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

2. Outline Soft Walls Problem Solution with Level Set Methods Moving Forward

3. 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

4. Design Objectives Maximize Pilot Authority!

5. 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

6. Unsaturated Control No-fly zone Even under the maximum control bias, the pilot can make a sharper turn away from the no-fly zone

7. 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.

8. Discussion Reducing pilot control is dangerous –reduces ability to respond to emergencies

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

10. Discussion Reducing pilot control is dangerous –reduces ability to respond to emergencies There is no override –switch in the cockpit

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

12. 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

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

14. 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?

15. Deployment Fly-by-wire aircraft –a software change Older aircraft –autopilot level Phase in –prioritize airports

16. $4 billion development effort 40-50% system integration & validation cost

17. 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

18. 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.

19. 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

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

21. 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

22. 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

23. Backwards Reachable Sets (Tomlin, Lygeros, Sastry) We model the aircraft the dynamics as: where x is the state, u c is the control input, and u p 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

24. 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

25. 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 u c there exists a disturbance u p 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

26. Backwards Reachable Sets (Tomlin, Lygeros, Sastry) The set G(t) represents the set of states such that for all controls u c there exists a disturbance u p which drives the state into the target set in time t or less G(0) G(t 1 )G(t 2 ) G = G(  ) 0 < t 1 < t 2 < 

27. 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) GoGo g(x)

28. 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)

29. 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

30. 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

31. 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

32. Demo

33. 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

34. Dynamics Model We used this simple dynamics model, because the level-set computations work only for a small dimension  V pilot inputcontrol input

35. 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

36. Dynamics Model (Menon, Sweriduk, Sridhar) We are considering control strategies that scale better to the higher dimensions of this model rudder and ailerons elevator throttle pilot input control input

37. Simulation Interface Soft Walls interface for Microsoft Flight Simulator Real-time controller created in Ptolemy II

38. 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

39. Acknowledgements Ian Mitchell Iman Ahmadi Zhongning Chen Xiaojun Liu Steve Neuendorffer Shankar Sastry Clair Tomlin