north carolina agricultural and technical state university modeling driver behavior at intersections...

North Carolina Agricultural and Technical State University

Modeling Driver Behavior at Intersections with Takagi-Sugeno Fuzzy Models

By: Saina Ramyar Advisors: Dr. Homaifar

Dr. Karimoddini


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1• Introduction

2• Background

3• Methodology

4• Simulation

5• Results

6• Discussion/Future Work


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Traffic collisions are the number one cause for

teenage deaths [1].• The risk of motor vehicle crashes is higher among 16-

19 year-olds than among any other age group. • Young people (19-24) account for 30% ($19 billion) of

the total costs of motor vehicle injuries

Reasons:• Teens are more likely to underestimate or not recognize

hazardous situations• Teens are more likely than older drivers to speed and

allow shorter headways• Teens are more likely to drive under the influence of

alcohol.

Introduction

Solution: Advanced Driving

Assistance Systems:

• Warn the driver• Take over control

When necessary[1]Centers for Disease Control and Prevention. Web-based Injury Statistics Query and Reporting System (WISQARS). National Center for Injury Prevention and Control, Centers for Disease Control and Prevention. 2012. (online)


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Goal:

Designing an Advanced Driving Assistance System (ADAS)

Objectives• Predict other drivers actions to avoid crashes• Detect and warn drivers of their dangerous driving• Detect driver distraction and take over more control

Challenge:• In urban environment there is more interaction with humans and

other vehicles.• People’s driving patterns are different and complex

Introduction

Future Work


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Modeling Driver Behavior

5

Driver’s actions at an intersection:

Right TurnLeft TurnStraightStop

The Scenario of interest in this study:

High Number of

other vehicles

High Number of

Pedestrians

Intersection


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Background

Approaches for modeling and estimation of Driver Behavior

Dynamic Bayesian Network

Clustering or Classification Techniques [4,5]

Hidden Markov Model (HMM) [7,8]

Rule Based Estimation [6]

[2] Gerdes, A., "Driving manoeuvre recognition," in Proceedings of the 13th World Congress and Exhibition on Intelligent Transport Systems and Services, 2006. [3] Robert Schubert, Karsten Schulze, and Gerd Wanielik, "Situation assessment for automatic lane-change maneuvers," IEEE Transactions on Intelligent Transportation Systems, vol. 11,

no. 3, pp. 607-616, Sept. 2011. [4] Christoph Hermes, Christian Wahlert, Konrad Schenkt and Franz Kummert, "Long-term vehicle motion prediction," in IEEE Intelligent Vehicles Symposium, 2009. [5] F. Large, D. A. V. Govea, T. Fraichard, and C. Laugier, "Avoiding cars and pedestrians using velocity obstacles and motion prediction," in IEEE Intelligent Vehicle Symposium, 2004. [6] Vijay Gadepally, arda Kurt, Ahok Krishnamurthy, and Umit Ozguner, "Driver/Vehicle Estimation and Detection," in 14th International IEEE Conferance on Intelligent Tranportation

Systems (ITS), 2011. [7] A. Kurt, J. Yester, Y. Mochizuki, U. Ozguner, "Hybrid-state driver/vehicle modeling estimation and prediction," in 13th International IEEE Conferance on Intelligent Transportation

Systems (ITSC), 2010. [8] V. Gadepally, A. Krishnamurthy, and Ü. Özgüner, "A Framework for Estimating Driver Decisions near Intersections," Trans. Intell. Transp. Syst., vol. 15, no. 2, 2014.

Modeling driver behavior [2]Making lane change decisions [3]


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The ADAS requires data from the vehicle to estimate its motions.

Obtaining information about other vehicles

Proposed Model

a) Define each maneuver as a nonlinear function

b) Estimate the nonlinear functions with local Takagi-Sugeno fuzzy models

GPSV2V (Vehicle to Vehicle Communication)

V2I (Vehicle to Infrastructure Communication)


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a) Defining Driver’s Actions Nonlinear Models

8

Driver’s actions at an intersection in the proposed technique:

Stop is not important so it is eliminated for simplicity.

Right TurnLeft TurnStraight

Required Observations

Velocity

AccelerationYaw-rate


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a) Defining Driver’s Actions Nonlinear Models

Proposed model:

velocity (V), acceleration (A) and yaw-rate (ω) are nonlinear functions of the

observations at one or two time steps before.

V and A : functions of velocity at two time steps before

Yaw-rate: function of yaw rate at two time steps before


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b) Approximating The Nonlinear maneuver models

Identifying the nonlinear models

It is very difficult to find an explicit global model for such systems using

basic physical principles.

Takagi-Sugeno fuzzy models:

universal approximator can approximate any nonlinear function

It is used for modeling the system [9, 10]

[9] Sugeno, T. Takagi and M., "Fuzzy identification of systems and its application to modeling and control," IEEE Trans. Syst., Man, Cybern.,, Vols. SMC-15, pp. 116 -132, 1985.

[10] Homaifar, A., Bikdash, M., and Clifton, C, "Feedback Implementation of Optimal Control Laws," Special Issue on Formal Methods for Fuzzy Modeling and Control of the Journal of Fuzzy sets and Systems, pp. 39-57, 2001.


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TS fuzzy model:

consists of “if-then” rules

The consequent functions are the local models in the regions specified by the

antecedent membership functions [11, 12].

• membership functions in the antecedent • linear function in the consequent

Ri : If x is Ai(x) then y^ = aiTx + b [wi]


[11] Kang, M. Sugeno and G. T., "Fuzzy modeling and control of multilayer incinerator," Fuzzy Sets Syst., vol. 18, pp. 329 -346, 1986. [12] Clifton, C., Homaifar, A., and Bikdash, M., "Design of Generalized Sugeno Controllers By Approximating Hybrid Fuzzy-PID Controllers,”," in Proceedings of the Fifth the

IEEE Conference on Fuzzy Systems,, New Orleans, Louisiana, Sept. 2011.


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Construction of a TS model:

1) Determining membership functions in the antecedents

2) The parameters of the consequent functions are estimated

Techniques for determining MFs:

Determining the consequent parameters: Least Square error

• Gradient-descent neuro-fuzzy optimization• Genetic Algorithm [13]• Fuzzy Clustering [14]


[13] Homaifar, A., and McCormick, V. E., "Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms," IEEE Transactions on Fuzzy Systems, vol. 3, pp. 129-139, May 1995.

[14] Janos Abonyi, Robert Babu, "Modified Gath-Geva Fuzzy Clustering for Identification of Takagi-Sugeno Fuzzy Models," IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, vol. 32, no. 5, pp. 612-621, October 2002.


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A modified Gath-Geva fuzzy clustering is used for identification of the TS

models [14]

1) The modified GG algorithm uses a Gaussian mixture model for the

membership functions and calculates its parameters from the data.

2) Then Least Square estimation is applied for obtaining the coefficients of the

consequent.

Identification Algorithm:

Gath-Geva fuzzy clustering + Expectation Maximization of the Guassian Mixture

Models

c) Modified Gath-Geva Fuzzy Clustering for Identification of Takagi-

Sugeno Fuzzy Models

[14] Janos Abonyi, Robert Babu, "Modified Gath-Geva Fuzzy Clustering for Identification of Takagi-Sugeno Fuzzy Models," IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, vol. 32, no. 5, pp. 612-621, October 2002.


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Compute the distance measure Di,k2

Start

Update the partition matrix (MF)

End

Yes

No

Calculate the parameters of the clusters• Centers of membership functions

• Standard deviation of Gaussian membership functions• Parameters of the local models• Priori probabilities of clusters

• Weights of the rules


Sugeno Fuzzy Models


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Step 1: Calculate cluster parameters

Modeling Driver Behavior (elaborate more)c) Modified Gath-Geva Fuzzy Clustering for Identification of Takagi-

Sugeno Fuzzy Models

Centers of MFs

Standard deviation of MFs:

Parameters of the Sugeno model


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Sugeno Fuzzy Models

Step 2: compute the distance measures

Distance between cluster centers and input data x

Performance of the local linear models


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Sugeno Fuzzy Models

Step 3: Update the partition matrix


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Advantages:

1) It does not use transformed input variables; therefore, the results are more

easily interpretable.

2) Number of rules is equal to the given number of clusters



Sugeno Fuzzy Models

Computation complexity


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Data Analysis and Simulations

a) Experimental Setup

The driver behavior data used in this study was collected by the Ohio State

University (OSU) (CITR) [8].

Vehicle: a sensor equipped 2012 Honda Accord

Driving location: Columbus, OH

Driving paths: routine daily routes

Sensors: 1. NovAtel GPS unit: provides GPS latitude, GPS longitude, timestamp of reading and others;

2. Controller Area Network (CAN): bus provides timestamp of reading, yaw rate, lateral acceleration,

speed, and others.

3. Three HD cameras: provide views of the front, left side, and right side of the vehicle[8] V. Gadepally, A. Krishnamurthy, and Ü. Özgüner, "A Framework for Estimating Driver Decisions near Intersections," Trans. Intell. Transp.

Syst., vol. 15, no. 2, 2014.


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a) Experimental Setup

Data Extraction:

manually marking the collected videos and the corresponding data (velocity,

acceleration, and yaw-rate) time series are extracted.

The obtained time-series observations are then used to train the membership

functions and TS local models.


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b) Simulations

The training data for each model input

consists of three time series from three

incidents. These time series are put

together back to back with two zeros

between them for separation.

The training data is the used to train

models for acceleration, velocity and yaw-

rate of each maneuver.

Example of the Right Turn Velocity

model:


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Once all the nine TS models are identified for the three maneuvers, the model

is ready for testing.

The maneuver that its local models result in the smallest error for all three

observation models is the estimated model.

To compensate for the experimental error, a voting strategy is employed, such

that if two models of a specific maneuver produce the smallest error, that

maneuver is considered as the estimated driver action.


c) Simulations


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One example of each maneuver is used as testing data

In this table, the combination of MSEs from all the models of maneuvers is

presented as a matrix for each example.

The rows represent the maneuvers: straight, right turn and left turn,

respectively.

The columns represent the error: velocity, acceleration and the yaw rate for

each maneuver respectively.

Simulation Results

a) Simulations


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Simulation Results

a) MSE MATRIX

The rows represent the maneuvers:

straight, right turn and left turn,

respectively.

The columns represent the error:

velocity, acceleration and the yaw

rate for each maneuver

respectively.


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Acceleration

models simulation

with Right Turn

data

Right Turn model

has the best

performance.


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Velocity models

Simulation with

Straight Data:

Straight model

has the best

performance.


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Summary

Introduction of Takagi-Sugeno model

Gath-Gava fuzzy clustering for TS model identification

Modified Gath-Gava fuzzy clustering for TS model identification

Examples of applications of the proposed method

Modeling of Driver Behavior with GG fuzzy clustering


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Perform a more comprehensive survey on modeling

techniques

Expand the proposed model to predict the driver behavior

more steps into the future

Train the model recursively so we can use it for online

applications.

Future Work


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Questions

How to train the models using multiple

experiments?

What is the necessary threshold time window for

predicting drivers action in future?

How to obtain SHRP2 data???


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