Formal Multi-Lane Traffic Diagrams - Uni OldenburgTom Urbanik. Tra c signal timing manual. Technical...
Transcript of Formal Multi-Lane Traffic Diagrams - Uni OldenburgTom Urbanik. Tra c signal timing manual. Technical...
Motivation Diagrams Conclusion
Formal Multi-Lane Traffic Diagrams
Sven Linker
Carl von Ossietzky Universitat Oldenburg
07.12.2012
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Motivation Diagrams Conclusion
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Motivation Diagrams Conclusion
Motivation
Scenario: Automated traffic on highways
Defined maneuovres for cars [HESV91]
Changing lanesKeeping distance. . .
Ensure safety of traffic by formal methods
E.g., no collisions
Highly dynamical, complex systems
Formal machinery also very complex, hard to understand
Use suitable abstraction of dynamics
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Motivation Diagrams Conclusion
Abstraction
E
Cars use full width of lane
Physical size + length for braking
Distinguish space used by cars:
Reservation must not be violated by other cars, needed foremergency brake, etc.
Claim indicator, whenever a car wants to change a lane(setting turn signals)
4/9 Sven Linker Traffic Diagrams
Motivation Diagrams Conclusion
Abstraction
E
Cars use full width of lane
Physical size + length for braking
Distinguish space used by cars:
Reservation must not be violated by other cars, needed foremergency brake, etc.
Claim indicator, whenever a car wants to change a lane(setting turn signals)
4/9 Sven Linker Traffic Diagrams
Motivation Diagrams Conclusion
Abstraction
E
E
Reservation
Claim
Cars use full width of lane
Physical size + length for braking
Distinguish space used by cars:
Reservation must not be violated by other cars, needed foremergency brake, etc.
Claim indicator, whenever a car wants to change a lane(setting turn signals)
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Motivation Diagrams Conclusion
Diagrams with mathematical semantics
Intuitive way to reason about space
Logical reasoning with diagrams possible [AB96]
Different diagrammatic languages established
Formal Euler/Venn Diagrams
Conceptual Graphs CAT : ∗ on MAT : ∗
Spider Diagrams. . .
Spatial properties seldom captured by diagrams
Queries for spatial databases [ES99]Time-space diagrams [KRL+08]
t
x
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Motivation Diagrams Conclusion
Traffic Diagrams
ego
a c(2, 5)
(2, 5)
Layer
Lane separation
Claim/Reservation
Distance Arrow
Auxillary lines
Central Car
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Motivation Diagrams Conclusion
Traffic Diagrams
ego
a c(2, 5)
(2, 5)
Layer
Lane separation
Claim/Reservation
Distance Arrow
Auxillary lines
Central Car
6/9 Sven Linker Traffic Diagrams
Motivation Diagrams Conclusion
Traffic Diagrams
ego
a c(2, 5)
(2, 5)
Layer
Lane separation
Claim/Reservation
Distance Arrow
Auxillary lines
Central Car
6/9 Sven Linker Traffic Diagrams
Motivation Diagrams Conclusion
Traffic Diagrams
ego
a c(2, 5)
(2, 5)
Layer
Lane separation
Claim/Reservation
Distance Arrow
Auxillary lines
Central Car
6/9 Sven Linker Traffic Diagrams
Motivation Diagrams Conclusion
Traffic Diagrams
ego
a c(2, 5)
(2, 5)
Layer
Lane separation
Claim/Reservation
Distance Arrow
Auxillary lines
Central Car
6/9 Sven Linker Traffic Diagrams
Motivation Diagrams Conclusion
Traffic Diagrams
ego
a c(2, 5)
(2, 5)
Layer
Lane separation
Claim/Reservation
Distance Arrow
Auxillary lines
Central Car
6/9 Sven Linker Traffic Diagrams
Motivation Diagrams Conclusion
Traffic Diagrams
ego
a c(2, 5)
(2, 5)
Layer
Lane separation
Claim/Reservation
Distance Arrow
Auxillary lines
Central Car
6/9 Sven Linker Traffic Diagrams
Motivation Diagrams Conclusion
Traffic Diagrams
ego
a c(2, 5)
(2, 5)
Layer
Lane separation
Claim/Reservation
Distance Arrow
Auxillary lines
Central Car
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Motivation Diagrams Conclusion
Abstract Syntax
Mathematical structure capturing elements/relations
Transformation rules
Suitable formalisms:
Meta-modelsGraph grammars
Here: Graph grammars
Spatial constraintsApplication conditions of rulesTransformation rules also within grammar
Non-terminal edges replaced by graphs
Graphs without NT ⇒ syntactically correct diagrams
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Motivation Diagrams Conclusion
Abstract Syntax: Example
start
layer
lane
sep
lane
cars free cars
({a}, ∅) ({c}, ∅)
free cars free
({ego}, ∅)
at
ci
at in
s t s t s t
l
r l
r
s
t
at
n i s t s t s t
l r
ego
a c(2, 5)
(2, 5)
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Motivation Diagrams Conclusion
Abstract Syntax: Example
start
layer lane
sep
lane
cars free cars
({a}, ∅) ({c}, ∅)
free cars free
({ego}, ∅)
at
ci at i
n
s t s t s t
l
r l
r
s
t
at
n i
s t s t s t
l r
ego
a c(2, 5)
(2, 5)
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Motivation Diagrams Conclusion
Abstract Syntax: Example
start
layer lane
sep
lane
cars free cars
({a}, ∅) ({c}, ∅)
free cars free
({ego}, ∅)
at
ci at i
ns t s t s t
l
r l
r
s
t
at
n i s t s t s t
l r
ego
a c
(2, 5)
(2, 5)
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Motivation Diagrams Conclusion
Abstract Syntax: Example
start
layer lane
sep
lane
cars free cars
({a}, ∅) ({c}, ∅)
free cars free
({ego}, ∅)sarrow
constr
(2, 5)
at
ci at i
ns t s t s t
l
r l
r
s
t
at
n i s t s t s t
l r
s
tty
cis
ego
a c(2, 5)
(2, 5)
8/9 Sven Linker Traffic Diagrams
Motivation Diagrams Conclusion
Abstract Syntax: Example
start
layer lane
sep
lane
cars free cars
({a}, ∅) ({c}, ∅)
free cars free
({ego}, ∅)sarrow
constr
(2, 5)
sarrow
constr (2, 5)
at
ci at i
ns t s t s t
l
r l
r
s
t
at
n i s t s t s t
l r
s
tty
cis
s
t
tycis
ego
a c(2, 5)
(2, 5)
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Motivation Diagrams Conclusion
Conclusion
Diagrams expressing traffic situations
Abstract syntax by graph grammar
Not Shown
Real-time aspects
Semantics
Compatible with existing logic (same semantic model)
Future Work
Expressivity
Calculus
Decidability
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Motivation Diagrams Conclusion
Conclusion
Diagrams expressing traffic situations
Abstract syntax by graph grammar
Not Shown
Real-time aspects
Semantics
Compatible with existing logic (same semantic model)
Future Work
Expressivity
Calculus
Decidability
9/9 Sven Linker Traffic Diagrams
Motivation Diagrams Conclusion
Conclusion
Diagrams expressing traffic situations
Abstract syntax by graph grammar
Not Shown
Real-time aspects
Semantics
Compatible with existing logic (same semantic model)
Future Work
Expressivity
Calculus
Decidability
9/9 Sven Linker Traffic Diagrams
Motivation Diagrams Conclusion
Gerard Allwein and Jon Barwise, editors.Logical reasoning with diagrams.Oxford University Press, Inc., New York, NY, USA, 1996.
Martin Erwig and Markus Schneider.Visual Specification of Spatio-Temporal Developments.In VL ’99, page 187. IEEE Computer Society, 1999.
Ann Hsu, Farokh Eskafi, Sonia Sachs, and Pravin Varaiya.The design of platoon maneuver protocols for ivhs.Technical Report UCB-ITS-PRR-91-6, University of California,Berkeley, April 1991.
Peter Koonce, Lee Rodegerdts, Kevin Lee, Shaun Quayle,Scott Beaird, Cade Braud, Jim Bonneson, Phil Tarnoff, andTom Urbanik.Traffic signal timing manual.Technical report, U.S. Department of Transportation, FederalHighway Administration, 2008.
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