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Example 1: Aircraft Collision Avoidance

‘evader’ (control). ‘pursuer’ (disturbance). Example 1: Aircraft Collision Avoidance. Two identical aircraft at fixed altitude & speed:. y. v. y. u. x. v. d. y. x. y. Continuous Reachable Set. safety filter’s input modification. evader’s actual input. unsafe set.

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Example 1: Aircraft Collision Avoidance

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  1. ‘evader’ (control) ‘pursuer’ (disturbance) Example 1: Aircraft Collision Avoidance Two identical aircraft at fixed altitude & speed: y v y u x v d

  2. y x y Continuous Reachable Set

  3. safety filter’s input modification evader’s actual input unsafe set collision set pursuer evader evader’s desired input pursuer’s input Collision Avoidance Filter Simple demonstration • Pursuer: turn to head toward evader • Evader: turn to head right Movies…

  4. Collision Avoidance Control • http://www.cs.ubc.ca/~mitchell/ToolboxLS/

  5. Overapproximating Reachable Sets Exact: Approximate: Overapproximative reachable set: [Khrustalev, Varaiya, Kurzhanski] • Polytopic overapproximations for nonlinear games • Subsystem level set functions • “Norm-like” functions with identical strategies to exact [Hwang, Stipanović, Tomlin] ~1 sec on 700MHz Pentium III (vs 4 minutes for exact)

  6. Can separation assurance be automated? Requires provably safe protocols for aircraft interaction Must take into account: • Uncertainties in sensed information, in actions of the other vehicle • Potential loss of communication • Intent, or non-intent

  7. unsafe set with choice to maneuver or not? Example 2: Protocol design unsafe set without maneuver safe unsafe ? unsafe set with maneuver

  8. Protocol Safety Analysis safe with switch • Ability to choose maneuver start time further reduces unsafe set unsafe with or without switch safe without switch unsafe to switch

  9. controlled transition (s1) q5 qs forced transition safe at present always safe safe to s1 SAFE q3 q4 safe at present will become unsafe safe to s1 safe at present always safe unsafe to s1 q1 q2 qu safe at present will become unsafe unsafe to s1 unsafe at present will become unsafe unsafe to s1 UNSAFE Implementation: a finite automaton • It can be easier to analyze discrete systems than continuous: use reachable set information to abstract away continuous details q5 qu q3 q4 q2 q1

  10. Example 3: Closely Spaced Approaches Photo courtesy of Sharon Houck

  11. Example 3: Closely Spaced Approaches EEM Maneuver 1: accelerate EEM Maneuver 2: turn 45 deg, accelerate EEM Maneuver 3: turn 60 deg [Rodney Teo] evader

  12. Sample Trajectories Segment 2 Segment 3 Segment 1

  13. Tested on the Stanford DragonFly UAVs Dragonfly 2 Dragonfly 3 Ground Station

  14. Tested at Moffett Federal Airfield Accelerate and turn EEM Put video here North (m) East (m) Separation distance (m) EEM alert Above threshold time (s)

  15. Tested at Moffett Federal Airfield Coast and turn EEM Put video here North (m) East (m) Separation distance (m) EEM alert Above threshold time (s)

  16. Tested at Edwards Air Force Base T-33 Cockpit [DARPA/Boeing SEC Final Demonstration: F-15 (blunderer), T-33 (evader)]

  17. Photo courtesy of Sharon Houck; Tests conducted with Chad Jennings

  18. Implementation: Display design courtesy of Chad Jennings, Andy Barrows, David Powell R. Teo’s Blunder Zone is shown by the yellow contour Red Zone in the green tunnel is the intersection of the BZ with approach path. The Red Zone corresponds to an assumed 2 second pilot delay. The Yellow Zone corresponds to an 8 second pilot delay

  19. R. Teo’s Blunder Zone is shown by the yellow contour Red Zone in the green tunnel is the intersection of the BZ with approach path. The Red Zone corresponds to an assumed 2 second pilot delay. The Yellow Zone corresponds to an 8 second pilot delay

  20. Map View showing a blunder The BZ calculations are performed in real time (40Hz) so that the contour is updated with each video frame.

  21. Map View with Color Strips The pilots only need to know which portion of their tunnel is off limits. The color strips are more efficient method of communicating the relevant extent of the Blunder zone

  22. Example 4: Aircraft Autolander Aircraft must stay within safe flight envelope during landing: • Bounds on velocity (), flight path angle (), height () • Control over engine thrust (), angle of attack (), flap settings • Model flap settings as discrete modes • Terms in continuous dynamics depend on flap setting body frame wind frame inertial frame

  23. Autolander: Synthesizing Control For states at the boundary of the safe set, results of reach-avoid computation determine • What continuous inputs (if any) maintain safety • What discrete jumps (if any) are safe to perform • Level set values and gradients provide all relevant data

  24. TOGA TOGA flaps retracted maximum thrust flaps retracted maximum thrust flare flare flaps extended minimum thrust flaps extended minimum thrust rollout rollout flaps extended reverse thrust flaps extended reverse thrust slow TOGA flaps extended maximum thrust Application to Autoland Interface • Controllable flight envelopes for landing and Take Off / Go Around (TOGA) maneuvers may not be the same • Pilot’s cockpit display may not contain sufficient information to distinguish whether TOGA can be initiated existing interface controllable TOGA envelope intersection revised interface controllable flare envelope

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