Control Strategies for Restricting the Navigable Airspace of Commercial Aircraft

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Control Strategies for Restricting the Navigable
Airspace of Commercial Aircraft

• Adam Cataldo and
• Edward Lee

NASA JUP Meeting 28 March 2003 Stanford, CA
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Outline

• Soft Walls Problem
• Solution with Level Set Methods
• Moving Forward

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Softwalls

• Carry on-board a 3-D database with
  no-fly-zones
• Enforce no-fly zones using on-board avionics
  (aviation electronics)
• Non-networked, non-hackable

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Design Objectives
Maximize Pilot Authority!
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Design Objectives

• Apply zero bias when possible
• For all pilot actions, controller can still
  prevent entry into the no-fly zone
• Bias pilots input with a control input
• Do not attenuate pilot control
• Do not make instantaneous changes in bias
• Give pilot maximum authority
• Can always turn away from the no-fly zone
• Prevent controls from saturating

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Unsaturated Control
Even under the maximum control bias, the pilot
can make a sharper turn away from the no-fly zone
No-fly zone
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Sailing Analogy Weather Helm
with turned rudder
with straight rudder
force of the wind on the sails
turned rudder keeps the trajectory straight
Even with weather helm, the craft responds to
fine-grain control as expected.
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Discussion

• Reducing pilot control is dangerous
• reduces ability to respond to emergencies

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Is There Any Aircraft Emergency that Justifies
Trying to Land on Fifth Ave?
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Discussion

• Reducing pilot control is dangerous
• reduces ability to respond to emergencies
• There is no override
• switch in the cockpit

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No-Fly Zone with Harsher Enforcement
There is no override in the cockpit that allows
pilots to fly through this.
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Objections

• Reducing pilot control is dangerous
• reduces ability to respond to emergencies
• There is no override
• switch in the cockpit
• Localization technology could fail
• GPS can be jammed

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Localization Backup
Inertial navigation provides backup to GPS. Drift
implies that when GPS fails, aircraft has limited
time to safely approach urban airports.
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Objections

• Reducing pilot control is dangerous
• reduces ability to respond to emergencies
• There is no override
• switch in the cockpit
• Localization technology could fail
• GPS can be jammed
• Deployment could be costly
• Software certification? Retrofit older aircraft?

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Deployment

• Fly-by-wire aircraft
• a software change
• Older aircraft
• autopilot level
• Phase in
• prioritize airports

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4 billion development effort
40-50 system integration validation cost
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Objections

• Reducing pilot control is dangerous
• reduces ability to respond to emergencies
• There is no override
• switch in the cockpit
• Localization technology could fail
• GPS can be jammed
• Deployment could be costly
• how to retrofit older aircraft?
• Complexity
• software certification

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Not Like Air Traffic Control
This seems entirely independent of air traffic
control, and could complement safety methods
deployed there. Self-contained on a single
aircraft.
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Objections

• Reducing pilot control is dangerous
• reduces ability to respond to emergencies
• There is no override
• switch in the cockpit
• Localization technology could fail
• GPS can be jammed
• Deployment could be costly
• how to retrofit older aircraft?
• Deployment could take too long
• software certification
• Fully automatic flight control is possible
• throw a switch on the ground, take over plane

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UAV Technology
Northrop Grumman argues that the Global Hawk UAV
system can be dropped-in to passenger airliners.
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Potential Problems with Ground Control

• Human-in-the-loop delay on the ground
• authorization for takeover
• delay recognizing the threat
• Security problem on the ground
• hijacking from the ground?
• takeover of entire fleet at once?
• coup detat?
• Requires radio communication
• hackable
• jammable

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Outline

• Soft Walls Problem
• Solution with Level Set Methods
• Backwards Reachable Set in Soft Walls
• Finding the Backwards Reachable Set with Level
  Set Methods
• Control from Implicit Surface Function
• Moving Forward

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Backwards Reachable Sets(Tomlin, Lygeros, Sastry)

• We model the aircraft the dynamics as
• where x is the state, uc is the control input,
  and up is the pilot input
• Let X be the set of all possible states
• Let the target set G(0) describe the no-fly zone,
  where

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Backwards Reachable Sets(Tomlin, Lygeros, Sastry)

• The backwards reachable set is the set of states
  for which safety cannot be guaranteed for all
  possible disturbances

Target Set (unsafe states)
Reachable set
Safe States
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Backwards Reachable Sets(Tomlin, Lygeros, Sastry)

• We denote the backwards reachable set G
• The backwards reachable set is the set of states
  such that for all controls uc there exists a
  disturbance up which drives the state into the
  target set
• For any state outside the reachable set, we can
  find a control input that can guarantee the state
  is kept outside the reachable set

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Backwards Reachable Sets(Tomlin, Lygeros, Sastry)

• The set G(t) represents the set of states such
  that for all controls uc there exists a
  disturbance up which drives the state into the
  target set in time t or less

G(t1)
G(t2)
G G(?)
G(0)
0 lt t1 lt t2 lt ?
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Finding the Reachable Set(Mitchell, Tomlin)

• Given the target set G(0), we create a cost
  function g(x)
• g(x) lt 0 if and only if x ? G(0)

g(x)
Go
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Finding the Reachable Set(Mitchell, Tomlin)

• We solve for ?(x,t) from the Hamilton-Jacobi-Isaac
  s PDE
• where
• Then ?(x,t) lt 0 if and only if x in G(t)

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Finding the Reachable Set(Mitchell, Tomlin)

• Solving for ?(x,?) gives us G G(?) since ?(x,t)
  lt 0 if and only if x in G(t)
• We can solve ?(x,?) numerically using level-set
  PDE techniques

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Control from Implicit Surface

• Make g(x) so that its magnitude is the distance
  from the target set boundary
• Then g(x) is a signed distance function since it
  is positive outside the target set and negative
  inside the target set
• We can compute ?(x,?) such that it is also a
  signed distance function

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Control from Implicit Surface

• If ?(x,?) is decreasing, the aircraft is
  approaching the reacable set
• We choose a bias such that when ?(x,?) 0
• We start biasing the aircraft at the first state
  which satisfies ?(x,?) d
• We increase the bias as ?(x,?) approaches 0

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Demo
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Outline

• Soft Walls Problem
• Solution with Level Set Methods
• Backwards Reachable Set in Soft Walls
• Finding the Backwards Reachable Set with Level
  Set Methods
• Control from Implicit Surface Function
• Moving Forward
• Dynamics Model
• Simulation Interface
• Prototype

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Dynamics Model

• We used this simple dynamics model, because the
  level-set computations work only for a small
  dimension

V
?
pilot input
control input
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Dynamics Model (Menon, Sweriduk, Sridhar)

• A more realistic model
• Thrust T
• Drag D
• Mass m
• Flight Path Angle ?
• Bank Angle ?
• Fuel Flow Rate Q
• Lift L
• Load Factor n
• Height h

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Dynamics Model (Menon, Sweriduk, Sridhar)
rudder and ailerons
control input
elevator
throttle
pilot input

• We are considering control strategies that scale
  better to the higher dimensions of this model

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Simulation Interface

• Soft Walls interface for Microsoft Flight
  Simulator
• Real-time controller created in Ptolemy II

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Prototype(Richard Murray, in conjunction with
SEC)

• Hovercraft with controlled by two fans
• Test bed for Soft Walls algorithm
• Remote driver can steer craft while a control
  bias prevents collision with a wall

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Acknowledgements

• Ian Mitchell
• Iman Ahmadi
• Zhongning Chen
• Xiaojun Liu
• Steve Neuendorffer
• Shankar Sastry
• Clair Tomlin