2 freeway stop-and-go traffic
TRANSCRIPT
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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
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Freeway Stop-and-Go Traffic
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Arterial Operations
Suboptimal timing – extra delay
Stop-and-go waves – excessive fuel consumptions
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Adverse Impacts
Congestion Exacerbate delay (3.7 billion hours/year) and
congestion cost ($78 billion per year)
Tampa Bay Areahttp://www.tampabay.com/
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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
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Adverse Impacts
Safety hazards 2,200,000 injuries 33,000 fatalities
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Connected and Automated Vehicles
Information sharing
Human drivers → robot drivers
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CAV for operations
Enable trajectory-level vehicle control and coordination
Fundamentals of highway traffic operations Past – accommodating human drivers Future - designing robot drivers
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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
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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
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CAV-based Traffic Operations
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CAV Trajectory Optimization
Signalized Intersections Coordinate signal timing with vehicle trajectory
control
Human-driven traffic CAV traffic
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Infrastructure
Single lane highway segment 0, Fixed signal timing , , , …at location
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Entry Boundary Condition
Indexed by 1, 2, …, Entry time , speed , known a priori
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Physical Bounds
Trajectory
Speed ∈ 0, , acc. ∈¯,
( )np t
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Exit Boundary Constraint
Exit during green time:
mod ,
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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
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Travel Time MOE
1: ( ) / ,n nn
T p L t N
N
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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
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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
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Trajectory Optimization (TO)
min ≔
subjectto0;,∀ (entry)
0 ;
¯,∀ , (kinematics)
mod , , ∀ (exit)
, ∀ 1 (safety)
Infinite dimensionHigh nonlinearity
Differentialequations
Non-convexity
Vehicle interactions
TOO DIFFICULT TO SOLVE
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Solution Parsimonious Algorithms
Shooting heuristic (SH) A small number of analytical sections
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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.
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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
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Time (s)
Dis
tanc
e (m
)
(a)
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(b)Time (s)
Dis
tanc
e (m
)
IVSL1
IVSL2
0 50 100 150 200 250 300 3500
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Time (s)
Dis
tanc
e (m
)
·IVSL1
IVSL2
(f)
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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
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Joint Trajectory and Signal Optimization
Problem setting
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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
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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
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Deep Learning Based Trajectory Control
• Using deep neural networks to design adaptive CAV controllers
Implication to Capacity Analysis & Planning
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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.
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Capacity Analysis
CAV technology uncertainties Will CAV reduce headways?
Google car pulled over for being too slowhttp://www.bbc.com/news/technology-34808105
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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.
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Capacity Analysis
CAV market penetration rate
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Low CAV market penetration rate
High CAV market penetration rate
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Capacity Analysis
CAV platooning intensity
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Low CAV platooning intensity
High CAV platooning intensity
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Analytical Capacity Formulation
Markov chain model
1 0
1,,
,,
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Analytical Capacity Formulation
Markov chain model ∈ 0,1 : CAV market penetration rate ∈ 1,1 : CAV platooning intensity
≔
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Analytical Capacity Formulation
Approximate capacity ≔
∑ ∑ ∑ ∈ , ∈
Theorem 1: ≤ for any finite N Theorem 2: When 1, → → ∞
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Capacity analysis
Numerical analysis
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Optimistic Headway Conservative Headway
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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.
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Field Experiments
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Field Experiments – Pure HVs
15 HVs following tests in Harbin, China (collaborating with Harbin Institute of Technology)
spee
d
Lead vehicle Following vehicles
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Data Collection on Public Roads Video-Based Intelligent Road Traffic Universal Analysis Tool
(VIRTUAL) (Provisional Patent #. 62/701,978)
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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
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Fields Experiments – Pure CAVs
Turner Fairbank Highway Research Center
Level-1 Automated Cadillac
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Field Experiments
HV following CAV/HV at the 2.4 km test track at Chang’an University, China
Test different drivers, different CAV speed
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Field Experiments
HV following CAV/HV at the 2.4 km test track at Chang’an University, China
Test different drivers, different CAV speed
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Field Experiments – Mixed Traffic
Difference between HV →CAV and HV→HV
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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: [email protected]: 813-974-0778; Fax: 813-974-2957Website: http://cee.eng.usf.edu/faculty/xiaopengli/