Talk charts for presentation at the 2009 AIAA Guidance, Navigation, and Control Conference & Exhibit, held August 10-13, 2009, Chicago, IL

1. An Autonomous Onboard Targeting
Algorithm using Finite Thrust
Maneuvers
Sara K. Scarritt, Belinda G. Marchand, MichaelW.Weeks
AIAA Guidance, Navigation, and Control Conference & Exhibit
10-13August 2009, Chicago, IL
AIAA 2009-6104
1

2. Introduction
 Onboard guidance for Orion lunar return
 Two-level targeting algorithm
 Based on linear system theory
 Designed for impulsive maneuvers
 In a main engine failure scenario, impulsive approximation
invalid
 Adapt two-level targeter to incorporate finite burns while
retaining its simplicity
22

3. Classical Impulsive Level I Process
Goal: Position Continuity Only Control Variables: DV’s
BEFORE LEVEL I
AFTER LEVEL I

4. Classical Level II Process:
Goal: Meet Specified Constraints (e.g. Velocity Continuity),
Control Variables: Time & Position of Patch States
BEFORE LEVEL II
IMPLEMENTATION
IN THE N/L SYSTEM
LEVEL II:
LINEAR CORRECTION

5. T
kr
1k 
k
T
Level 1: Impulsive vs. Finite Burn
5
1
Constraint:
Control Variables: ,
k
k Tt



r 0
u1
Constraint:
Control Variables:
k
k



D
r 0
v
IMPULSIVE FINITE BURN
kr
1kDv
1k 
k
11 1
g
m
m

 
 
 
  
 
 
  
r
v
x
u
6 1
 
  
 
r
x
v

6. Variational Equations:
Impulsive vs. Finite Burn
6
, 1 , 1 1 1 1
, 1 , 1 1 1 1
k k k kk k k k k k
k k k kk kk k k k
A Bt t
C Dt t
   
   
 
    
   
    
     
    
     
r v r v
v a v a
IMPULSIVE
FINITE BURN
, 1 , 1 , 1 , 1 , 1
, 1 , 1 , 1 , 1 , 1
, 1 , 1 , 1 , 1 , 1
, 1 , 1 , 1 , 1 , 1
T
T T
T
T k T k T k T k T kT T T
T k T k T k T k T kT T T
T k T k T k T k T kT g T
T k T k T k T k T kg g T
T g T
A B E F Gt
C D H I Jt
K L M N Om m t
P Q R S Tm m t
t
 
 
 
 
 

    
 
    
 
    
 
    
 
 
 
 
  
 
 
  
r v
v a
u u
1
1 1
1 1 1
1 1 1
1 1
1
, 1 , 1 , 1 , 1 , 1 1 1 1
k
k k
k k k
k k k
k g k
g g k
T k T k T k T k T k k k k
t
t
m m t
m m t
U V W X Y t
 
 
 
 
 

 

  
 
  
 
 
 

 
       
  
     
  
  
  
      
r v
v a
u u
, 1 , 1 1 1 1
, 1 , 1 1 1 1
k k k kk k k k k k
k k k kk kk k k k
A Bt t
C Dt t
   
   

  

 
  


   
     
    
     
r v r v
v a v a
, 1 , 1 1 1 1
, 1 , 1 1 1 1
k k k kk k k k k k
k k k kk kk k k k
A Bt t
C Dt t
   
   

  

 
  


   
     
    
     
r v r v
v a v a
, ,
, ,
k T k Tk k k T T T
k T k Tk k T Tk T
A Bt t
C Dt t
   
   
 
   
     
    
     
r v r v
v a v a

7. Level 1 Targeting
 Direct fromTEI-3 to Earth entry
 Entry targets:
 GeodeticAltitude (km) 121.92
 Longitude (deg) 175.6365
 GeocentricAzimuth (deg) 49.3291
 Geocentric Flight PathAngle (deg) -5.86
7

8. Level II Algorithm:
Impulsive vs. Finite Burn
8
k

v
k

v
1k 
k
1k 
 
 
1 2 1
0 0 1 1
Constraints: , , , , , , , , , , v
Control Var , ,iables: , , ,,
jn TEI
j
n n
h
t t t
 
  
 
  

 
D D D D D 
 
V = v v v A =
b = r r r
k

v
k

v
1k 
k
1k 
T
IMPULSIVE FINITE BURN
 
1T
M
T
M MM
 
 

D 
 D D   
     
    
  


V
V Vb
A A
b
bb
A

9. Variational Equations:
Impulsive vs. Finite Burn
9
, 1 , 1 1 1 1
, 1 , 1 1 1 1
k k k kk k k k k k
k k k kk kk k k k
A Bt t
C Dt t
   
   
 
    
   
    
     
    
     
r v r v
v a v a
IMPULSIVE
FINITE BURN
, 1 , 1 , 1 , 1 , 1
, 1 , 1 , 1 , 1 , 1
, 1 , 1 , 1 , 1 , 1
, 1 , 1 , 1 , 1 , 1
T
T T
T
T k T k T k T k T kT T T
T k T k T k T k T kT T T
T k T k T k T k T kT g T
T k T k T k T k T kg g T
T g T
A B E F Gt
C D H I Jt
K L M N Om m t
P Q R S Tm m t
t
 
 
 
 
 

    
 
    
 
    
 
    
 
 
 
 
  
 
 
  
r v
v a
u u
1
1 1
1 1 1
1 1 1
1 1
1
, 1 , 1 , 1 , 1 , 1 1 1 1
k
k k
k k k
k k k
k g k
g g k
T k T k T k T k T k k k k
t
t
m m t
m m t
U V W X Y t
 
 
 
 
 

 

  
 
  
 
 
 

 
       
  
     
  
  
  
      
r v
v a
u u
, 1 , 1 1 1 1
, 1 , 1 1 1 1
k k k kk k k k k k
k k k kk kk k k k
A Bt t
C Dt t
   
   

  

 
  


   
     
    
     
r v r v
v a v a
, 1 , 1 1 1 1
, 1 , 1 1 1 1
k k k kk k k k k k
k k k kk kk k k k
A Bt t
C Dt t
   
   

  

 
  


   
     
    
     
r v r v
v a v a
, ,
, ,
k T k Tk k k T T T
k T k Tk k T Tk T
A Bt t
C Dt t
   
   
 
   
     
    
     
r v r v
v a v a

10. Total Cost Constraint:
Impulsive vs. Finite Burn
10
v | |k k k
 
D  v v
 
0v ln 1 kg T k
k sp
k
m t t
I g
m
 
D    
 
 v , ,k k T kf t t mD 
 
 
1 1
1 1
, , ,
, , ,
k k k k k k
k k k k k k
t t
t t
 
 
 
 


v v r r
v v r r
IMPULSIVE
FINITE BURN
1
0
1
[ ]
n
k g burn j
j
m m m t


  D

11. Main Engine Simulation
 Initial guess data
 Epoch: 4-Apr-2024 15:30:00TDT
 Initial mass: 20339.9 kg (total fuel =
8063.65 kg)
 Main EngineThrust: 33,361.6621 N
 Main Engine Isp: 326 sec
 State (J2000 Moon-centered inertial
frame):
 X: -1236.7970783385588 km
 Y: 1268.1142350088496 km
 Z: 468.38317094160635 km
 Vx: 0.0329108058365355 km/sec
 Vy: 0.589269803607714 km/sec
 Vz -1.528058717568413 km/sec
 Entry constraints:
 GeodeticAltitude (km): 121.92
 Longitude (deg): 175.6365
 GeocentricAzimuth (deg): 49.3291
 Geocentric Flight PathAngle (deg): -
5.86
11

12. Results (1/2)
12 MCI Frame Perspective
Earth
Moon

13. Results (2/2)
 Comparison of finite burn and impulsive algorithms:
13

14. Auxiliary Engine Simulation
 Same initial guess data and constraints
 Assume main engine failure afterTEI-1
 TEI-2 andTEI-3 performed using auxiliary engines:
 Auxiliary EngineThrust: 4,448.0 N
 Auxiliary Engine Isp: 309 sec
1414

15. Results
 Maneuver and final constraint data:
1515

16. Lunar Cycle Simulations
 Simulations run for 10 different days spanning February 2024
 Patch points from converged impulsive runs
 Initial lunar orbit of 100 km, targeting altitude (121.9 km)
and flight path angle (-5.86o)
 Auxiliary engines used forTEI-2 andTEI-3

17. Results

18. Delayed Patch Points
 Patch points associated with specific epoch
 Targeter must converge even if the patch points are not
current
 Using February 1 input file from previous example, initial
epoch delayed for (a) 3 hours and (b) 12 hours

19. Results

20. Conclusions and Future Work
 Two-level targeting algorithm developed for finite burn
maneuvers
 Algorithm successfully targets lunar return trajectory
 Using main engines
 Using auxiliary engines following simulated failure of main
engines afterTEI-1
 Future work
 Implementing thruster steering law
 Automated patch point selection
20