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.

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

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

16. Resolution of the grid means loss of precision

19. Resulting Map

20. Dynamic Obstacles, Static Maps

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…