View
218
Download
0
Tags:
Embed Size (px)
Citation preview
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