Ultimately 1/12 Simplifying Assumptions Vehicles have positive - - PowerPoint PPT Presentation

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Ultimately 1/12 Simplifying Assumptions Vehicles have positive - - PowerPoint PPT Presentation

Feb 07, 2023 259 likes •823 views

Safe Intersections: At the Crossing of Hybrid Systems and Verification Sarah M. Loos and Andr Platzer Computer Science Department Carnegie Mellon University October, 2011 Ultimately 1/12 Simplifying Assumptions Vehicles have

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Sarah M. Loos and André Platzer Computer Science Department Carnegie Mellon University October, 2011

Safe Intersections:

At the Crossing of Hybrid Systems and Verification

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Ultimately…

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Simplifying Assumptions

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  • Vehicles have positive velocity
  • Accurate sensing
  • Instantaneous braking and acceleration
  • Time synchronization
  • Delay for sensor updates is bounded
  • Straight lane dynamics
  • Cars represented as points, lanes as lines
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Previous Work: Highway Control

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  • Verified multilane highway system
  • Arbitrary number of cars
  • Arbitrary number of lanes
  • Proof of safety for distributed control

built from two-car “building blocks.”

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Intersection Building Blocks

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Intersection Building Blocks

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Intersection Building Blocks

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Intersection Building Blocks

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Intersection Building Blocks

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Intersection Building Blocks

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Intersection Building Blocks

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Intersection Building Blocks

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This is similar to a merge on the highway.

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T-Intersection Building Block

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Intersection Building Blocks

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Intersection Building Blocks

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Intersection Building Blocks

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Intersection Building Blocks

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Straight Lane Building Block

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Di Different ntial Dyna l Dynami mic L Logic*

*

Initial Conditions → [Model] Requirements

*The

he s sho hort v version. n.

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SLIDE 20

Initial Conditions → [Model] Requirements

Di Different ntial Dyna l Dynami mic L Logic

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Initial Conditions → [Model] Requirements

logical formula logical formula

Di Different ntial Dyna l Dynami mic L Logic

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SLIDE 22

Initial Conditions → [Model] Requirements

logical formula logical formula

Di Different ntial Dyna l Dynami mic L Logic

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SLIDE 23

Initial Conditions → [Model] Requirements

logical formula logical formula

Di Different ntial Dyna l Dynami mic L Logic

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SLIDE 24

Initial Conditions → [Model] Requirements

logical formula logical formula hybrid program

Di Different ntial Dyna l Dynami mic L Logic

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Initial Conditions → [Model] Requirements

logical formula logical formula hybrid program discrete control continuous dynamics

Di Different ntial Dyna l Dynami mic L Logic

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logical formula logical formula hybrid program

→ [(ctrl;dyn)*]

discrete control continuous dynamics

Di Different ntial Dyna l Dynami mic L Logic

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logical formula logical formula hybrid program

→ [(ctrl; x’= v; v’= a)*]

discrete control continuous dynamics

Di Different ntial Dyna l Dynami mic L Logic

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

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Single Lane Stoplight

Initial Conditions → [Model] Requirements

To Prove:

h

✔

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Intersection

Initial Conditions → [Model] Requirements

To Prove:

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Intersection

Initial Conditions → [Model] Requirements

To Prove: Cars can stop initially

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Intersection

Initial Conditions → [Model] Requirements

To Prove: Cars can stop initially No collision

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Intersection

Initial Conditions → [Model] Requirements

To Prove:

Cars can stop initially

No collision

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Intersection

Initial Conditions → [Model] Requirements

To Prove:

Cars can stop initially

No collision

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Intersection

Initial Conditions → [Model] Requirements

To Prove:

Cars can stop initially

No collision

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Intersection

Initial Conditions → [Model] Requirements

To Prove:

Cars can stop initially

No collision

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Intersection

Initial Conditions → [Model] Requirements

To Prove:

Cars can stop initially

No collision

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Intersection

Initial Conditions → [Model] Requirements

To Prove:

Cars can stop initially

No collision

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Intersection

Initial Conditions → [Model] Requirements

To Prove:

Cars can stop initially

No collision

h

✔

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Conclusions Future Work

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 Curved road dynamics  Distributed car dynamics  Combinations of merge and cross protocols  Noisy and delayed sensor data  Delayed braking and acceleration reaction  Non-synchronized time  Non-zero car lengths and lane widths

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Cha halle lleng nges Solu lutions ns

 Infinite, continuous, and evolving

state space, R∞

 Simulation and testing only

partially prove safety

 Continuous dynamics  Discrete control decisions  Large branching factor

Conclusions

 We give a formal proof for a two-lane

intersection with one car on each lane

 Semi-automated proof generation  Variations in system design  Demonstrated potential for formal

safety verification in car control, even when models have high branching factor

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Conclusions Thank You!

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Conclusions Reference

12/12 The full length paper for this research can be found here: Sarah M. Loos and André Platzer. Safe Intersections: At the Crossing of Hybrid Systems and Verification. In the 14th International IEEE Conference on Intelligent Transportation Systems, ITSC 2011, Washington, D.C., USA, Proceedings, 2011.