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Synthesizing Controllers for Multi-Lane Traffic Maneuvers

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Presentation on theme: "Synthesizing Controllers for Multi-Lane Traffic Maneuvers"— Presentation transcript:

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


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