An Autonomous Onboard Targeting

Algorithm using Finite Thrust

Maneuvers

Sara K. Scarritt, Belinda G. Marchand, Michael W. Weeks

AIAA Guidance, Navigation, and Control Conference & Exhibit

10-13 August 2009, Chicago, IL

AIAA 2009-6104

1

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

2 2

Classical Impulsive Level I Process Goal: Position Continuity Only Control Variables: DV’s

BEFORE LEVEL I

AFTER LEVEL I

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

T

kr

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 kr

1kDv

1k

k

11 1

g

m

m

r

v

x

u

6 1

rx

v

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 , 11 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 kk 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

Level 1 Targeting Direct from TEI-3 to Earth entry

Entry targets:

Geodetic Altitude (km) 121.92

Longitude (deg) 175.6365

Geocentric Azimuth (deg) 49.3291

Geocentric Flight Path Angle (deg) -5.86

7

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

1

T

M

TM MM

D D D

V

V Vb

A A

b

bbA

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 , 11 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 kk 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

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 tI 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 jj

m m m t

D

Main Engine Simulation Initial guess data

Epoch: 4-Apr-2024 15:30:00 TDT

Initial mass: 20339.9 kg (total fuel =

8063.65 kg)

Main Engine Thrust: 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:

Geodetic Altitude (km): 121.92

Longitude (deg): 175.6365

Geocentric Azimuth (deg): 49.3291

Geocentric Flight Path Angle (deg): -

5.86

11

Results (1/2)

12 MCI Frame Perspective

Earth

Moon

Results (2/2)

Comparison of finite burn and impulsive algorithms:

13

Auxiliary Engine Simulation

Same initial guess data and constraints

Assume main engine failure after TEI-1

TEI-2 and TEI-3 performed using auxiliary engines:

Auxiliary Engine Thrust: 4,448.0 N

Auxiliary Engine Isp: 309 sec

14 14

Results

Maneuver and final constraint data:

15 15

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 for TEI-2 and TEI-3

Results

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

Results

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 after TEI-1

Future work

Implementing thruster steering law

Automated patch point selection

20