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Goddard Space Flight Center 6 October 2004 Pursuit/Evasion of Fixed-wing Aircraft through Model-Predictive Control The new album by Jonathan Sprinkle Featuring,

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Presentation on theme: "Goddard Space Flight Center 6 October 2004 Pursuit/Evasion of Fixed-wing Aircraft through Model-Predictive Control The new album by Jonathan Sprinkle Featuring,"— Presentation transcript:

1 Goddard Space Flight Center 6 October 2004 Pursuit/Evasion of Fixed-wing Aircraft through Model-Predictive Control The new album by Jonathan Sprinkle Featuring, Mike Eklund, Jin Kim and Shankar Sastry

2 10/6/2004Jonathan Sprinkle, et al., UC Berkeley2 Overview Motivation NMPC and PEGs –Earlier work –Algorithm –Early results Whats the idea? (proof of concept) –Architecture –Tools –Simulation results Capstone Demonstration –Background –Development and simulation environment –Experimental test flight results Featuring great movies! Future Work & Conclusions

3 10/6/2004Jonathan Sprinkle, et al., UC Berkeley3 Motivation UAVs are very useful for intelligence gathering –Small, low-observable, inexpensive, remote- piloted (with autonomous tendencies…) Time-lag associated with remote control –Acceptable, or annoying, when in steady-state flight Waypoint flying, high-altitude loitering or scanning –Tactically interfering when rapid feedback is required Landing, hazardous weather, or stressful maneuvers

4 10/6/2004Jonathan Sprinkle, et al., UC Berkeley4 Motivation Consider the following: –Intelligence gathering UAV in flight –Alerted (internally, or by an observer) of an adversary over the horizon Either piloted, or perhaps fired (missile) –Large amounts of data recently gathered, but not transmitted What to do? –Time lag is too large for remote escape –Adversary will most likely locate UAV shortly –Not enough time to transmit back all data

5 10/6/2004Jonathan Sprinkle, et al., UC Berkeley5 Motivation: Our proposal: –The pilot should be able to turn over autonomy to the aircraft will take evasive maneuvers as best it can not necessarily guaranteed to save the aircraft, but hopefully will be able to transmit back data –Aircraft will return autonomy if it escapes –The use of various strategies for control will enable this capability, and do so in an aircraft independent manner

6 10/6/2004Jonathan Sprinkle, et al., UC Berkeley6 Model Predictive Control MPC is a method for restricting/encouraging behavior A fortune teller controller Restricts input ranges, as well as encourages some inputs based on safety/stability concerns Very useful for nonlinear systems, due to the ability to get good optimizations with non-linear abstractions

7 10/6/2004Jonathan Sprinkle, et al., UC Berkeley7 How does it work? Basic algorithm: –Examine the mathematical abstraction of the system (PDE) –Determine value along N time steps into the future –Optimize this value, according to some a priori specifications (to ) J = 0

8 10/6/2004Jonathan Sprinkle, et al., UC Berkeley8 System Model In the form of, Obviously, very system-dependent Sometimes an abstraction of the actual system in order to speed up computation Accuracy of the prediction, directly tied to the abstraction Eventually, arrive at a snapshot N steps in the future [ x 1 ; x 2 ;:::; x N ] _ x = f ( x ; u )

9 10/6/2004Jonathan Sprinkle, et al., UC Berkeley9 Example: Aircraft Control Begin End L ( ¢ ), x T k X 0 x k + u T k U 0 u k + b T m 1 B 0 1 b m 1 ( 1 )

10 10/6/2004Jonathan Sprinkle, et al., UC Berkeley10 Example: Aircraft Control Begin End Obstacle L ( ¢ ), x T k X 0 x k + u T k U 0 u k + b T m 1 B 0 1 b m 1 ( 1 ) + b T m 2 B 0 2 b m 2 ( 3 )

11 10/6/2004Jonathan Sprinkle, et al., UC Berkeley11 Example: Aircraft Control Begin End Obstacle Boundary L ( ¢ ), x T k X 0 x k + u T k U 0 u k + b T m 1 B 0 1 b m 1 ( 1 ) + b T m 2 B 0 2 b m 2 ( 2 ) + b T m 3 B 0 3 b m 3 ( 3 )

12 10/6/2004Jonathan Sprinkle, et al., UC Berkeley12 Example: Aircraft Control? Enemy… Begin End Obstacle Boundary L ( ¢ ), x T k X 0 x k + u T k U 0 u k + b T m 1 B 0 1 b m 1 ( 1 ) + b T m 2 B 0 2 b m 2 ( 2 ) + b T m 3 B 0 3 b m 3 ( 3 ) + b T m ? B 0 ? b m ? ( 4 ) ( 5 )

13 10/6/2004Jonathan Sprinkle, et al., UC Berkeley13 Example: Aircraft Control Now, what do you do? –Hope that you dont get caught? –First, fight with you left hand, and then surprise you opponent by not being left-handed –Encode getting away from your opponent into the cost-function I admit it, you are better than I am Then why are you smiling? Because *I* am not left-handed

14 10/6/2004Jonathan Sprinkle, et al., UC Berkeley14 Earlier UC Berkeley Pursuit/Evasion Experiments (David Shim, Jin Kim, et al) BErkeley Aerobot Project (BEAR), 1996- –Goal: to build a coordinated, intelligent network with multiple heterogeneous agents 11 Rotorcraft-based unmanned aerial vehicles (UAVs) 5 Unmanned ground vehicles (UGVs) Shipdeck simulator (landing platform) Stochastic Pursuit-Evasion Games (PEG) –Self-localization –Target detection –Map building –Pursuit policy –Trajectory generation –Control / Action

15 10/6/2004Jonathan Sprinkle, et al., UC Berkeley15 Experimental Results: Pursuit Evasion Games with 4 UGVs and 1 UAV (Spring 01) Sub-problems for Pursuit Evasion Games –Sensing Navigation sensors -> Self-localization Detection of objects of interest –Framework for communication and data flow –Map building of environments and evaders How to incorporate sensed data into agents belief states probability distribution over the state space of the world (i.e. possible configuration of locations of agents and obstacles) How to update belief states –Strategy planning Computation of pursuit policy mapping from the belief state to the action space – Control / Action

16 10/6/2004Jonathan Sprinkle, et al., UC Berkeley16 Nonlinear Model Predictive Trajectory Control (NMPTC) Explicitly addresses nonlinear systems with constraints on operation and performance A cost minimization problem in the presence of state and input constraints –Control resulting in the minimum cost is determined over a model predicted horizon Previously demonstrated in rotary wing UAVs[1] [1] H.J. Kim, D.H. Shim and S. Sastry, ACC, 2002

17 10/6/2004Jonathan Sprinkle, et al., UC Berkeley17 NMPTC: Fixed wing application Dynamics and constraints are quite different than for rotary wing aircraft –Entirely new aircraft model required Tactics –Function of constraints on fixed wing aircraft, in particular Minimum airspeed Maximum turn rate

18 10/6/2004Jonathan Sprinkle, et al., UC Berkeley18 NMPTC: For Pursuit/Evasion Games In this application, the low level control is done independently by the platform –Basically a tactics & trajectory generation problem Same controller is used for pursuit and evasion –Cost function components and gains are changed E.g. AOT not used for pursuer Implemented as stand-alone application with Matlab interface for testing and controller tuning Integrated in OCP for Capstone Demonstration (using a real flight avionics feedback model)

19 10/6/2004Jonathan Sprinkle, et al., UC Berkeley19 NMPTC: Cost Function Definition Cost function is defined by:

20 10/6/2004Jonathan Sprinkle, et al., UC Berkeley20 NMPTC: Cost function illustration

21 10/6/2004Jonathan Sprinkle, et al., UC Berkeley21 NMPTC: Cost function minimization A gradient decent method is used to minimize the cost function Initialization with previous result reduces the number of iterations required –Usually 3-4 iterations are required The number of iterations in limited to prevent overruns in real-time –In rapidly changing situation this can result in suboptimal solution –Sudden changes may take several time steps –However, this is not a problem because the situation is changing and unpredictable anyway

22 10/6/2004Jonathan Sprinkle, et al., UC Berkeley22 NMPTC: PEG game conditions In this game the evader tries to cross the playing area while not being targeted by the pursuer The pursuer tries to target the evader Target cone definition (θ=10˚,d=3 nm) Left: F15 not behind UAV, middle: F15 not pointed at UAV, right: F15 behind AND pointed at UAV

23 10/6/2004Jonathan Sprinkle, et al., UC Berkeley23 NMPTC: Early simulation results

24 10/6/2004Jonathan Sprinkle, et al., UC Berkeley24 NMPTC: Early simulation results

25 10/6/2004Jonathan Sprinkle, et al., UC Berkeley25 NMPTC: Early simulation results

26 10/6/2004Jonathan Sprinkle, et al., UC Berkeley26 Example: Cost functions

27 10/6/2004Jonathan Sprinkle, et al., UC Berkeley27 Why are we doing this?

28 10/6/2004Jonathan Sprinkle, et al., UC Berkeley28 Software Enabled Control The goal of SEC is to develop new controls and software technology that will enable new applications that are impractical or intractable using current approaches.

29 10/6/2004Jonathan Sprinkle, et al., UC Berkeley29 SEC Capstone Demonstration Capstone Demonstrations were proposed to highlight and test the technologies developed in the SEC program One would be a fixed wing UAV flight test –6 participant technology developers (TDs) Honeywell, Northrop Grumman, U Minnesota, MIT, Stanford, and UCB/U Colorado/CalTech –System Integrator was Boeing –OCP would be software framework –A T-33 trainer as UAV surrogate –An F-15 as wingman/opponent 12-14 month schedule May 03 – June 04

30 10/6/2004Jonathan Sprinkle, et al., UC Berkeley30 Demo: Non-Determinism in Experiments Customer comment: –The timing and scope of these (pop-up events, like faults, targets, threats) should not be totally known a- priori by the TDs. Capstone Demo Approach –For flight test safety, platform owners and flight crews are more comfortable with constraints on non- determinism Temporal non-determinism Spatial non-determinism UCB Pursuit/Evasion Approach: –Two airplanes, no pre-determinism at all –Favorite responses at the last PI meeting: You really dont know who is going to win?!?! What day is your test flight scheduled? Ill be there

31 10/6/2004Jonathan Sprinkle, et al., UC Berkeley31 Demo: Dryden Flight Research Center (DFRC)

32 10/6/2004Jonathan Sprinkle, et al., UC Berkeley32 Demo: DFRC Flight Demonstration Venue NASA provides range access, and approves test vehicles and missions Boeing provides vehicles and flight plans, and conducts flights NASA facilities –Fully instrumented Western Aeronautical Test Range –Mission Control Center – Restricted public access Boeing facilities –UCAV Flight Operations Control Center – Boeing only Flight test instrumentation, displays, telemetry recording, post-processing –UCAV Van – DoD only SEC Workstation control and display, Link 16 Terminal –TDs were to be provided with a tent But we got to share a camper van with A/C with the VIPs some of the time

33 10/6/2004Jonathan Sprinkle, et al., UC Berkeley33 Demo: R-2508 Range Complex

34 10/6/2004Jonathan Sprinkle, et al., UC Berkeley34 Demo: R-2515 Range Area

35 10/6/2004Jonathan Sprinkle, et al., UC Berkeley35 Demo: Mission Area Example in R-2515

36 10/6/2004Jonathan Sprinkle, et al., UC Berkeley36 Demo: Mission Guidelines Day, Visual Flight Rules – See and Avoid Mission Schedule –Flight duration: 1:10 in mission area for both aircraft –Two flight per day can be supported Airspeed –T-33 alone: 250 kts typical –T-33 and F-15 joint operations: 300 kts typical Altitude –Normal operations: 10,000 ft to 20,000 ft MSL –Limited operations: Below 10,000 ft to surface with approval –Edwards-Dryden runways: 2,300 ft MSL –Terrain in R-2515: 2,300 ft to 6,000 ft MSL Formation –1 nmi radial separation –+/- 500 ft

37 10/6/2004Jonathan Sprinkle, et al., UC Berkeley37 Demo: TD deliverables Software –Design consistent with defined OCP interfaces –Source code For emergency fixes and recompilations For safety of flight reviews –Binaries for linking –OCP application artifacts Simulink mdl file, ComponentInfo files Test check cases –Allow us to quickly assess correct functional behavior when hosting in our desktop development system and in platform integration labs (F-15, UCAV) Documentation –Describing software –Describing test check cases

38 10/6/2004Jonathan Sprinkle, et al., UC Berkeley38 Demo: State data available for control All UAV state data available –Limits due to lack of sensors on T-33, e.g. alpha, beta measurements Different set of F-15 state available –Transmitted by F-15 to the T-33 –Rate information Data captured from UCAV avionics at 20 Hz Baseline TD application execution rate is 2 Hz Freshest 10 state data sets buffered as input at 2 Hz From F-15 at 1 Hz

39 10/6/2004Jonathan Sprinkle, et al., UC Berkeley39 Demo: Fighter State on UAV Fighter state data that will be made periodically available to TD applications on the UAV (sent over comms link) –Rate information Data captured from F-15 avionics at 20 Hz Freshest state data set is sent over Link-16 to UAV at 1 Hz –Data member list (shown at right)

40 10/6/2004Jonathan Sprinkle, et al., UC Berkeley40 Demo: T-33 Software Architecture

41 10/6/2004Jonathan Sprinkle, et al., UC Berkeley41 Demo: Final integration and testing Development in desktop environment at UCB Sent to Boeing –Testing in UCAV AIC (HWIL) facility. Confidence testing of Laptop Demo Applications Use scripted scenarios with actual mission plans for Dryden –Multi-Vehicle configuration testing –Integration of TD Software Components Integration into new OCP release B2.6.x

42 10/6/2004Jonathan Sprinkle, et al., UC Berkeley42 Demo: UCB PEG Development 20 – 60 min. games confirm NMPTC feasibility at real-time –Evader goal: get to final waypoint or avoid evader –Pursuer goal: target evader Pursuer and evader restricted to same performance limits Planes on the same logical plane, but separated by 6000ft altitude at all times Evader and pursuer have a few scenarios –UAV as evader –UAV can become pursuer OCP Experiment Controller Snapshot T-33: Evader (yellow) F-15: Pursuer (blue)

43 10/6/2004Jonathan Sprinkle, et al., UC Berkeley43 Demo: Controller Coverage Final waypoint is the major component Travel to the waypoint can be interrupted by the actions of the pursuer –Relative positions –Angle-off-tail –Distance from each other –Proximity to boundaries of the testing area –Physical limitations of the aircraft Velocity, climb/turn rate Use a simpler model for predictive behavior under certain conditions –Still use the Boeing-supplied (DemoSim) model for behavioral simulations Approx. same timePursuer goes for target cone Evader turns away (regardless of endpoint) Endpoint Target cone definition (θ=10˚,d=3 nm) Left: F15 not behind UAV, middle: F15 not pointed at UAV, right: F15 behind AND pointed at UAV

44 10/6/2004Jonathan Sprinkle, et al., UC Berkeley44 UCB PEA Experiment #1 Test Plan: UAV as Evader UAV attempts to cross Scenario Area (SA) from East to West without being targeted by the F15 UAV wins by: –Reaching the RVPT –Not being targeted for 20 minutes F15 wins by targeting the UAV Note: F15 performance is restricted

45 10/6/2004Jonathan Sprinkle, et al., UC Berkeley45 Crew/Pilot Instructions Event No. EventUAV TaskF15 TaskWhat to Expect 1Move to stationsUnder pilot control, west of SA from INPT between 10,000 and 12,000 altitude, heading 90° In SA, east of W117° 30 between 18,000 and 20,000 altitude 2Set up UAVEnters SA at INPT under pilot control J-UCAS Mission Plan sets up UAV in hand over conditions As above 3Verification of UAV setup Monitor Hdg, Alt, Spd commands consistent with handover conditions As above 4Start experimentPress CMD-ON buttonEngage UAV 5Pursuit-Evasion proceeds Attempts to reach RVPT while not being targeted by F15 Note: game can be aborted by pressing the GO EGPT button Attempts to target UAV Interesting maneuvers 6Win condition detected TD software monitors game conditions and outputs appropriate win conditions As aboveWIN: F15 - targeted UAV WIN: UAV - reached End Zone!! WIN: UAV – time expired 7End game or continue playing Game continues after win condition by default to allow experiment to continue Press GO EGPT to end As above 8Return to EGPTPress CMD-OFF button, pilot flies to EGPTFly to EGPT or remain in SA if further experiments UAV returning to INPT/EGPT

46 10/6/2004Jonathan Sprinkle, et al., UC Berkeley46 UCB PEA Experiment #2 Test Plan: UAV as Evader and Pursuer UAV attempts to cross Scenario Area (SA) from East to West without being targeted by the F15, however, UAV will attempt to target F15 if suitable conditions arise UAV wins by: –Reaching the END ZONE –Not being targeted for 20 minutes –Targeting the F15 F15 wins by targeting the UAV Note: F15 performance is restricted

47 10/6/2004Jonathan Sprinkle, et al., UC Berkeley47 Demo: Experiment #2 Test Plan Event No. EventUAV TaskF15 TaskWhat to Expect 5Pursuit- Evasion proceeds Attempts to reach RVPT while not being targeted by F15 GIB can select one of three modes: UAV as evader by pressing Evade button UAV as pursuer by pressing Pursue button UAV determines whether to evade or pursue by pressing the Ev/Pu button Attempts to target UAV More interesting maneuvers Test plan is identical to Experiment #1 except for Event No. 5:

48 10/6/2004Jonathan Sprinkle, et al., UC Berkeley48 Demo: Experiment #1 Simulation Results Using 2 nd UAV pretending to be an F15

49 10/6/2004Jonathan Sprinkle, et al., UC Berkeley49 Demo: Experiment #2 Simulation Results Using Fixed Wing Control Interface with simple way point plan to allow Boeing hardware testing

50 10/6/2004Jonathan Sprinkle, et al., UC Berkeley50 Demo: Experiment #2 Simulation Results Using 2 nd UAV pretending to be an F15 to allow for controller tuning and software testing

51 10/6/2004Jonathan Sprinkle, et al., UC Berkeley51 Demo: Flight Test

52 10/6/2004Jonathan Sprinkle, et al., UC Berkeley52 Demo: Flight Test Results 1

53 10/6/2004Jonathan Sprinkle, et al., UC Berkeley53 Demo: Flight Test Results 1 (faster)

54 10/6/2004Jonathan Sprinkle, et al., UC Berkeley54 Demo: Flight Test Results 2

55 10/6/2004Jonathan Sprinkle, et al., UC Berkeley55 Demo: Flight Test Feedback Very positive responses Pilot comment: –UAV behaved as he would have expected a trained pilot Results still being analyzed for final report

56 10/6/2004Jonathan Sprinkle, et al., UC Berkeley56 Future: Improving implementation Cost functions of the NMPTC can be improved –Check against known fighter tactics, try to duplicate behavior –Using desktop environment Enhancing/verifying our predictive model –Boeings model is an executable –We are using a mathematical version approximations are necessary results in loss of accuracy, but increased performance

57 10/6/2004Jonathan Sprinkle, et al., UC Berkeley57 Conclusions MPC can be used to provide interesting behaviors for linear and non-linear control systems We hope to reduce the development cycle by at least –Providing a cost-function independent optimizer –Inventing an intuitive interface to generate the cost function –Developing a method/tool to tune the cost function for desired behaviors –Experimenting with ways to reverse engineer values for the matrices, based on desired behaviors under stimuli Experience in the SEC program and with OCP has been very positive

58 10/6/2004Jonathan Sprinkle, et al., UC Berkeley58 Questions? Well HAL, Im damned if I can find anything wrong with it. Yes. Its puzzling. I dont think Ive ever seen anything quite like this before. -- 2001: A Space Odyssey

59 10/6/2004Jonathan Sprinkle, et al., UC Berkeley59 Future: NMPTC plans Currently implementing a new NMPTC problem using different models and designs Will be developing the NMPTC interface to provide the behavior for this new application Evaluate the new MATLAB MPC toolbox, to see what benefits it offers

60 10/6/2004Jonathan Sprinkle, et al., UC Berkeley60 Future: The NMPTC Problem Making it work is nice, but –How in the devil did we come up with those Equations Individual components Matrix values –Is there a way to derive these from the application constraints? Additionally –How hard was it to write a fast optimizer? –Is there a way to make this interface easily usable?

61 10/6/2004Jonathan Sprinkle, et al., UC Berkeley61 Future: Toward a solution Optimizer CostFunction Input Constraints Application Constraints Safety Constraints x ranges u ranges Behaviors System Model System-dependent, Behavior-dependent, Independent ( J = 0 )

62 10/6/2004Jonathan Sprinkle, et al., UC Berkeley62 Future: Toward a solution System-dependent –Can be derived for a particular systems mathematical definition –In general, quite easy to obtain Independent –Software engineering exercise –Once defined, will be reused Behavior-dependent –By far the hardest piece of the solution –Not generally derivable, but there are tricks that should be available for all future implementers, that a parameterized approach can provide

63 10/6/2004Jonathan Sprinkle, et al., UC Berkeley63 NMPTC: Behavior-dependent tricks Use the itemized pieces of the cost function to examine overall volatility under certain criteria Steer inputs to provide an order of magnitude cost function behavior Provide a mechanism to translate math definitions into computer code

64 10/6/2004Jonathan Sprinkle, et al., UC Berkeley64 SMART BIRD Single-Man Aerial Reconnaisance Tool: Battlefield Information Recon Deployment UC Berkeley, S. Shankar Sastry, PI Single operator, stealth, back-pack size, hand launch/recovery, modular, 48 electric-powered wing, 2.5 lb UAV (1 lb payload), 2-mi. range, loitering ability (day/night) without GPS, autopilot (wing leveler & altitude hold), 2.4 GHz video/data downlink, requires no tools for assembly/disassembly

65 10/6/2004Jonathan Sprinkle, et al., UC Berkeley65 PDA-based Control/Monitoring Simplified user interface Connects to the vehicle through wireless LAN High-speed Real-time vehicle monitoring Control console to send various commands Backdrop picture of 2D birds eye view with 0.3m resolution

66 10/6/2004Jonathan Sprinkle, et al., UC Berkeley66 And of course, NASA... How many of you spent at least 24 hours per day for the past 3 weeks working on H&RT Proposals? –Can I get an amen? Boeing-led –Open Robotic Space Control Platform (ORSCP) –for transitioning OCP to space exploration: –Co-Lead is UCB (Shankar Sastry) One of two SEC Capstone Demo participants involved Berkeley-led –Infrastructure & Architecture for Crew-centered Operations (IACO) –for deployment of mission-critical decisions to spacecraft and autonomous robots, rather than mission control

67 10/6/2004Jonathan Sprinkle, et al., UC Berkeley67 Demo: Simulation Results 1

68 10/6/2004Jonathan Sprinkle, et al., UC Berkeley68 Demo: Simulation Results 2


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