R2-D2 Goes to Buggy Emily Yeh & Anastassia Kornilova 1/33 - - PowerPoint PPT Presentation

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R2-D2 Goes to Buggy Emily Yeh & Anastassia Kornilova 1/33 - - PowerPoint PPT Presentation

May 01, 2023 240 likes •591 views

R2-D2 Goes to Buggy Emily Yeh & Anastassia Kornilova 1/33 Buggy R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh 2/33 Vehicle Safety in the Real World R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh 3/33 R2-D2

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R2-D2 Goes to Buggy

Emily Yeh & Anastassia Kornilova

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Buggy

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Vehicle Safety in the Real World

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R2-D2 enters the races

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Basics of the Model Track: Helix with fixed width and varying parameters Parameters: Model 1. Varying helix radii Model 2. Varying helix slope Buggy Control (with R2D2): acceleration Buggy Evolution: circular motion

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Physics: circles and inclines

Figure from: http://physatwes.com/SecondLawHonors.aspx Figure form: http://www.ux1.eiu.edu/~cfadd/1150/05UCMGrav/Curve.html

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Physics: circles and inclines

Figure from: http://physatwes.com/SecondLawHonors.aspx Figure form: http://www.ux1.eiu.edu/~cfadd/1150/05UCMGrav/Curve.html

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Are we safe? Are we efficient?

  • Buggy’s Radius: buggyR = v^2/fr
  • Stay in track: trackR <= buggyR <= trackR+width
  • Maintain reasonable velocity: vMin <= v <= vMax

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Approach to problem

initial conditions -> ( /* track generation decision */ tRate = -inRate OR tRate = -outRate OR tRate=0 /* acceleration */ a := A if safe OR a := -B if safe OR a := 0 if safe /* ODEs - continuous evolution by physics */ )@loop invariant /* ensure final safety conditions */

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Model 1. The Helix

  • Constant slope
  • Radius can expand, shrink or remain the same
  • Two challenges:
  • How to test for safety?
  • How to ensure safe condition exists?

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Simple case: The circular track

  • Track Radius does not change
  • Can coast safely (a=0)

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Finding a safe decision

inner = trackR_1+outRate*t

  • uter = trackR_1+width+outRate*t

t radius

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Finding a safe decision: coasting?

inner = trackR_1+outRate*t

  • uter = trackR_1+width+outRate*t

t radius

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Finding a safe decision: accelerating?

buggyR = (v+A*t)^2/fr t radius

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Finding a safe decision: Defining Constraints

  • When the track is expanding:
  • Coast safely in the outer half
  • Accelerate safely in the inner one
  • When the track is shrinking:
  • Coast safely in the inner half
  • Brake in the outer half
  • When track is not changing:
  • Coast safely everywhere
  • Define formulas to ensure these

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Constraint: coasting on expanding track

  • Outer edge is moving away - can’t cause collision
  • Inner Edge will approach middle the faster

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Another challenge for constraints: Safe at the end, but not the middle!

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Another challenge for constraints: Safe at the end, but not the middle!

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t

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Constraint: accelerating on expanding track Outer edge: Inner Edge:

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Safety of Helix Model

  • Define 6 constraints for guaranteed safe decisions
  • Constraints use constants and remain true
  • Inequalities use extreme values - can be extended

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Model 2. The helix with hills

Track slope changes over time. Track radius stays the same. Safety: Don’t Crash! Track chooses new slope change, not new slope.

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Case 1. flat Slope

  • Slope = 0
  • Fg = G*cos(0) = G

Risks:

  • No new risks introduced by slope

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Case 2. Downhill

  • Fg > 0

Risks:

  • Crashing into the outer edge (high v)

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

DOwnhill safety Constraints added to ensure: Inner half of track means… acceleration is safe. Outer half of track means… deceleration is safe.

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

DOwnhill safety Constraints added to ensure: Inner half of track means… acceleration is safe. Outer half of track means… deceleration is safe.

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Case 3. uphill

  • Fg < 0

Risks:

  • Crashing into inner edge (low v)

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Uphill safety Constraints added to ensure: Inner half of track means… acceleration is safe. Outer half of track means… deceleration is safe.

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Uphill safety Constraints added to ensure: Inner half of track means… acceleration is safe. Outer half of track means… deceleration is safe.

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Model controls

  • Choices: A, -B, 0
  • Makes choice based on tests that

make sure we won’t crash Tests:

  • Crash into inner edge?
  • Crash into outer edge?

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Model 2 Summary

  • Makes decisions based on upcoming

slope changes

  • Constraints use constants
  • Constraints and tests ensure safety
  • Model is limited by conservative

constraints

  • Model doesn’t analyze Ffr change

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Future Directions

  • Better efficiency: find best path around track segment
  • More Diverse Tracks
  • Combine changes in slope and radius
  • Allow for straight segments
  • Looking ahead in tracks to find better paths
  • Less synchronized controls

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Summary & Significance

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R2D2 Goes to Buggy by Anastassia Kornilova & Emily Yeh

Thank you.

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