Control Strategies for Restricting the Navigable Airspace of Commercial Aircraft Adam Cataldo and Edward Lee NASA JUP Meeting 28 March 2003 Stanford, CA.

Control Strategies for Restricting the Navigable Airspace of Commercial Aircraft

Adam Cataldo andEdward Lee

NASA JUP Meeting28 March 2003Stanford, CA

Outline

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

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

Design Objectives

Maximize Pilot Authority!

Design Objectives

• Apply zero bias when possible– For all pilot actions, controller can still

prevent entry into the no-fly zone

• Bias pilot’s 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

Unsaturated Control

No-flyzone

Even under the maximum control bias,the pilot can make a sharper turn away from the no-fly zone

Sailing Analogy – Weather Helm

force of the wind on the sails

turned rudder keeps the trajectory straight

with straight rudder

with turned rudder

Even with weather helm, the craft responds to fine-grain control as expected.

Discussion

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

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

Discussion

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

• There is no override– switch in the cockpit

No-Fly Zone with Harsher Enforcement

There is no override in the cockpit that allows pilots to fly through this.

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

Localization Backup

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

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?

Deployment

• Fly-by-wire aircraft– a software change

• Older aircraft– autopilot level

• Phase in– prioritize airports

$4 billion development effort40-50% system integration & validation cost

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

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.

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

UAV Technology

Northrop Grumman argues that the Global Hawk UAV system can be dropped-in to passenger airliners.

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 d’etat?

• Requires radio communication– hackable– jammable

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

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

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

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

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(0)G(t1)G(t2)G = G()

0 < t1 < t2 <

Finding the Reachable Set(Mitchell, Tomlin)

• Given the target set G(0), we create a cost function g(x)

• g(x) <= 0 if and only if x G(0)

Go

g(x)

Finding the Reachable Set(Mitchell, Tomlin)

• We solve for (x,t) from the Hamilton-Jacobi-Isaacs PDE

where

• Then (x,t) <= 0 if and only if x in G(t)

Finding the Reachable Set(Mitchell, Tomlin)

• Solving for (x,) gives us G = G() since (x,t) <= 0 if and only if x in G(t)

• We can solve (x,) numerically using level-set PDE techniques

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

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

Demo

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

Dynamics Model

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

V

pilot input control input

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

Dynamics Model (Menon, Sweriduk, Sridhar)

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

rudder and ailerons

elevator

throttlepilot input

control input

Simulation Interface

• Soft Walls interface for Microsoft Flight Simulator

• Real-time controller created in Ptolemy II

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

Acknowledgements

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