Decentralized model predictive control for smooth coordination of automated vehicles at intersection

ECC’15, 17 July 2015 Center for Robotics, Ecole des Mines de Paris

(Jun) Xiangjun Qian, Jean Gregoire, Arnaud de La Fortelle, Fabien Moutarde

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[de La Fortelle et al, 2014]

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Coordination of automated vehicles in conflicting scenarios

Representative scenario

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A Mesoscopic – Microscopic problem • Mesoscopic traffic control: efficiency, deadlock avoidance, etc • Microscopic vehicle control: safety, fuel economy, comfort, etc

We propose a mathematical framework that separates the coordination problem into two problems. The focus of this paper is on vehicle control

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Interests of traffic authorities and vehicles are not aligned

Literature

Dresner, Kurt, and Peter Stone. "A multiagent approach to autonomous intersection management." Journal of artificial intelligence research (2008): 591-656. Campos, Gabriel R., et al. "Cooperative receding horizon conflict resolution at traffic intersections." Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on. IEEE, 2014. Kamal, Md, et al. "A vehicle-intersection coordination scheme for smooth flows of traffic without using traffic lights." (2014). …

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• System Model • Priority-based Coordination • MPC Problem Formulation • Simulations • Conclusion

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System Model

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Setting: • a collection of robots • fixed geometric paths • Non-decreasing trajectory along the paths

Goals: • Reaching goal regions

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Each vehicle i controlled in acceleration (bounded)

State:

Bounded acceleration:

Dynamics:

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Priority-based Coordination

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robot i curvilinear coordinate xi

robot j curvilinear coordinate xj

Physical space Coordination space

[Kant & Zucker 1988, Lavalle 1996, Laumond 1999]

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Homotopie classes

Physical space

2 1

1 2

Priority relation

Coordination space 25/09/2015 12

Physical space Coordination space

[Kant & Zucker 1988, Lavalle 1996, Laumond 1999]

09/04/2014 14 Coordination de véhicules aux intersection

Priority graph

Relative order of vehicles to go through the intersection

Priority-based coordination framework

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Centralized Priority Assignment Controller

Local Vehicle Controller

Traffic related criteria; A complex combinatorial problem

Respect priorities! Optimization using ego vehicle related criteria;

Advantage: satisfy the needs of traffic authorities and ego vehicles

MPC Problem Formulation

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Priority preserving condition with reactive safety

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Reactive safety

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Priority preserving condition with reactive safety

How to predict the states of prior vehicles ?

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Perfect case: sequential calculation

Infinit horizon MPC

Infinit horizon MPC using v1

Infinit horizon MPC using v1 and v2

Nash Equilibrium

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Simple case: asynchronic calculation

Finit horizon MPC

Finit horizon MPC, assuming v1 constant

Finit horizon MPC, assuming v1 and v2 constant

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Better case: asynchronic calculation

Finit horizon MPC

Finit horizon MPC, using v1’s MPC result as input

Finit horizon MPC, using v1’s and v2’s MPC results as inputs

Approximating Nash Equilibrium

Simulations

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Reactive safety

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Conclusion

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• The conflict resolution problem => priority-based approach: • Priority assignment • Priority preserving control

• Next steps • Efficient priority assignment methods • Implementation on automated vehicles (Scania trucks) • Manually driven vehicles

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Thank you

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Decentralized model predictive control for smooth �coordination of automated vehicles at intersectionIntroductionIntroductionIntroductionIntroductionSlide Number 6System ModelSystem Model- the multi robot coordination problemSystem Model-vehicle dynamicsPriority-based CoordinationThe coordination spacePrioritiesThe coordination spacePrioritiesSlide Number 15MPC Problem FormulationMPC FormulationMPC FormulationMPC FormulationInformation sharing/Nash EquilibriumInformation sharing/Nash EquilibriumInformation sharing/Nash EquilibriumSimulationsExample: Reactive SafetyExample: A snapshot of the overall systemConclusionConclusionThank you