8/16/18

1

Xiaopeng (Shaw) LiAssociate Professor, Susan A. Bracken Faculty Fellow

Department of Civil and Environmental Engineering,

University of South Florida

8/16/2018

CUTR Webinar Series

Operations and Planning for Connected Autonomous Vehicles: From Trajectory Control to Capacity Analysis

2

Freeway Stop-and-Go Traffic

8/16/18

2

3

Arterial Operations

Suboptimal timing – extra delay

Stop-and-go waves – excessive fuel consumptions

4

Adverse Impacts

Congestion Exacerbate delay (3.7 billion hours/year) and

congestion cost ($78 billion per year)

Tampa Bay Areahttp://www.tampabay.com/

8/16/18

3

5

Adverse Impacts

Increase fuel consumption & emission• 2.3 billion gallons of fuel /year

• 70% U.S. petroleum fuel consumption

• 30% U.S. greenhouse gas emission

Beijing, China New York City, U.S

6

Adverse Impacts

Safety hazards 2,200,000 injuries 33,000 fatalities

8/16/18

4

7

Connected and Automated Vehicles

Information sharing

Human drivers → robot drivers

8

CAV for operations

Enable trajectory-level vehicle control and coordination

Fundamentals of highway traffic operations Past – accommodating human drivers Future - designing robot drivers

8/16/18

5

9

CAV for Planning: Capacity Booster?

People expect connected automated vehicles can significantly increase (or even multiple) high way capacity

How to realize this potential?

Human-driven traffic CAV traffic

10

Steps to Improve CAV Capacity

Microscopic trajectory control Reduce headway Improve traffic smoothness

Macroscopic capacity analysis Understand the relationship between cav traffic

characteristics (e.g., CAV penetration ratio) and macroscopic measures (e.g., traffic throughput)

Validation Field experiments Data analysis

8/16/18

6

CAV-based Traffic Operations

12

CAV Trajectory Optimization

Signalized Intersections Coordinate signal timing with vehicle trajectory

control

Human-driven traffic CAV traffic

8/16/18

7

13

Infrastructure

Single lane highway segment 0, Fixed signal timing , , , …at location

14

Entry Boundary Condition

Indexed by 1, 2, …, Entry time , speed , known a priori

8/16/18

8

15

Physical Bounds

Trajectory

Speed ∈ 0, , acc. ∈¯,

( )np t

16

Exit Boundary Constraint

Exit during green time:

mod ,

8/16/18

9

17

Vehicle Following Safety

Two consecutive vehicles n-1 and n

Shadow trajectory s

Reaction time Safety spacing s

Safety constraint:s

1( ) ( )n np t p t

18

Travel Time MOE

1: ( ) / ,n nn

T p L t N

N

8/16/18

10

19

Fuel Consumption MOE

E.g., VT-micro, CMEM, MOVES

1 ( )

1

: ( ), ( ), ( ) /n

n

N p L

n n ntn

E e p t p t p t dt N

20

Safety MOE

Surrogate measure – Inverse Time-To-Collision (iTTC)

11 ( ) iTTC 1

1 1

( ) ( ): /

( ) ( )

n

n

N p Ln n

tn n n

p t p tS H h dt N

p t p t l

Time-To-Collision

8/16/18

11

21

Trajectory Optimization (TO)

min ≔

subjectto0;,∀ (entry)

0 ;

¯,∀ , (kinematics)

mod , , ∀ (exit)

, ∀ 1 (safety)

Infinite dimensionHigh nonlinearity

Differentialequations

Non-convexity

Vehicle interactions

TOO DIFFICULT TO SOLVE

22

Solution Parsimonious Algorithms

Shooting heuristic (SH) A small number of analytical sections

8/16/18

12

23

Benchmark vs. SH

Reference *Ma, J., Li, X., Zhou, F., Hu, J. and Park, B. 2017. “Parsimonious shooting heuristic for trajectory design of connected automated traffic part II: Computational issues and optimization” Transportation Research Part B, 95, 421-441.*Zhou, F., Li, X. and Ma, J. 2017. “Parsimonious shooting heuristic for trajectory design of connected automated traffic part I: Theoretical analysis with generalized time geography.” Transportation Research Part B, 95, 394-420.* Li, X., Ghiasi, A. and Xu, Z. “A piecewise trajectory optimization model for connected automated vehicles: Exact optimization algorithm and queue propagation analysis” Transportation Research Part B, under revision.

24

CAV Trajectory Optimization

Signalized Intersections Mixed Traffic (CAVs + Human-driven vehicles

(HVS))

Reference *Yao, H., Cui, J., Li, X., Wang, Y. and An, S., 2018, “A Trajectory Smoothing Method at Signalized Intersection based on Individualized Variable Speed Limits with Location Optimization”, Transportation Research Part D, 62, pp. 456-473

0 50 100 150 200 250 300 3500

100

200

300

400

500

600

700

800

900

1000

Time (s)

Dis

tanc

e (m

)

(a)

0 50 100 150 200 250 300 3500

100

200

300

400

500

600

700

800

900

1000

(b)Time (s)

Dis

tanc

e (m

)

IVSL1

IVSL2

0 50 100 150 200 250 300 3500

100

200

300

400

500

600

700

800

900

1000

Time (s)

Dis

tanc

e (m

)

·IVSL1

IVSL2

(f)

8/16/18

13

25

CAV Trajectory Optimization

Freeway Speed Harmonization

I. Predictionproblem

II. Shootingheuristicproblem

Reference: * Ghiasi, A., Li, X., Ma, J. and Qu, X. 2018. “A Mixed Traffic Speed Harmonization Model with Connected Automated Vehicles”, Transportation Research Part C. Under Revision

Exit time

26

Joint Trajectory and Signal Optimization

Problem setting

8/16/18

14

27

Joint Trajectory and Signal Optimization

Signalized intersection

2000, 1500 vph 20 m/s 500 m

4000 vph 40 6 m

7 m 2.7 s 0.6 s

28

Joint Trajectory and Signal Optimization

Work-zone

2000, 1500 vph 20 m/s 500 m

4000 vph 40 6 m

250 m 27 s 0.6 s

8/16/18

15

29

Deep Learning Based Trajectory Control

• Using deep neural networks to design adaptive CAV controllers

Implication to Capacity Analysis & Planning

8/16/18

16

31

Trajectory Control → Capacity Analysis

CAV control → Heterogeneous headways in mixed traffic

0.7 2.4 h (s)

Freq.

0.3 2.0 h (s)

0.5 2.6 h (s)

0.6 2.6 h (s)

Freq.

Freq.

Freq.

32

Capacity Analysis

CAV technology uncertainties Will CAV reduce headways?

Google car pulled over for being too slowhttp://www.bbc.com/news/technology-34808105

8/16/18

17

33

Capacity Analysis

Different technology scenarios

0.7 2.4 h (s)

Freq.

0.3 2.0 h (s)

0.5 2.6 h (s)

0.6 2.6 h (s)

Freq.

Freq.

Freq.

34

Capacity Analysis

CAV market penetration rate

34

Low CAV market penetration rate

High CAV market penetration rate

8/16/18

18

35

Capacity Analysis

CAV platooning intensity

35

Low CAV platooning intensity

High CAV platooning intensity

36

Analytical Capacity Formulation

Markov chain model

1 0

1,,

,,

8/16/18

19

37

Analytical Capacity Formulation

Markov chain model ∈ 0,1 : CAV market penetration rate ∈ 1,1 : CAV platooning intensity

≔

37

38

Analytical Capacity Formulation

Approximate capacity ≔

∑ ∑ ∑ ∈ , ∈

Theorem 1: ≤ for any finite N Theorem 2: When 1, → → ∞

38

8/16/18

20

39

Capacity analysis

Numerical analysis

39

Optimistic Headway Conservative Headway

40

Application – Lane Management

Determine the optimal number of CAV lanes

≔ 1/≔ ,

≔0, 1,

≔1

∑ ∈ , ∈

≔ min ,

Reference: * Ghiasi, A., Hussein, O., Qian, S.Z. and Li, X., 2017. “A mixed traffic capacity analysis and lane management model for connected automated vehicles: a Markov chain method”, Transportation Research Part B, 106, pp. 266-292.

8/16/18

21

Field Experiments

42

Field Experiments – Pure HVs

15 HVs following tests in Harbin, China (collaborating with Harbin Institute of Technology)

spee

d

Lead vehicle Following vehicles

8/16/18

22

43

Data Collection on Public Roads Video-Based Intelligent Road Traffic Universal Analysis Tool

(VIRTUAL) (Provisional Patent #. 62/701,978)

44

Data Collection on Public Roads Video-Based Intelligent Road Traffic Universal

Analysis Tool (VIRTUAL) (Provisional Patent #. 62/701,978)

Veh ID Frame ID x(ft) y(ft) Speed(ft/s)

Acceleration(ft/s2) Lane Number

18 4 533.02 153.43 59.14 -2.91 0

18 6 536.96 149.49 58.94 1.16 0

18 8 540.89 145.56 59.02 -3.6 0

18 10 544.83 141.62 58.78 -1.13 0

18 12 548.75 137.70 58.7 -0.1 0

18 14 552.66 133.79 58.7 -2.75 0

18 16 556.57 129.88 58.51 -0.85 0

18 18 560.47 125.98 58.46 -1.45 0

18 20 564.37 122.08 58.36 -1.9 0

18 22 568.26 118.19 58.23 -1.28 0

18 24 572.14 114.31 58.15 -2.96 0

18 26 576.02 110.43 57.95 2.46 0

18 28 579.88 106.57 58.11 9.57 0

18 30 583.76 102.69 58.75 9.6 0

8/16/18

23

45

Fields Experiments – Pure CAVs

Turner Fairbank Highway Research Center

Level-1 Automated Cadillac

46

Field Experiments

HV following CAV/HV at the 2.4 km test track at Chang’an University, China

Test different drivers, different CAV speed

8/16/18

24

47

Field Experiments

HV following CAV/HV at the 2.4 km test track at Chang’an University, China

Test different drivers, different CAV speed

48

Field Experiments – Mixed Traffic

Difference between HV →CAV and HV→HV

8/16/18

25

49

Acknowledgements Students Fang Zhou (Li’s student) Amir Ghiasi (Li’s student) Omar Hussain (Li’s student) Handong Yao (Harbin Institute of Technologies) Zhen Wang (Chang’an University)

Collaborators Jiaqi Ma (University of Cincinnati) Zhigang Xu (Chang’an University) Jianxun Cui (Harbin Institute of Technologies) Sean Qian (CMU)

Funding agencies

Thank you！Q & A?

Xiaopeng (Shaw) Li, Ph.D.Assistant Professor, Susan A. Bracken Faculty FellowDepartment of Civil and Environmental EngineeringUniversity of South Florida4202 E. Fowler Avenue, ENG 207 Tampa, FL 33620-5350E-mail: xiaopengli@usf.eduPhone: 813-974-0778; Fax: 813-974-2957Website: http://cee.eng.usf.edu/faculty/xiaopengli/