Traffic Flow Theory in the Era of Autonomous Vehicles

Transcription

1 Traffic Flow Theory in the Era of Autonomous Vehicles Michael Zhang University of California Davis A Presenta8on at The Symposium Celebra8ng 50 Years of Traffic Flow Theory, August 1113, 2014, Portland, Oregon USA

2 Outline From individual driving to traffic flow Prominent features of traffic flow Models of traffic flowhuman driven vehicles Models of traffic flowautonomous vehicles The future of traffic flow

3 The Driving Task as Feedback Control Actual System: Road Environment Traffic Environment Disturbances Boundary cond. Measurements: {(x,y ),g,r }, v, s, Control Law: DirecKon/Lane Speed/Spacing Steering Angle Acc/Dec rate (throsle/braking) Vehicle Dynamics Traffic Dynamics {(x,y), g, R}, v, s, {(x,y), g, R}, v, s,

4 Human Drivers vs Autonomous Vehicles From A Control PerspecDve Human Drivers Sensing is imprecise but more versakle Response is slower but more robust Best at processing fuzzy informakon and is highly adapkve Strength: handles complex tasks such as lane tracking, obstacle avoidance more easily Autonomous Vehicles (Robo Cars) Sensing is more precise but less versakle Response is faster but less robust Best at exercising precise controls and is less adapkve: Strength: handles procedural tasks such as speed control, car following more easily

5 The Essence of Traffic Flow Theory is to Infer The SpeedSpacing Control Law of Each Driver v n (t)={?}( s n (t),,e) E={speed limits, grades, radius, surface condikons, visibility,.} And the colleckve dynamics of an OPEN ManyParKcle Dynamical System with random inserkons and removals (refleckng LANE CHANGE interackons) controlled by these driver control laws { x n (t)= v n (t), n=1,2,,n}

6 Example: The California Motor Code Rule For every 10 mph of speed, leave one car length of space This translates to or v(t)= s(t) l/t with speed limits v(t)=min{ V f, s(t) l/t } s(t) l= v(t)/10 l Tv(t)

7 If Human Drivers are IdenDcal Robots with super fast reackon Kme and vehicles capable of infinite accelerakon and decelerakon Micro model x (t)=v(t) v (t)=a(t) a(t)={ 0, T, v(t)<v f v(t)= V u(t) v(t)/ Traffic Stream Model (steadystate) V(s)=min{ V f, s/t} Macro (conknuum) model (in vehicle coordinate) s t v n =0, v=v(s)

8 What are These Models and what phenomena do they produce? Micro model: linear CF model of Pipes AcceleraKon waves DeceleraKon waves Stream model: Triangular FD Capacity: 2640 pcphpl (l=20c, T=1.36sec, Vf=60mph) Jam wave speed: 10 mph Macro model: LWR with Triangular FD k t + Q x (k)=0 Shock waves Expansion (accelerakon) waves v q l Q m V 1/T f 1/ s l/ T = 1 0 V f s = V f T+l 1/l s k

9 When All Vehicles Follow the Same Rule Q V m f l/ 10mph T = 1 1/ 0 2l m Trucks p h 1/l Cars k Normalized by vehicle length The slope of the jam wave speed is a good indicator whether drivers of different type of vehicles follow the same driving rule or not q Q m V f l/ T = 1 0 m p h 1/l k

10 In reality, human drivers Differ from each other in driving ability and habits Cannot assess mokon and distances precisely Respond with delay and finite accelerakon/decelerakon Do not follow rules exactly Consequence: Traffic flow in the real world is much more complex

11 Prominent Features of Real Traffic Flow Phase transikons Nonlinear waves StopandGo Waves (periodic mokon)

12 Phase transitions

13 Nonlinear waves Vehicle platoon traveling through two shock waves flow-density phase plot

14 StopandGo Waves (OscillaDons) Scatter in the phase diagram is closely related to stop-and-go wave motion

15 Some Classical Traffic Models Microscopic Modified Pipes model Newell Model Bando model { ( ( ) ) } { λ ( ) } x& = min v, s t l / τ n f n x& ( t+ τ) = v 1 exp ( s t l)/ v n f n f ( ( ) & * )( ) x& n() t = a u sn xn t, a = 1/ τ Macroscopic conknuum LWR model PayneWhitham model AwRascle, Zhang model vs (speedspacing) relakon is central to all these models t ( ρ) ρ + q = t * 0 x + ( ) = 0, vt ( vv) ρ ρv ( ) ( ) ( ) ( ) ρ = 1/ su, s = v ρ, q= ρvq, ρ = ρv ρ t * * * * x 2 c0 + + ρ x x = ρ v* v + v c ρ v = + ( ) = 0, t ( ) ρ ρv x ( ) x v * ( ρ) τ ρ v ( ) τ ' ( ρ) = ρ ( ρ) c v * v

16 The Difficulty of Modeling Real Flow Each driver is different Driving rules are hidden Sensing is imprecise Behavior is adapkve, nonlinear, and perhaps inconsistent (Driving environment is complex)

17 When Robo Cars Take Over the Road Behavior is uniform and consistent Sensing and control is more precise Rules are always obeyed (Driving environment is skll complex) More importantly, driving rules are by design, leaving rooms for opkmizing flow and safety Feedback Control Problem

18 Traffic Flow Theory For Robo Cars Longitudinal Control Example RoboCar#1 a(t+τ)= k r {V(s) v},v(s)=min{ V f, s/t} Human: τ=12s, T=1.362s; Robo Car: τ=0.40.6s, T=0.81.2s, Capacity: 1/T, +70%, But this may be too rosy a predickon in the inikal deployment stage (liability) Measurements: v, s Actual System: Road Environment Traffic Environment Control Law Speed/Spacing disturbance Acc/Dec rate (throsle/braking) Traffic Dynamics v, s v,s

19 Example RoboCar#2 a(t+τ)= k r {V(s) v}+ k v {u v} Faster response and higher throughput than RoboCar#1 τ=0.40.6s, T= s Actual System: Road Environment Traffic Environment Measurements: v, s, u Control Law Speed/Spacing disturbance Acc/Dec rate (throsle/braking) Traffic Dynamics v, s, u v,s,u

20 Example RoboCar#3 (RoboCar#2 with V2V) a(t+τ)= k a a u (t) +k r {V(s) v}+ k v {u v} Actual System: Road Environment Traffic Environment Measurements: v, s, u, a Control Law Speed/Spacing disturbance Acc/Dec rate (throsle/braking) Traffic Dynamics v, s, u,a v, s, u, a And the list goes on: you can come up with other models that meet safety and stability requirements

21 Expected throughput with vehicle platooning Throughput Throughput (veh/hr) Tg=0.55 s Tg=0.60 s Tg=0.65 s Tg=0.70 s Platoon Size N Throughput of CACC platooning with different platoon size and intraplatoon Kme gap sepng 21

22 Future of Traffic Flow Theory Research (1) Do the Arrival of Robo Cars Mean The End of Traffic Flow Research? AutomaKon creates uniformity and standardizakon, suppresses randomness: From billions of drivers to a handful: Google Car, GM Car, Toyota Car. Behavior of each Robo Car is consistent and known q q k From Human Drivers to Robots k

23 Future of Traffic Flow Theory Research (2) In the short term design of driving models for Robo cars Robo car friendly infrastructure In the intermediate term Mixed traffic with Robo Cars, Platooning of Robo Cars Lightless interseckons with invehicle signal control Rich micro level data for understanding and modeling traffic, and validakng traffic models

24 Future of Traffic Flow Theory Research (3) In the long term, full automakon of highway traffic OpKmal scheduling and pricing for congeskon free networks Robust Recovery from DisrupKons New services and shared use of autonomous vehicles Robo Taxi Services Last and firstmile of transit (flexible transit) Seamless integrakon of mulkple modes And the list goes on

25 Concluding Remarks Autonomous Vehicles will In the long run bring more order to traffic flow and simplify traffic flow theory Produce rich data for traffic flow research Brings a host of brand new research problems for modeling, design and operakons of transportakon systems