Proportional Navigation with Adaptive Terminal … 670.6 670.8 671 671.2 671.4 228 230 232 234 236...

AFRL-VA-WP-TP-2007-312 PROPORTIONAL NAVIGATION WITH ADAPTIVE TERMINAL GUIDANCE FOR AIRCRAFT RENDEZVOUS (PREPRINT) Austin L. Smith FEBRUARY 2007

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4. TITLE AND SUBTITLE

PROPORTIONAL NAVIGATION WITH ADAPTIVE TERMINAL GUIDANCE FOR AIRCRAFT RENDEZVOUS (PREPRINT)

5c. PROGRAM ELEMENT NUMBER N/A

5d. PROJECT NUMBER

N/A 5e. TASK NUMBER

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6. AUTHOR(S)

Austin L. Smith

5f. WORK UNIT NUMBER

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Structural Design and Development Branch (AFRL/VACD) Control Sciences Division Air Vehicles Directorate Air Force Materiel Command, Air Force Research Laboratory Wright-Patterson Air Force Base, OH 45433-7542

REPORT NUMBER AFRL-VA-WP-TP-2007-312

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14. ABSTRACT

PN with adaptive terminal guidance is shown to be a viable guidance method for aircraft rendezvous in 6DOF simulation.

Adaptive PN and Velocity controller combination is shown to effect successful rendezvous. Adaptation accounts for errors caused by assumptions (stationary RZ location), wind, and tanker maneuvers.

15. SUBJECT TERMS Proportional Navigation, Aircraft Rendezvous, Aerial Refueling, Terminal Guidance

16. SECURITY CLASSIFICATION OF: 19a. NAME OF RESPONSIBLE PERSON (Monitor) a. REPORT Unclassified

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17. LIMITATION OF ABSTRACT:

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18. NUMBER OF PAGES

26 Gary K. Hellmann 19b. TELEPHONE NUMBER (Include Area Code)

N/A Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18

Proportional Navigation with Adaptive Terminal Guidance for

Aircraft Rendezvous

Austin [email protected]

1

2

2

Background Automated Aerial Refueling (AAR) requires

receiver-to-tanker rendezvous A trajectory/guidance algorithm is necessary

to provide a path/FCS commands for the aircraft rendezvous Optimization algorithms are computationally

intensive Geometric solutions limit UAV maneuvering Trajectory solutions may jump around

2

Current CONOPS for AAR is the trajectory algorithm brings the UAV to a 1-NM trail position, where a tanker relative control law is engaged

Very difficult to embed an iterative optimization algorithm in a FCS running at high rates

Geometric solutions (even when iterative) may not control speed or provide a smooth rendezvous (zero turn rate at RZ)

Useful to look at a simple algorithm that meets rendezvous contraints (same V, Psi, Pos at same time) that can be embedded in a FCS

3

3

Requirements Able to embed into UAV FCS and run real-

time Use same information as FCS (AAR PGPS) Must obey vehicle limits, and tactical and

operational CONOPS Execute successful rendezvous

3

Must be able to embed guidance algorithm into FCS running at high rate

Must use same information as inner/outer loop, Precision Differential GPS

4

Proposed Guidance System

A proportional navigation guidance system with adaptive terminal guidance,And a velocity control loop that Commands UAV to RZ location with the same speed and

heading as tanker, at same time Obeys velocity, acceleration, and turn rate limits Is robust to winds and tanker maneuvering

4

5

5

Design Treat target as stationary,

using an adaptive tanker estimator, based on kinematics, to determine a rendezvous (RZ) location

RZ location approaches tanker as receivers heading and position approach tankers heading and position

Velocity loop will control speed

2-D (constant altitude)

Design Approach

5

N (YI)

E (XI)

(XR,YR)

f

RZ

(XT,YT)

T

W

Use estimator to determine a target location, prevent prolonged tail chasesWind component

The adaptive terminal guidance pronav will provide a turn rate command to align UAV heading with tanker heading at or before rendezvous locationTwo main coordinate systems, flat earth N-E and RFE (tanker relative)Tanker estimator depends on turn rate of tanker for locating a rendezvous point based on tanker states and UAV states

6

6

Guidance LawProportional Navigation

6

1=com 2))(())(()(

sTyRyTxRxTxRxTyRy

dtfd

=

=

2),,(2),,( TIYRIYTIXRIXs +=

where

and

Variation of control law from Lu, Doman, Schierman

assuming

0,0 == TyTxs

N (YI)

E (XI)

( Negative as shown)

RZ Location

Note different definitions for heading and LOS orientationS is range-to-go

Phi final is a function of final heading constraint

7

7

Guidance LawAdaptive Update

7

)()(

1

=

f

f

Initially

or )sgn(max = fcom

011 > s

ff => 221

( )))(())((121 TyRyTyRyTxRxTxRxs +

+=

Adaptation

} Guidance Law Properties

where

= f += )

2( f

gainconstant=

An initial PN gain calc is made, it must be greater than two to guarantee the final heading constraint is met, if it is not >2, then the aforementioned turn rate command is used, which will eventually increase the PN gain above 2

Adaptation ensures final heading constraint is met even when: guidance commands exceed maneuverability of vehicle (alg uses kinematics), limits are saturated, movements in the target caused by tanker drift, winds, etc.

Final LOS angle definition ensures receiver will approach tanker from behind as it nears its final heading

8

8

Guidance LawVelocity Controller

8

)sgn(1 11

2

11

TVRVsTVRVkcomA Tt

RtTtRt

+++

+

=

11

+

+

TtRt = time-to-target ratio

-Increases or decreases target velocity

-Neither tR or tT is a guess of the RZ time or the actual time of arrival to target

-The ratio gives a relative sense of how far ahead or behind the tanker the UAV is from the target RZ location

(tR+1)/( tT+1) -> 1 as Receiver and Tanker approach RZ

Time-to-Target ratio is receiver time-to-target over tanker time-to-target

Less than one, receiver slows down; greater than one, receiver speeds up

9

Results

9

Simulation- 6DOF Tanker and

UAV models- Tanker

t=0=0 V=670ft/s

- UAV Vt=0=750ft/s

- Wind

UAV Limits +-2 deg/s turn rate +-2 ft/s2 accel/decel 600-800 ft/s V range

MATLAB & Simulink

RoushRVText Box*Everything not listed is variable

10

Results

10

t=0=90, no wind, Pt=0=(-40000,15000)ft

-Tanker flying straight leg

11

Results

-20

0

20

40

60

80

100P s iUA V P s iTNK

0 5 0 1 0 0 1 5 0 2 0 0 2 50

1

2

3

4

5

6

7

8

R a n g e

660

680

700

720

740

760

780V UA V V TNK

V (f

t/s)

Psi

(deg

)

Ran

ge (N

M)

t (s)

228 230 232 234 236 238 240 242 244 246 248

669.6

669.8

670

670.2

670.4

670.6

670.8

671

671.2

671.4

228 230 232 234 236 238 240 242 244 246 248-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

228 230 232 234 236 238 240 242 244 246 2480

5

10

15

20

25

30

35

(ft)

12

Results

12

t=0=110, no wind, Pt=0=(-50000,30000)ft

-Tanker turns with 15 bank at t=30s

13

Results

13

Psi

(deg

)

t (s)

V (f

t/s)

660

680

700

720

740

760

780

800

V UA V V TNK

0 50 100 150 200 250 30-20

0

20

40

60

80

100

120

140

160

180

P s iUA V P s iTNK

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 00

1

2

3

4

5

6

7

8

9

1 0

R a n g e

Ran

ge (N

M)

254 256 258 260 262 264 266 268 270 272 27669.5

670

670.5

671

671.5

254 256 258 260 262 264 266 268 270 272 27

164

166

168

170

172

174

176

178

254 256 258 260 262 264 266 268 270 272 270

5

10

15

20

25

30

35

40

(ft)

RoushRVText BoxTurn rate saturated, Receiver crosses tanker path, but comes back around and hitsRZ location (but well behind tanker)Crossing path behind tanker presents a problem with guidance law because phif -phi -> 0, but RZ is not occurringlogic was introduced to handle this

14

Results

14

t=0=90, Wind SE @ 50KT for 100s, Pt=0=(-40000,15000)ft


15

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 00

1

2

3

4

5

6

7

8

R a n g e

Results

15

V (f

t/s)

Psi

(deg

)

t (s)

Ran

ge (N

M)

(ft)

660

680

700

720

740

760

780V UA V V TNK

-20

0

20

40

60

80

100 Ps iUA V Ps iTNK

230 232 234 236 238 240 242 244 246 248 250669.5

670

670.5

671

671.5

672

230 232 234 236 238 240 242 244 246 248 250-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

230 232 234 236 238 240 242 244 246 248 2500

5

10

15

20

25

30

35

RoushRVText BoxThis has both a PN gain re-initialization and winds that test the adaptationSequence of target locations reflects tanker maneuver and wind effects

16

Results

16

t=0=70, Wind SE @ 50KT for entire sim, Pt=0=(-40000,15000)ft

- Tanker turns with 15 bank at t=30s

RoushRVText Box1st intermediate location based on straight path, when tanker turns, PN gain processrestarted for new RZ location on turn

17

0 5 0 1 0 0 1 5 0 2 0 0 2 50

1

2

3

4

5

6

7

8

R a n g e

ResultsV

(ft/s

)

Psi

(deg

)

t (s)

Ran

ge (N

M)

(ft)

660

680

700

720

740

760

780

800V UA V V TNK

-20

0

20

40

60

80

100

120

140

160 P s iUA V P s iTNK

214 216 218 220 222 224 226 228 230 232 23

674

675

676

677

678

679

680

681

214 216 218 220 222 224 226 228 230 232 23

140

142

144

146

148

150

152

154

156

214 216 218 220 222 224 226 228 230 232 230

5

10

15

20

25

30

35

40

45

18

Discussion and Conclusion

18

PN with adaptive terminal guidance is shown to be a viable guidance method for aircraft rendezvous in 6DOF simulation

Adaptive PN and Velocity controller combination is shown to effect successful rendezvous

Adaptation accounts for errors caused by assumptions (stationary RZ location), wind, and tanker maneuvers

19

References

19

[1] Lu, P., Doman, D.P., Schierman, J.D., Adaptive Terminal Guidance for Hypervelocity Impact in Specified Direction,Journal of Guidance, Control, and Dynamics, Vol. 29, No. 2, 2006, pp.269-278

[2] Lu, P., Intercept of Nonmoving Targets at Arbitrary Time-Varying Velocity, Journal of Guidance, Control, and Dynamics, Vol. 21, No. 1, 1998, pp.176-178

[3] Ochi, Y., Kominami, T., Flight Control for Automatic Aerial Refueling via PNG and LOS Angle Control, AIAA Guidance, Navigation, and Control Conference and Exhibit, Aug. 2005

Proportional Navigation with Adaptive Terminal Guidance for Aircraft RendezvousBackgroundRequirementsProposed Guidance SystemDesign ApproachGuidance LawProportional NavigationGuidance LawAdaptive UpdateGuidance LawVelocity ControllerResultsResultsResultsResultsResultsResultsResultsResultsResultsDiscussion and ConclusionReferences

Proportional Navigation with Adaptive Terminal Guidance for Aircraft Rendezvous

Austin Smith

[email protected]

*

*

Background

Automated Aerial Refueling (AAR) requires receiver-to-tanker rendezvous

A trajectory/guidance algorithm is necessary to provide a path/FCS commands for the aircraft rendezvous

Optimization algorithms are computationally intensive

Geometric solutions limit UAV maneuvering

Trajectory solutions may jump around

*





*

Requirements

Able to embed into UAV FCS and run real-time

Use same information as FCS (AAR PGPS)

Must obey vehicle limits, and tactical and operational CONOPS

Execute successful rendezvous

*



*

Proposed Guidance System

A proportional navigation guidance system with adaptive terminal guidance,

And a velocity control loop that

Commands UAV to RZ location with the same speed and heading as tanker, at same time

Obeys velocity, acceleration, and turn rate limits

Is robust to winds and tanker maneuvering

*

*

Design Approach

Design

Treat target as stationary, using an adaptive tanker estimator, based on kinematics, to determine a rendezvous (RZ) location

RZ location approaches tanker as receivers heading and position approach tankers heading and position

Velocity loop will control speed

2-D (constant altitude)

*

N (YI)

E (XI)

W

Use estimator to determine a target location, prevent prolonged tail chases

Wind component

The adaptive terminal guidance pronav will provide a turn rate command to align UAV heading with tanker heading at or before rendezvous location

Two main coordinate systems, flat earth N-E and RFE (tanker relative)

Tanker estimator depends on turn rate of tanker for locating a rendezvous point based on tanker states and UAV states

*

Guidance Law

Proportional Navigation

*

where

and

Variation of control law from Lu, Doman, Schierman

assuming

Note different definitions for heading and LOS orientation

S is range-to-go


*

Guidance Law

Adaptive Update

*

Initially

or

Adaptation

Guidance Law Properties

where




*

Guidance Law

Velocity Controller

*

= time-to-target ratio

Increases or decreases target velocity

Neither tR or tT is a guess of the RZ time or the actual time of arrival to target

The ratio gives a relative sense of how far ahead or behind the tanker the UAV is from the target RZ location

(tR+1)/( tT+1) -> 1 as Receiver and Tanker approach RZ



*

Results

*

Simulation

6DOF Tanker and UAV models

Tanker

t=0=0

V=670ft/s

UAV

Vt=0=750ft/s

Wind

UAV Limits

+-2 deg/s turn rate

+-2 ft/s2 accel/decel

600-800 ft/s V range

MATLAB & Simulink

Everything not listed is variable

*

Results

*

t=0=90, no wind, Pt=0=(-40000,15000)ft


*

Results

V (ft/s)

Psi (deg)

Range (NM)

t (s)

(ft)

*

Results

*

t=0=110, no wind, Pt=0=(-50000,30000)ft

-Tanker turns with 15 bank at t=30s

*

Results

*

V (ft/s)

Psi (deg)

t (s)

Range (NM)

(ft)

Turn rate saturated, Receiver crosses tanker path, but comes back around and hits RZ location (but well behind tanker)

Crossing path behind tanker presents a problem with guidance law because phif - phi -> 0, but RZ is not occuringlogic was introduced to handle this

*

Results

*

t=0=90, Wind SE @ 50KT for 100s, Pt=0=(-40000,15000)ft


*

Results

*

V (ft/s)

Psi (deg)

t (s)

Range (NM)

(ft)

This has both a PN gain re-initialization and winds that test the adaptation

Sequence of target locations reflects tanker maneuver and wind effects

*

Results

*

t=0=70, Wind SE @ 50KT for entire sim, Pt=0=(-40000,15000)ft

- Tanker turns with 15 bank at t=30s

1st intermediate location based on straight path, when tanker turns, PN gain process restarted for new RZ location on turn

*

Results

V (ft/s)

Psi (deg)

t (s)

Range (NM)

(ft)

*

Discussion and Conclusion

*

PN with adaptive terminal guidance is shown to be a viable guidance method for aircraft rendezvous in 6DOF simulation

Adaptive PN and Velocity controller combination is shown to effect successful rendezvous

Adaptation accounts for errors caused by assumptions (stationary RZ location), wind, and tanker maneuvers

*

References

*

[1] Lu, P., Doman, D.P., Schierman, J.D., Adaptive Terminal Guidance for Hypervelocity Impact in Specified Direction, Journal of Guidance, Control, and Dynamics, Vol. 29, No. 2, 2006, pp.269-278

[2] Lu, P., Intercept of Nonmoving Targets at Arbitrary Time-Varying Velocity, Journal of Guidance, Control, and Dynamics, Vol. 21, No. 1, 1998, pp.176-178

[3] Ochi, Y., Kominami, T., Flight Control for Automatic Aerial Refueling via PNG and LOS Angle Control, AIAA Guidance, Navigation, and Control Conference and Exhibit, Aug. 2005







Use estimator to determine a target location, prevent prolonged tail chases

Wind component

The adaptive terminal guidance pronav will provide a turn rate command to align UAV heading with tanker heading at or before rendezvous location

Two main coordinate systems, flat earth N-E and RFE (tanker relative)

Tanker estimator depends on turn rate of tanker for locating a rendezvous point based on tanker states and UAV states

Note different definitions for heading and LOS orientation

S is range-to-go







Everything not listed is variable

Turn rate saturated, Receiver crosses tanker path, but comes back around and hits RZ location (but well behind tanker)

Crossing path behind tanker presents a problem with guidance law because phif - phi -> 0, but RZ is not occuringlogic was introduced to handle this

This has both a PN gain re-initialization and winds that test the adaptation

Sequence of target locations reflects tanker maneuver and wind effects

1st intermediate location based on straight path, when tanker turns, PN gain process restarted for new RZ location on turn

0

50

100

150

200

250

660

680

700

720

740

760

780

V

U

A

V

V

T

N

K

(

)

)

)(

(

)

)(

(

1

2

1

T

y

R

y

T

y

R

y

T

x

R

x

T

x

R

x

s

&

&

&

&

&

-

-

+

-

-

D

D

+

-

=

f

y

l

k

l

f

l

y

&

&

1

-

=

com

2

)

,

,

(

2

)

,

,

(

T

I

Y

R

I

Y

T

I

X

R

I

X

s

-

+

-

=

1

1

+

+

T

t

R

t

)

(

)

(

1

f

y

l

-

F

-

Y

-

=

f

f

)

sgn(

max

f

y

y

-

F

=

f

com

&

&

0

1

1

>

s

l

f

f

Y

-

-

=

F

>

2

2

1

p

l

)

sgn(

1

1

1

2

1

1

T

V

R

V

s

T

V

R

V

k

com

A

T

t

R

t

T

t

R

t

+

+

+

+

-

-

-

=

228

230

232

234

236

238

240

242

244

246

248

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0

50

100

150

200

250

0

1

2

3

4

5

6

7

8

Range

}

228

230

232

234

236

238

240

242

244

246

248

669.6

669.8

670

670.2

670.4

670.6

670.8

671

671.2

671.4

gain

constant

=

k

0

50

100

150

200

250

-20

0

20

40

60

80

100

Psi

U

A

V

Psi

T

N

K

228

230

232

234

236

238

240

242

244

246

248

0

5

10

15

20

25

30

35

y

y

-

Y

=

D

f

f

p

f

-

+

Y

-

=

D

)

2

(

f

0

50

100

150

200

250

300

-20

0

20

40

60

80

100

120

140

160

180

Psi

U

A

V

Psi

T

N

K

0

50

100

150

200

250

300

660

680

700

720

740

760

780

800

V

U

A

V

V

T

N

K

0

50

100

150

200

250

300

0

1

2

3

4

5

6

7

8

9

10

Range

254

256

258

260

262

264

266

268

270

272

274

669.5

670

670.5

671

671.5

254

256

258

260

262

264

266

268

270

272

274

164

166

168

170

172

174

176

178

254

256

258

260

262

264

266

268

270

272

274

0

5

10

15

20

25

30

35

40

0

50

100

150

200

250

300

0

1

2

3

4

5

6

7

8

Range

230

232

234

236

238

240

242

244

246

248

250

669.5

670

670.5

671

671.5

672

230

232

234

236

238

240

242

244

246

248

250

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

2

)

)(

(

)

)(

(

)

(

s

T

y

R

y

T

x

R

x

T

x

R

x

T

y

R

y

dt

f

d

-

-

-

-

-

=

-

F

=

&

&

&

&

&

q

f

0

,

0

=

=

T

y

T

x

&

&

0

50

100

150

200

250

300

660

680

700

720

740

760

780

V

U

A

V

V

T

N

K

0

50

100

150

200

250

300

-20

0

20

40

60

80

100

Psi

U

A

V

Psi

T

N

K

230

232

234

236

238

240

242

244

246

248

250

0

5

10

15

20

25

30

35

0

50

100

150

200

250

660

680

700

720

740

760

780

800

V

U

A

V

V

T

N

K

0

50

100

150

200

250

-20

0

20

40

60

80

100

120

140

160

Psi

U

A

V

Psi

T

N

K

0

50

100

150

200

250

0

1

2

3

4

5

6

7

8

Range

214

216

218

220

222

224

226

228

230

232

234

674

675

676

677

678

679

680

681

214

216

218

220

222

224

226

228

230

232

234

140

142

144

146

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Proportional Navigation with Adaptive Terminal … 670.6 670.8 671 671.2 671.4 228 230 232 234 236...

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Transcript of Proportional Navigation with Adaptive Terminal … 670.6 670.8 671 671.2 671.4 228 230 232 234 236...