1. Synthesizing Controllers for Multi-Lane Traffic Maneuvers
Gregor v. Bochmann1 , Martin Hilscher2 ,
Sven Linker2 , Ernst-Rüdiger Olderog2
1 - School of Electrical Engineering and Computer Science,
University of Ottawa, Ottawa, Ontario, Canada
2 - Department of Computing Science,
University of Oldenburg, Oldenburg, Germany
SETTA 2015
Nanjing (China), November 2015
Gregor v. Bochmann, University of Ottawa

2. Gregor v. Bochmann, University of Ottawa
Abstract
Abstract. The dynamic behavior of a car can be modeled as a hybrid system involving continuous state changes and discrete state transitions. However, we show that the control of safe (collision free) lane change maneuvers in multi-lane traffic on highways can be described by finite state machines extended with continuous variables coming from the environment.
We use standard theory for controller synthesis to derive the dynamic behavior of a lane-change controller. Thereby, we contrast the setting of interleaving semantics and synchronous concurrent semantics. We also consider the possibility of exchanging knowledge between neighboring cars in order to come up with the right decision.
Gregor v. Bochmann, University of Ottawa

3. Gregor v. Bochmann, University of Ottawa
Context of this work
Car traffic modeling on multi-lane highways
Previous work:
Proposed algorithm for lane change (using state machine modeling for each car)
Principle: Before changing lane, a car claims the space on the new lane. Then it reserves the space and moves to the new lane.
Proof of correctness (using interleaving semantics)
Main issue: conflicting claims by several cars of the same free space (see figure)
Gregor v. Bochmann, University of Ottawa

4. Example configuration
Several cars on a three-lane highway
Gregor v. Bochmann, University of Ottawa

5. Main results of this paper
Car modeling as a hybrid system containing several components.
Correct control algorithms can be obtained by synthesis. Two approaches:
Controller derivation
Protocol derivation (for communication between different system components)
Interleaving semantics is not suitable for modeling systems consisting of several independent state machines.
Gregor v. Bochmann, University of Ottawa

6. Gregor v. Bochmann, University of Ottawa
Car as a hybrid system
Gregor v. Bochmann, University of Ottawa

7. Simple lane change algorithm
Plant : Car A
A.res
Environment:
Collision condition for car A in lane m:
m ϵ A.res and exist car:
( m ϵ car.res and safetyOverlap (A, car))
safetyOverlap (A, B)
Controller synthesis:
Construct ( Plant x Environment (including control objectives) )
Hide non-visible interactions and determinize (N/A in this case)
Eliminate transitions to states that do not satisfy objectives ):
In our case:
Objectives for state A.2{m,n}{}:
not exist car: m ϵ car.res and safetyOverlap (A, car)
Add this condition as guard to transition r(m)
Gregor v. Bochmann, University of Ottawa

8. Considering two lane changing cars
Two cars, A and F
A.res
Fail if safetyOverlap (A, F)
Lane change alg. correct for interleaving semantics, - but not for the case of concurrent transitions.
Gregor v. Bochmann, University of Ottawa

9. Proposed lane change algorithm
Two cars, A and F
Car A - Idea: claim before reservation
Fail state elimination for concurrent transitions requires the following constraint for r(m): not exist car:
( m ϵ car.res or m ϵ car.clm )
and safetyOverlap (A, car)
Fail if safetyOverlap (A, F)
Lane change alg. is correct for concurrent transitions
Gregor v. Bochmann, University of Ottawa

10. Gregor v. Bochmann, University of Ottawa
Using a helper car
Issue: How to obtain information about safety distance of the car that is behind the space to be reserved ?
Proposal: Ask that car (“helper” car)
This requires communication with that car
Revised algorithm: an additional action: get-info
Gregor v. Bochmann, University of Ottawa

11. Protocol derivation (principle)
Start with the global transition model
Project it onto each component, keeping only those actions that are performed by that component
and add the required coordination messages for synchronization between the components
for more details, see references
Gregor v. Bochmann, University of Ottawa

12. Communication with helper car
Global view (revised algorithm)
Derived behavior for car A
Derived behavior for car Helper
Gregor v. Bochmann, University of Ottawa

13. Gregor v. Bochmann, University of Ottawa
Conclusions
Modular system design is important
Some aspects of system design can be synthesized (“correct by construction”)
Controller derivation
Protocol derivation (for communication between different system components)
When transitions of different components are not coordinated in time, one has to consider the possibility of concurrency
Interleaving semantics is not good enough
Gregor v. Bochmann, University of Ottawa

14. Gregor v. Bochmann, University of Ottawa
Thanks !
Any questions
or comments ??
For copy of slides, see
Gregor v. Bochmann, University of Ottawa