Road Traffic Rules Synthesis using Grammatical ... - Google Sites

Road Traffic Rules Synthesis using Grammatical Evolution Eric Medvet

Alberto Bartoli

Jacopo Talamini

Department of Engineering and Architecture University of Trieste Italy

EvoAPPS, 19/4/2017, Amsterdam (The Netherlands)

http://machinelearning.inginf.units.it

Driving Human driver (now)

Medvet et al. (UniTs)

Road traffic rules with GE

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Driverless car (the future)


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Both try to: get there avoid accidents comply to the rules



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Both try to: get there avoid accidents comply to the rules Are those rules “optimal” for both? Medvet et al. (UniTs)


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Re-writing the rules

If we could re-write the rules from scratch, we’d want the rules leading to high traffic efficiency (getting there) and high safety (avoiding accidents) How to write those rules?



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Re-writing the rules

If we could re-write the rules from scratch, we’d want the rules leading to high traffic efficiency (getting there) and high safety (avoiding accidents) How to write those rules? Our solution: write the rules automatically with an evolutionary approach



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In a nutshell

Evolutionary approach: individual → set of rules fitness → hefficiency, safetyi, simulated with those rules



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In a nutshell

Evolutionary approach: individual → set of rules fitness → hefficiency, safetyi, simulated with those rules Our contributions: 1

a model for traffic simulation, suitable for our scenario

2

a language for defining rules applicable to the model

3

a GE-based framework for automatic rules generation, with experimental evaluation



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The traffic model

Table of Contents

1

The traffic model

2

Language for rules

3

GE-based rules generation

4

Experimental evaluation



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The traffic model

The traffic model

Goals (and trade-offs): detailed enough to include concepts amenable to be regulated simple enough to allow for simulation Describes: the physical world the drivers’ behavior



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The traffic model

Physical world Infrastructure: road sections and intersections lanes in sections Cars: position (continuous longitudinally, discrete on lanes) speed status (in {alive, dead}) Collisions With discrete time



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The traffic model

Drivers’ behavior The driver’s algorithm: input: view ahead, speeds, distance to travel output: a list A of actions ↑: accelerate ←: move on left lane . . . and so on (↑, %, →, &, ↓, ., ←, -)



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The traffic model

Drivers’ behavior

Goal: just travel a target distance, no specific target position possibly at maximum (car) speed avoiding hitting other cars



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The traffic model

Drivers’ behavior and rules

The rules-aware driver’s algorithm: input: a list A of actions and a set R of rules output: the first action a ∈ A which breaks the lowest number of rules



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The traffic model

Drivers’ behavior and rules

The rules-aware driver’s algorithm: input: a list A of actions and a set R of rules output: the first action a ∈ A which breaks the lowest number of rules Why driver and rules-aware driver? model the driver’s “instinct” to perform his favorite action with no rules: “I drive as I like” with rules: “among preferred actions, I choose a permitted one”



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Language for rules

Table of Contents

1

The traffic model

2

Language for rules

3


4




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Language for rules

Rules

Rule: each rule is a predicate at a given time, for a given rule, a car breaks (false) or does not break (true) the rule Works on: the car status (speed, position in section/intersection, . . . ) other cars relative distances and speeds current section/intersection



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Language for rules

Language for the rules As a context-free grammar: r ::= hconditionsi hconditionsi ::= hconditioni | hconditionsi ∨ hconditioni hconditioni ::= hbaseConditioni | ¬hbaseConditioni hbaseConditioni ::= hnumericConditioni | hdeltaConditioni | hgraphConditioni hnumericConditioni ::= hnumericVariablei ≤ hnumericValuei hnumericVariablei ::= vˆx | vmax | v∆ | dview | d | xˆ | yˆ | ∆x−1 | ∆x0 | ∆x1 | l(p) | w (p) hnumericValuei ::= hdigiti.hdigitiehexpi hdigiti ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 hexpi ::= −1 | 0 | 1 hdeltaConditioni ::= δv−1 = hdeltaValuei | δv0 = hdeltaValuei | δv1 = hdeltaValuei hdeltaValuei ::= ∅ | opposite | − 1 | 0 | 1 hgraphConditioni ::= p ∈ S



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Language for rules

Language for the rules As a context-free grammar: r ::= hconditionsi hconditionsi ::= hconditioni | hconditionsi ∨ hconditioni hconditioni ::= hbaseConditioni | ¬hbaseConditioni hbaseConditioni ::= hnumericConditioni | hdeltaConditioni | hgraphConditioni hnumericConditioni ::= hnumericVariablei ≤ hnumericValuei hnumericVariablei ::= vˆx | vmax | v∆ | dview | d | xˆ | yˆ | ∆x−1 | ∆x0 | ∆x1 | l(p) | w (p) hnumericValuei ::= hdigiti.hdigitiehexpi hdigiti ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 hexpi ::= −1 | 0 | 1 hdeltaConditioni ::= δv−1 = hdeltaValuei | δv0 = hdeltaValuei | δv1 = hdeltaValuei hdeltaValuei ::= ∅ | opposite | − 1 | 0 | 1 hgraphConditioni ::= p ∈ S

Goal: express realistic rule like “stay on rightmost free lane” Medvet et al. (UniTs)


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Table of Contents

1

The traffic model

2

Language for rules

3


4




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GE

We have: the fitness (traffic efficiency and safety) the solution space (as a context-free grammar)

⇓ GE is the right tool!



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Fitness Traffic efficiency

Traffic safety



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Fitness Traffic efficiency → average speed ratio (ASR) 1 1 X dtot 1 1− nsim ncar cars ktot vmax Traffic safety → 1 − collision-per-time (CpT) 1

1 X ncollision nsim ncar cars ktot

Minimize a linear combination: f (R) = αtime (1 − ASR) + αcollision CpT



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Fitness Traffic efficiency → average speed ratio (ASR) 1 1 X dtot 1 1− nsim ncar cars ktot vmax Traffic safety → 1 − collision-per-time (CpT) 1

1 X ncollision nsim ncar cars ktot

Minimize a linear combination: f (R) = αtime (1 − ASR) + αcollision CpT Computed over many (nsim ) simulations (stochasticity) Medvet et al. (UniTs)


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Table of Contents

1

The traffic model

2

Language for rules

3


4




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Goals Traffic model: is it sound? find values for parameters



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Goals Traffic model: is it sound? find values for parameters GE-based rules generation: are generated rules better than no rules? are generated rules better than hand-written rules?



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Goals Traffic model: is it sound? find values for parameters GE-based rules generation: are generated rules better than no rules? are generated rules better than hand-written rules? For both: how does injected traffic affect efficiency and safety? congestion: no further increase in overall traveled distance



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Traffic model validation

1 0.8 0.6 0.4 0.2 0

CpT (Safety)

1 − ASR (Efficiency)

5 road sections, up to tens of cars, values averaged on 10 simulations

Low efficiency

High efficiency 0 ncar

10 20 (injected traffic)


1 0.8 0.6 0.4 0.2 0

·10−2 Low safety

High safety 0


ncar


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1 0.8 0.6 0.4 0.2 0

CpT (Safety)



0 ncar


low ncar high ncar Medvet et al. (UniTs)

1 0.8 0.6 0.4 0.2 0

·10−2

0 ncar


No rules Efficiency Safety high high low low


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1 0.8 0.6 0.4 0.2 0

CpT (Safety)



0 ncar


low ncar high ncar Medvet et al. (UniTs)


1 0.8 0.6 0.4 0.2 0

·10−2

0 ncar


Hand-written rules Efficiency Safety < ' ' >


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1 0.8 0.6 0.4 0.2 0

CpT (Safety)



0 ncar


low ncar high ncar


1 0.8 0.6 0.4 0.2 0

·10−2

0 ncar


Hand-written rules Efficiency Safety < ' ' >

Rules → lower efficiency, higher safety: sound! Medvet et al. (UniTs)


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1 0.8 0.6 0.4 0.2 0

CpT (Safety)


30 runs, each with a 100 individuals, 100 generations

0 ncar



1 0.8 0.6 0.4 0.2 0

·10−2

0


ncar


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1 0.8 0.6 0.4 0.2 0

CpT (Safety)


30 runs, each with a 100 individuals, 100 generations

0 ncar


Best GE rules

1 0.8 0.6 0.4 0.2 0

·10−2

0 ncar


:

slightly higher efficiency higher safety



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Congestion

Overall collisions

Bad 200

100

Good 0

0

2 4 6 Overall distance ·104



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Overall collisions

Congestion

One mark for each ncar value

200

100

0

0




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Overall collisions

Congestion


200

Congestion: increasing injected traffic does not increase overall distance

100

0

0




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Overall collisions

Congestion


200

Congestion: increasing injected traffic does not increase overall distance

100

GE vs. hand-written at congestion: 0

longer overall distance 0



less overall collisions


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))) Thanks! )))



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