Example 1 aircraft collision avoidance
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‘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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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


Continuous reachable set

y

x

y

Continuous Reachable Set


Collision avoidance filter

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…


Collision avoidance control

Collision Avoidance Control

  • http://www.cs.ubc.ca/~mitchell/ToolboxLS/


Overapproximating reachable sets

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)


Can separation assurance be automated

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


Example 2 protocol design

unsafe set with choice

to maneuver or not?

Example 2: Protocol design

unsafe set without maneuver

safe

unsafe

?

unsafe set with maneuver


Protocol safety analysis

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


Implementation a finite automaton

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


Example 3 closely spaced approaches

Example 3: Closely Spaced Approaches

Photo courtesy of Sharon Houck


Example 3 closely spaced approaches1

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


Sample trajectories

Sample Trajectories

Segment 2

Segment 3

Segment 1


Tested on the stanford dragonfly uavs

Tested on the Stanford DragonFly UAVs

Dragonfly 2

Dragonfly 3

Ground Station


Tested at moffett federal airfield

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)


Tested at moffett federal airfield1

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)


Tested at edwards air force base

Tested at Edwards Air Force Base

T-33 Cockpit

[DARPA/Boeing SEC Final Demonstration:

F-15 (blunderer), T-33 (evader)]


Example 1 aircraft collision avoidance

Photo courtesy of Sharon Houck;

Tests conducted with Chad Jennings


Example 1 aircraft collision avoidance

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


Example 1 aircraft collision avoidance

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


Example 1 aircraft collision avoidance

Map View showing a blunder

The BZ calculations are performed in real time (40Hz) so that the contour is updated with each video frame.


Example 1 aircraft collision avoidance

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


Example 4 aircraft autolander

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


Autolander synthesizing control

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


Application to autoland interface

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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