Formal Verification of V2I aided Autonomous Driving Ishan Pardesi - - PowerPoint PPT Presentation

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Formal Verification of V2I aided Autonomous Driving Ishan Pardesi - - PowerPoint PPT Presentation

Jan 05, 2023 467 likes •823 views

Formal Verification of V2I aided Autonomous Driving Ishan Pardesi Dhruv Mahajan A hybrid systems approach 1 The problem Safety of Autonomous cars is paramount! It is important to invest in developing formal verification techniques to

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Formal Verification of V2I aided Autonomous Driving A hybrid systems approach

Ishan Pardesi Dhruv Mahajan

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The problem

Safety of Autonomous cars is paramount! It is important to invest in developing formal verification techniques to ensure safety of autonomous vehicles.

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Proposed Solution

Formally verify all car maneuvers for safety using differential dynamic logic while designing the system Use smart road infrastructure to validate all car maneuvers for safety before the maneuver is made in real time

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If a car maintains sufficient distance from other cars such that it can

  • brake or
  • change lanes

in time to avoid a collision, then it is safe.

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Defining Safety

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Can that be Guaranteed?

An autonomous car always operates from a limited awareness of its environment. If only the car new everything about its environment well in advance, there would be no collisions.

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Smart Infrastructure as a solution

Intelligent nodes at regular distances

  • n the Highway
  • Allows the car to see beyond it’s

sensing capabilities

  • Enforces dynamic regulations,
  • eg. Speed Limits
  • Better & accurate control

decisions

  • Increases safety - more

determinism

  • Increases efficiency

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The Model

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Elements of the Model

Highway A two lane smart highway laid with intelligent nodes at regular distance creating a robust V2I infrastructure Autonomous Car Objective is to reach the goal without any collision Obstacles Obstructions for the car

  • static, or moving,

introduced one at a time every D/2 distance

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  • Two Lanes
  • Highway Speed Limit (VSL)-

~ 155 mph

  • Inter Node Distance (D/2)

= 150 meters (can be higher)

  • Range diameter of node - (D)

= 300 meters (can be higher)

  • Finite Time to change lanes

~ 1-2 seconds

  • Next Control Decision - within

1 meter

  • Can change lanes within D/2 distance (even at VSL )

General Assumptions - Highway

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Modelling overview

(Preconditions) -> [ (Controller; differential dynamics)* @ invariant ] (Post Condition)

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Let’s Build the Models Step by Step

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No obstacle on the road

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Introducing an obstacle

▸ Constant Velocity ▸ Car & obstacle in same lane ▸ Time to change lanes δ = 1 sec ▸ Single Obstacle

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Model Explained

Car is safe initially -> [ { {If sufficient distance to change lanes after 1 control cycle => Continue or change lanes Else Change lanes NOW}; {Differential dynamics} } @ {If lane changing =>must complete without collision OR it must be safe to change lanes} ] (No collision - Safety Condition)

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Limited Sensing Capability

▸ Upto 80-100 meters ▸ Can’t see beyond 1-2 vehicles ▸ Nodes allow to see beyond ▸ Allows better control decisions

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Model explained

▸ Constant Velocity ▸ Multiple obstacles on road ▸ New obstacle in next D/2 block of road ▸ New information available after each node

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Model explained

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Car is safe initially -> [ ] (No collision)

Model explained

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Car is safe initially -> [ {Crosses Node and gets info about next D distance} { {If sufficient distance to change lanes after 1 control cycle => Continue or change lanes Else Change lanes NOW}; ] (No collision)

Model explained

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Car is safe initially -> [ {Crosses Node and gets info about next D distance} { {If sufficient distance to change lanes after 1 control cycle => Continue or change lanes Else Change lanes NOW}; {Differential dynamics}} ] (No collision)

Model explained

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Car is safe initially -> [ {Crosses Node and gets info about next D distance} { {If sufficient distance to change lanes after 1 control cycle => Continue or change lanes Else Change lanes NOW}; {Differential dynamics}} @ {If lane changing =>must complete without collision OR it must be safe to change lanes} ] (No collision)

Model explained

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Consider all cases in the model. For example

Proof strategy intuition

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Consider all cases in the model. For example If lane change just completed

Proof strategy intuition

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Consider all cases in the model. For example If lane change just completed If the car just crossed a node

Proof strategy intuition

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Consider all cases in the model. For example If lane change just completed If the car just crossed a node If there is a node ahead in the same lane

Proof strategy intuition

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Consider all cases in the model. For example If lane change just completed If the car just crossed a node If there is a node ahead in the same lane If the car will not have time to change lanes after the next time cycle T

Proof strategy intuition

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Consider all cases in the model. For example If lane change just completed If the car just crossed a node If there is a node ahead in the same lane If the car will not have time to change lanes after the next time cycle T Begin the lane change procedure immediately.

Proof strategy intuition

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Consider all cases in the model. For example If lane change just completed If the car just crossed a node If there is a node ahead in the same lane If the car will not have time to change lanes after the next time cycle T Begin the lane change procedure immediately. Solve the ODE and check if the car is safe or not

Proof strategy intuition

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Subsequent Models

In the subsequent models, we allow the following capabilities while ensuring safety- ▸ Accelerate ▸ Decelerate ▸ Lane changing (even when not necessary)

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Future Work

▸ Moving Obstacles ▸ Dynamic change in # of lanes ▸ Combining all into one ▸ Hybrid Games (dGL) Approach

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Implications of the approach

Policy Implications Ownership of accident responsibility Infrastructure ensured safe driving - more freedom to automakers. Ensuring strict enforcement

  • f road laws

Technology Implications Brings determinism and safety guarantees in autonomous driving High driving efficiency by increased road awareness Allows better transport planning and traffic optimization.

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Acknowledgements

▸ Professor André Platzer ▸ Yong Kiam Tan (TA) ▸ Mengze Li (TA)

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References

  • Original reference of Image on slide 6 (largely modified)
  • https://bit.ly/2LaorIi
  • Presentation template by SlidesCarnival

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THANKS!

Questions?

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