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Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
Friday Seminar: A* Search for Collision Avoidance
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Friday Seminar: A* Search for Collision Avoidance

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In the ever-expanding world of unmanned flight, smaller, less expensive UAVs are being used for everything from search and rescue to military operations. In such situations, the working airspace can …

In the ever-expanding world of unmanned flight, smaller, less expensive UAVs are being used for everything from search and rescue to military operations. In such situations, the working airspace can become crowded and pose a danger to the UAVs themselves. To prevent collisions, the A* search algorithm can be used to dynamically plan paths. We will discuss the A* algorithm, its previous uses in path planning, and how it is being used for dynamic collision avoidance.

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Transcript

  • 1. A* Search for UAV Collision Avoidance
    Thomas Crescenzi, Tyler Young,
    and Andrew Kaizer
  • 2. A* Overview
    A* Easy:
  • 3. A* Overview
    A* with Planes (Obstacles):
  • 4. Everything You Always Wanted to Know About Sparse A*
    (*But Were Afraid to Ask)
    Searching for a best path is NP-complete
    At worst, exponential time complexity
    A good heuristic, though, can reduce this to polynomial time
  • 5. Simplifying the Search
    Can add the following constraints:
    Minimum route leg length
    Maximum turning angle
    Total route distance
    Fixed heading on approach to target
    . . . to speed up search without losing optimality.
  • 6. Simplifying the Search
  • 7. Simplifying the Search
    Can add the following constraints:
    Maximum queue depth
    Weighted estimates
    . . . to speed up search, at the risk of getting a (slightly?) sub-optimal solution.
  • 8. Simplifying the Search
  • 9. Predicting Planes
    • Assumptions:
    • 10. Planes will stay moving in a line to their goal
    • 11. Planes exist in a world of grids
    • 12. Planes can turn on a dime, instantaneously
    • 13. Obviously those are some big assumptions, so how to address them?
  • Planes Will Move in a Line
    • Surprisingly enough the planes, with our A* algorithm, will tend to move in lines.
    • 14. As such, this is actually not much of an issue
  • Straight Lines?
  • 15. Planes Exist in a World of Grids
    • Sadly, the Earth is curved
    • 16. Resolution of the grid means loss of precision
    • 17. To account for this, a sort of “probability field” is generated around the plane
  • Planes Can Turn on a Dime
    • As of now, we don't even know what the turning radius is
    • 18. This will be restricted in the later editions of plane prediction
  • 7 Easy Steps to Plane Prediction
    Find a straight line to the goal
    Find the angle to the goal
    Find the closest “straight line” to that angle
    Find the offset to that line
    Place offset in the square following the line
    Place remainder in the next closest square
    Branch back to step 1
  • 19. Resulting Map
  • 20. Dynamic Obstacles, Static Maps
  • 21.
  • 22. A* Analysis
    Two sets: 20x20 Grid and 46x42
    Heuristics
    Modified Manhattan/Walking Distance
    Chebyshev Distance (Minkowski: L∞)
    Euclidean Distance
    Terminology
    Stalls
    Stalls avoided
  • 23. 20 x 20 Stalls
  • 24. 46 x 42 Stalls
  • 25. Stalls: What Do We Know?
    Stalls are predictable by:
    NUM_OF_PLANES
    SPACE_OF_GRID
    The probability of a stall increases dramatically as we add planes into a smaller area…
  • 26. 20 x 20 Stalls Avoided
  • 27. 46 x 42 Stalls Avoided
  • 28. Stall Avoidance: What do we know?
    Stall avoidance is predictable by:
    NUM_OF_PLANES
    SPACE_OF_GRID
    Stall avoidance is a precursor to collision avoidance—avoiding a potential stall means you also avoid a potential collision
    Counter-intuitive: Euclidean needed to avoid the least stalls; is it the best heuristic?
  • 29. 20x20 Optimality Difference
  • 30. 46x42 Optimality Difference
  • 31. Optimality Difference: WDWK?
    Euclidean problems
    More planes = Less optimal under basic heuristics
    Goal: Create a heuristic that will be closer to the optimal line (0 difference)
  • 32. 20x20 Way Points per Plane
  • 33. 46x42 Way Points per Plane
  • 34. WP/P: What do we know?
    Each plane added beyond the “safe” number starts to decrease our waypoint realization
    Implies that a very basic heuristic that only avoids collisions immediately is prone to certain problems…

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