation, each fuzzy control rule having a corresponding interpolation node. This way the linguistic fuzzy inferences can be implemented by look-up-tables.

d very small small medium great

positive great

1 zero

2 positive small

3 positive great

4 positive great

positive small

5 negative small

6 zero

7 positive small

8 positive great

zero 9 negative small

10 zero

11 zero

12 positive small

negative small

13 negative great

14 negative small

15 zero

16 positive small

cd

negative great

17 negative great

18 negative great

19 negative small

20 zero

Table 1. The control rules of the distance controller

The PD fuzzy-interpolative cruise controllerThe PD fuzzy-interpolative cruise controller

1PD

PD fuzzy-interpolative

0.75

Gain23

Gain1

22

Gaindu/dt

Derivative

1

error

Row (distance error): [-10 -5 0 5 10] Column (error derivate): [-10 0 10] Output: [-1 -1 -1; -1 -0.3 0; -0.2 0 0.2; 0 0.3 1; 1 1 1]

Such simple controllers can stand for the best possible control solution, if provided with relevant knowledge about the specific controlled process and about the way we want the system to perform. This knowledge becomes compatible with control-lers if it can be modeled. Models can be used either directly (as internal models included into the con-trol algorithm) or indirectly, by assisting the design of the Planning Systems. In this case the essential knowledge about the car following system is represented by the di(v2) mapping.

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t [s ]

v [k

m/h

] V 1

linear

C TTC

Fig. 6. The performance of a CTTC compared to a linear di(v2)

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time [s]

d [m

]

TTC=4s

TTC=10s

time [s]

Fig. 9. Distance-gaps for TTC=4 and TTC=10s

The Traffic Management by CTTC !The Traffic Management by CTTC !CTTC is opening the perspective of managing CTTC is opening the perspective of managing

the traffic flow by means of appropriate TTC values, the traffic flow by means of appropriate TTC values, imposed by the highway’s administrations to all the imposed by the highway’s administrations to all the participants of the traffic, according to the driving participants of the traffic, according to the driving con-ditions. con-ditions.

This procedure is creating an even distribution of This procedure is creating an even distribution of the collision risk of all the automobiles that are form-the collision risk of all the automobiles that are form-ing a CTTC platoon. Thanks to the fact that ding a CTTC platoon. Thanks to the fact that d ii(v(v22,TTC) ,TTC) planners can be designed for any automobile type the planners can be designed for any automobile type the big differences existing among the technical data of big differences existing among the technical data of the highway cars will not affect the flow. the highway cars will not affect the flow.

5. Constant Time to Collision Platoons5. Constant Time to Collision Platoons

The CTTC platoons are highway cars formations composed by automobiles provided with CCTC cruise controllers.

One can imagine such large platoons leaded by “safety cars.”

Each car has its own technical parameters: weights between 1000 and 1400kg (M), engine powers between 100% and 180% of the generic Car1 power (Gain) and its own CTTC planner (Di(V2,TTC) look-up-tables). The initial speed Vo and position Xo of each car can be as well adjusted.

Simulation Results Simulation Results

The scenario

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1 s

peed

[km

/h]

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t [s]

Sum

of d

ista

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gaps

[m]

Figure 14. The sum of the distance gaps (linear PD)

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t [s]

dist

ance

gap

s [m

]

d12

d23

d34

d45

Fig. 15. The formation of the platoon (linear PD)

The platoon’s length dependence with the speed, for TTC=7s

The positions of the cars during the aggregation of the platoon

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t [s]

Sum

of t

he d

ista

nce

gaps

[m]

Fig. 18. The sum of the distance gaps (PD fuzzy-interpolative)

0 2 4 6 8 10 12 14 16 18 203

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d12

d23

d34

d45

Fig. 19. The formation of the platoon (PD fuzzy-interpolative)

The The Constant Time to Collision Criterion Constant Time to Collision Criterion CTTCCTTC is an optimization is an optimization criterion that in the case of two following cars is imposing a particular criterion that in the case of two following cars is imposing a particular distance gap, such way that the time to collision between cars is constant distance gap, such way that the time to collision between cars is constant for any speed of the following car. for any speed of the following car.

When each car is equipped with a CTTC cruise controller the traffic When each car is equipped with a CTTC cruise controller the traffic management center can impose the same TTC to all the cars. The management center can impose the same TTC to all the cars. The smaller the imposed TTC is, the smaller the distance gaps between cars smaller the imposed TTC is, the smaller the distance gaps between cars will be, and the higher the traffic flow and the collision risk (that is will be, and the higher the traffic flow and the collision risk (that is evenly distributed over all the high way section) will be. evenly distributed over all the high way section) will be.

The highway system becomes distributed, each car trying to reach The highway system becomes distributed, each car trying to reach and to maintain an optimized position. and to maintain an optimized position.

Besides the simplicity and the advantageous interpolative implemen-Besides the simplicity and the advantageous interpolative implemen-tation, all the TTC based tools have a common feature: they are embed-tation, all the TTC based tools have a common feature: they are embed-ding precise knowledge about the technical data of the automobiles ding precise knowledge about the technical data of the automobiles thanks to the functional computer model that stands behind their design. thanks to the functional computer model that stands behind their design.

ConclusionsConclusions

Thank you for your attention!Thank you for your attention!