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Examples of Supervisory Interaction with Route Optimizers Oliver Turnbull and Arthur Richards oliver.turnbull@bristol.ac.uk arthur.richards@bristol.ac.uk Overview The SESAR Concept of Operations calls for: Extensive use of automation


  1. Examples of Supervisory Interaction with Route Optimizers Oliver Turnbull and Arthur Richards oliver.turnbull@bristol.ac.uk arthur.richards@bristol.ac.uk

  2. Overview • The SESAR Concept of Operations calls for: “Extensive use of automation support to reduce operator task load, but in which controllers remain in control as managers” • Much work has been performed on trajectory optimization • Rarely are humans included in the trajectory design process • Part of SUPEROPT project whose goal is to: “Develop tools to facilitate interactions between humans and trajectory optimizers” • Trajectory optimization can play a key role in automation support

  3. Overview • How do we facilitate supervisor interaction?

  4. Overview • How do we facilitate supervisor interaction? Sense Constraints • What are sense constraints? • Why are they useful?

  5. Outline 1. MILP – Fast – Global optimum – Linearized – 3D dynamics model – Extension of sense constraints to 3D 2. Collocation with Polar Sets – Nonlinear model – More general problems, eg noise as cost – Explicit modelling of time – 4D obstacles 3. Conclusions

  6. Assumptions • 4-D trajectories (RBTs) • Trajectories updated via data-link • Free routing

  7. MILP Obstacle Avoidance • Approximate obstacle with multiple avoidance constraints 4 D y a 1 D x a 2 3   r a k r a k D ( , ) ( , ) x 2 1 x 1 1 x    r ( a , k ) r ( a , k ) D x 2 1 x 1 1 x 1 2   r a k r a k D ( , ) ( , ) y 2 1 y 1 1 y    r ( a , k ) r ( a , k ) D y 2 1 y 1 1 y           k 1 , , N , k 1 , , N : ( k k ) 1 t 2 t 1 2

  8. MILP Obstacle Avoidance • Approximate obstacle with multiple avoidance constraints 4 • Define “binary” variables that D y enable each avoidance constraint a 1 D x a 2 to be relaxed 3    r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 1 ) x 2 1 x 1 1 x a 1 2 1 2     r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 2 ) 1 2 x x x a 2 1 1 1 1 2 1 2    r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 3 ) y 2 1 y 1 1 y a 1 2 1 2     r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 4 ) y 2 1 y 1 1 y a 1 2 1 2           k 1 , , N , k 1 , , N : ( k k ) 1 t 2 t 1 2

  9. MILP Obstacle Avoidance • Approximate obstacle with multiple avoidance constraints 4 • Define “binary” variables that enable each avoidance constraint to be relaxed D y a 1 D x • Require at least one of the constraints to a 2 be enforced 3    r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 1 ) x 2 1 x 1 1 x a 1 2 1 2     r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 2 ) x x x a 2 1 1 1 1 2 1 2 1 2    r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 3 ) y 2 1 y 1 1 y a 1 2 1 2     r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 4 ) y 2 1 y 1 1 y a 1 2 1 2 4   b ( a , a , k , k , i ) 3 a 1 2 1 2  i 1           k 1 , , N , k 1 , , N : ( k k ) 1 t 2 t 1 2

  10. MILP Sense Constraints • We can force a trajectory to pass to one side of an obstacle by 4 “freezing” the appropriate binary: a 1    r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 1 ) a 2 x 2 1 x 1 1 x a 1 2 1 2     r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 2 ) 3 x 2 1 x 1 1 x a 1 2 1 2    r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 3 ) y 2 1 y 1 1 y a 1 2 1 2     r ( a , k ) r ( a , k ) D Mb ( a , a , k , k , 4 ) 1 2 y 2 1 y 1 1 y a 1 2 1 2 4   b ( a , a , k , k , i ) 3 a 1 2 1 2  i 1  b ( a , a , k , k , 3 ) 1 a 1 2 1 2           k 1 , , N , k 1 , , N : ( k k ) 1 t 2 t 1 2

  11. Sense Constraints in ATC Three Requirements: 1. Binaries to define relative position 2. 3-D dynamics model: derived from BADA 3. Resolve class of problem: Fix in 1 or more dimensions. – The problem is to resolve only in a certain way – Other dimensions should not change

  12. Sense Constraints in ATC F001 over F002 F002 over F001 (Unconstrained)

  13. Sense Constraints in ATC • Vertical: • Common notion of up/down • Horizontal • Direction (left/right) relative to heading • Define as ahead/behind • Enforced by applying the constraints at the present time and all future time-steps

  14. Sense Constraints in ATC F002 ahead of F001 F002 behind F001 (Unconstrained; 2D)

  15. Sense Constraints in ATC F002 ahead of F001 F002 behind F001 (Unconstrained)

  16. Sense Constraints in ATC F002 ahead of F001 F002 behind F001 (Unconstrained)

  17. Sense Constraints in ATC F002 ahead of F001 F002 behind F001 (Unconstrained)

  18. Sense Constraints in ATC F002 ahead of F001 F002 behind F001 (Unconstrained)

  19. Multi-Sector Controller (MSC)

  20. MSC - Input

  21. MSC - Input • 3 pairs of conflicting aircraft

  22. MSC - Input • 3 pairs of conflicting aircraft

  23. MSC - Input • 3 pairs of conflicting aircraft • Select constraints

  24. MSC – Input • 3 pairs of conflicting aircraft • Select constraints • Relative Cost history

  25. MSC – Input • 3 pairs of conflicting aircraft • Select constraints • Relative Cost history • Highlight specific aircraft

  26. MSC - Input • 3 pairs of conflicting aircraft • Select constraints • Relative Cost history • Highlight specific aircraft • Generate Plans

  27. MSC – Step 1 • Conflict free trajectories in green • Original trajectories in red

  28. MSC – Step 1 • Highlight specific aircraft • Alternative cost functions

  29. MSC – Step 1 • Trajectories now reach destinations earlier

  30. MSC – Step 2 • Request horizontal resolution

  31. MSC – Step 2 • Request horizontal resolution

  32. MSC – Step 2 • Request horizontal resolution • Increased cost (expected)

  33. MSC – Step 3 • Vertical resolution

  34. MSC – Step 3 • Vertical resolution • F042 over F036

  35. MSC – Step 3 • Vertical resolution • F042 over F036

  36. MSC – Step 4 • F036 over F042

  37. MSC – Step 4 • F036 over F042 • Large increased cost

  38. MSC – Step 5 • F036 over F042 • Large increased cost • F039 over F062 • Small increased cost

  39. MSC – Step 5 • F036 over F042 • Large increased cost • F039 over F062 • Small increased cost

  40. MSC – Step 5 • F036 over F042 • Large increased cost • F039 over F062 • Small increased cost

  41. MSC – Step 6 • F036 over F042 • Large increased cost • F039 over F062 • Small increased cost

  42. MILP Summary • Well established for trajectory optimization – Fast (typically < 1 sec) – Robust – Globally optimal • Extended to allow input of user preference for conflict resolution • Assumptions – Linearized dynamics/constraints/cost

  43. Collocation with Polar Sets • Generalization to a nonlinear model is a logical step – Collocation method to model aircraft dynamics – Polar sets for obstacle avoidance

  44. Collocation with Polar Sets • First we find a point, y , that lies within the polar    set of the obstacle: T x R y x 1  0 y R • Where y becomes a decision variable 1/R R v 2 y v 1 x Cartesian Polar

  45. Collocation with Polar Sets • First we find a point, y , that lies within the polar    set of the obstacle: T x R y x 1  0 y R • Next we ensure that the aircraft remains outside of the obstacle (within the polar set) at all time-steps:  r   ( t ) ( t )   r      obs T  ( t ) 1 t 2 , , N   y  t   t t obs

  46. Polar Set Sense Constraints • Equivalent to fixing MILP binaries • Sense constraints imply removing vertices from the polar set: Cartesian Polar • Alternatively we can restrict the location of the point y e (t) within the polar set, eg to cause a 1 to pass under an obstacle we would require:         y a N ( , 3 , ) 0 2 , , 1 1 1 t

  47. 4-D Obstacle • 2 closed sectors

  48. 4-D Obstacle • 2 closed sectors • Trajectory avoids closed sector

  49. 4-D Obstacle • 2 closed sectors • Trajectory avoids closed sector • Sector re-opened • Trajectory resumes shortest path (through sector)

  50. Collision Avoidance • Planned for F001 (cyan line) – represented by series of temporal obstacles • Planned for F002 (cyan line) • Add F003 (blue-dotted line) • Allows planning over independent time-scales

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