Interaction with Route Optimizers Oliver Turnbull and Arthur - - PowerPoint PPT Presentation

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Interaction with Route Optimizers Oliver Turnbull and Arthur - - PowerPoint PPT Presentation

Dec 01, 2022 555 likes •1.14k views

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

slide-1
SLIDE 1

Examples of Supervisory Interaction with Route Optimizers

Oliver Turnbull and Arthur Richards

  • liver.turnbull@bristol.ac.uk

arthur.richards@bristol.ac.uk

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SLIDE 2

Overview

  • The SESAR Concept of Operations calls for:

“Extensive use of automation support to reduce

  • perator task load, but in which controllers remain in

control as managers”

  • Much work has been performed on trajectory
  • ptimization
  • 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

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SLIDE 3

Overview

  • How do we facilitate supervisor

interaction?

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SLIDE 4

Overview

  • How do we facilitate supervisor

interaction?

Sense Constraints

  • What are sense constraints?
  • Why are they useful?
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SLIDE 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

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SLIDE 6

Assumptions

  • 4-D trajectories (RBTs)
  • Trajectories updated via data-link
  • Free routing
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SLIDE 7

MILP Obstacle Avoidance

  • Approximate obstacle with multiple

avoidance constraints

4 3 1 2 a1 a2 Dy Dx

   

) ( : , , 1 , , , 1 ) , ( ) , ( ) , ( ) , ( ) , ( ) , ( ) , ( ) , (

2 1 2 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2

k k N k N k D k a r k a r D k a r k a r D k a r k a r D k a r k a r

t t y y y y y y x x x x x x

               

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SLIDE 8

MILP Obstacle Avoidance

  • Approximate obstacle with multiple

avoidance constraints

  • Define “binary” variables that

enable each avoidance constraint to be relaxed

4 3 1 2 a1 a2 Dy Dx

   

) ( : , , 1 , , , 1 ) 4 , , , , ( ) , ( ) , ( ) 3 , , , , ( ) , ( ) , ( ) 2 , , , , ( ) , ( ) , ( ) 1 , , , , ( ) , ( ) , (

2 1 2 1 2 1 2 1 1 1 1 2 2 1 2 1 1 1 1 2 2 1 2 1 1 1 1 2 2 1 2 1 1 1 1 2

k k N k N k k k a a Mb D k a r k a r k k a a Mb D k a r k a r k k a a Mb D k a r k a r k k a a Mb D k a r k a r

t t a y y y a y y y a x x x a x x x

                   

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SLIDE 9

MILP Obstacle Avoidance

  • Approximate obstacle with multiple

avoidance constraints

  • Define “binary” variables that enable each

avoidance constraint to be relaxed

  • Require at least one of the constraints to

be enforced

4 3 1 2 a1 a2 Dy Dx

   

) ( : , , 1 , , , 1 3 ) , , , , ( ) 4 , , , , ( ) , ( ) , ( ) 3 , , , , ( ) , ( ) , ( ) 2 , , , , ( ) , ( ) , ( ) 1 , , , , ( ) , ( ) , (

2 1 2 1 4 1 2 1 2 1 2 1 2 1 1 1 1 2 2 1 2 1 1 1 1 2 2 1 2 1 1 1 1 2 2 1 2 1 1 1 1 2

k k N k N k i k k a a b k k a a Mb D k a r k a r k k a a Mb D k a r k a r k k a a Mb D k a r k a r k k a a Mb D k a r k a r

t t i a a y y y a y y y a x x x a x x x

                  

 

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SLIDE 10

   

) ( : , , 1 , , , 1 1 ) 3 , , , , ( 3 ) , , , , ( ) 4 , , , , ( ) , ( ) , ( ) 3 , , , , ( ) , ( ) , ( ) 2 , , , , ( ) , ( ) , ( ) 1 , , , , ( ) , ( ) , (

2 1 2 1 2 1 2 1 4 1 2 1 2 1 2 1 2 1 1 1 1 2 2 1 2 1 1 1 1 2 2 1 2 1 1 1 1 2 2 1 2 1 1 1 1 2

k k N k N k k k a a b i k k a a b k k a a Mb D k a r k a r k k a a Mb D k a r k a r k k a a Mb D k a r k a r k k a a Mb D k a r k a r

t t a i a a y y y a y y y a x x x a x x x

                   

 

MILP Sense Constraints

  • We can force a trajectory to pass to
  • ne side of an obstacle by

“freezing” the appropriate binary:

4 3 1 2 a1 a2

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SLIDE 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

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SLIDE 12

Sense Constraints in ATC

F002 over F001 (Unconstrained) F001 over F002

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SLIDE 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

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SLIDE 14

Sense Constraints in ATC

F002 ahead of F001 (Unconstrained; 2D) F002 behind F001

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SLIDE 15

Sense Constraints in ATC

F002 ahead of F001 (Unconstrained) F002 behind F001

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SLIDE 16

Sense Constraints in ATC

F002 ahead of F001 (Unconstrained) F002 behind F001

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SLIDE 17

Sense Constraints in ATC

F002 ahead of F001 (Unconstrained) F002 behind F001

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SLIDE 18

Sense Constraints in ATC

F002 ahead of F001 (Unconstrained) F002 behind F001

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SLIDE 19

Multi-Sector Controller (MSC)

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SLIDE 20

MSC - Input

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SLIDE 21

MSC - Input

  • 3 pairs of conflicting aircraft
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SLIDE 22

MSC - Input

  • 3 pairs of conflicting aircraft
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SLIDE 23

MSC - Input

  • 3 pairs of conflicting aircraft
  • Select constraints
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SLIDE 24

MSC – Input

  • 3 pairs of conflicting aircraft
  • Select constraints
  • Relative Cost history
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SLIDE 25

MSC – Input

  • 3 pairs of conflicting aircraft
  • Select constraints
  • Relative Cost history
  • Highlight specific aircraft
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SLIDE 26

MSC - Input

  • 3 pairs of conflicting aircraft
  • Select constraints
  • Relative Cost history
  • Highlight specific aircraft
  • Generate Plans
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SLIDE 27

MSC – Step 1

  • Conflict free trajectories in green
  • Original trajectories in red
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SLIDE 28

MSC – Step 1

  • Highlight specific aircraft
  • Alternative cost functions
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SLIDE 29

MSC – Step 1

  • Trajectories now reach

destinations earlier

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SLIDE 30

MSC – Step 2

  • Request horizontal resolution
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SLIDE 31

MSC – Step 2

  • Request horizontal resolution
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SLIDE 32

MSC – Step 2

  • Request horizontal resolution
  • Increased cost (expected)
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SLIDE 33

MSC – Step 3

  • Vertical resolution
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SLIDE 34

MSC – Step 3

  • Vertical resolution
  • F042 over F036
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SLIDE 35

MSC – Step 3

  • Vertical resolution
  • F042 over F036
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SLIDE 36

MSC – Step 4

  • F036 over F042
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SLIDE 37

MSC – Step 4

  • F036 over F042
  • Large increased cost
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SLIDE 38

MSC – Step 5

  • F036 over F042
  • Large increased cost
  • F039 over F062
  • Small increased cost
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SLIDE 39

MSC – Step 5

  • F036 over F042
  • Large increased cost
  • F039 over F062
  • Small increased cost
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SLIDE 40

MSC – Step 5

  • F036 over F042
  • Large increased cost
  • F039 over F062
  • Small increased cost
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SLIDE 41

MSC – Step 6

  • F036 over F042
  • Large increased cost
  • F039 over F062
  • Small increased cost
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SLIDE 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

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SLIDE 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

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SLIDE 44

Collocation with Polar Sets

R y x 1/R v1 v2

  • First we find a point, y, that lies within the polar

set of the obstacle:

  • Where y becomes a decision variable

1 R y x y R x

T

   

Cartesian Polar

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SLIDE 45

Collocation with Polar Sets

 

t

  • bs
  • bs

T

N t t t t t t , , 2 1 ) ( ) ( ) (              r r y

  • Next we ensure that the aircraft remains outside of

the obstacle (within the polar set) at all time-steps:

  • First we find a point, y, that lies within the polar

set of the obstacle:

1 R y x y R x

T

   

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SLIDE 46

Polar Set Sense Constraints

  • Equivalent to fixing MILP binaries
  • Sense constraints imply removing vertices from the polar set:
  • Alternatively we can restrict the location of the point ye(t) within the

polar set, eg to cause a1 to pass under an obstacle we would require:

 

t

N a y , , 2 ) , 3 , (

1 1 1

     

Cartesian Polar

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SLIDE 47

4-D Obstacle

  • 2 closed sectors
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SLIDE 48

4-D Obstacle

  • 2 closed sectors
  • Trajectory avoids closed

sector

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SLIDE 49

4-D Obstacle

  • 2 closed sectors
  • Trajectory avoids closed

sector

  • Sector re-opened
  • Trajectory resumes shortest

path (through sector)

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SLIDE 50

Collision Avoidance

  • Planned for F001 (cyan

line) – represented by series

  • f temporal obstacles
  • Planned for F002 (cyan

line)

  • Add F003 (blue-dotted line)
  • Allows planning over

independent time-scales

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SLIDE 51

Collision Avoidance

  • Planned for first aircraft

(cyan line) – represented by series of temporal obstacles

  • Planned for F002 (cyan

line)

  • Add third aircraft (F003)
  • Require F003 to pass under

F002

  • Horizontal separation of

F001

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SLIDE 52

Collision Avoidance

  • Planned for first aircraft

(cyan line) – represented by series of temporal obstacles

  • Planned for F002 (cyan

line)

  • Add third aircraft (F003)
  • Require F003 to pass under

F002

  • Horizontal separation of

F001

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SLIDE 53

Collision Avoidance

  • Planned for first aircraft

(cyan line) – represented by series of temporal obstacles

  • Planned for F002 (cyan

line)

  • Add third aircraft (F003)
  • Require F003 to pass under

F002

  • Horizontal separation of

F001

  • Vertical separation (F003

under F002)

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SLIDE 54

Collision Avoidance

  • Planned for first aircraft

(cyan line) – represented by series of temporal obstacles

  • Planned for F002 (cyan

line)

  • Add third aircraft (F003)
  • Require F003 to pass under
  • ther aircraft
  • Horizontal separation of

F001

  • Vertical separation (F003

under F002)

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SLIDE 55

Collision Avoidance

  • Planned for first aircraft

(cyan line) – represented by series of temporal obstacles

  • Planned for F002 (cyan

line)

  • Add third aircraft (F003)
  • Require F003 to pass under
  • ther aircraft
  • Horizontal separation of

F001

  • Vertical separation (F003

under F002)

  • Alternative sense (F003
  • ver F002)
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SLIDE 56

Conclusion

  • Demonstrated two models that incorporate

sense constraints

  • Allows intuitive human input in terms of high-

level decision making

  • While still enabling the optimizer to do what it

does best: design efficient 4D trajectories subject to avoidance constraints

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SLIDE 57

Thanks!