jet propulsion laboratory california institute of technology meeting no. 96 aerospace control and...

Jet Propulsion LaboratoryCalifornia Institute of Technology

Meeting No. 96Aerospace Control and Guidance Systems

Committee

Micro-spacecraft GN&C

Greg Mungas Mission and Systems Architecture Group

Jet Propulsion Laboratory

Oct. 21, 2005

Work Sponsored through Mars Program Office’s Eureka Team and Next Generation Orbiters (MAX – Mars Aeronomy Explorer, Robert Shotwell, Andrew Gray), the Laboratory of Atmospheric and Space Physics’ Inner

Magnetospheric Explorer (IMEX)

2005 Aerospace Control and Guidance Systems Committee

Overview

• Motivation and requirements for micro-spacecraft performing science

• IMEX mission case study– Detumbling and Sun Acquisition system

• MAX mission case study– Low cost spacecraft constellation at Mars

• Conclusions and Wrapup


Micro Science Spacecraft

• Spacecraft need to address science mission objectives to be able to compete in NASA AO process $350M-$750M– Mission designs are often iteratively designed from

measurements and instrument payload up. • Most measurement approaches have some fundamental

limitations in scalability that limit sizing down to and selection of micro-spacecraft

– Bouy and Constellation missions are one exception• Relatively simple instrumentation with requirement for:

– Low-cost/long life measurements (i.e. aeronomy/space weather)– Simultaneous multi-spatial measurements (i.e. space weather)

• Navigation infrastructure for feed-forward missions (Mars/Lunar NAV/COM)

– Need to address developing low cost multi-spacecraft to fit within program budgets

• Minimizing Processors and Software (i.e. Qualification of Mars Science Lab FFT algorithm ~$300K out of ~$10M instrument budget)

• Solutions typically appear to involve use of additional “non-instantaneous”, non-sensor-based information available to user


• Inner Magnetospheric Explorer to survive in and study earth’s radiation belts over an extended duration of time.

• Proposed as a SMEX ~$15M hitchhiker spacecraft on last Titan IUS carrying ~$1B military spy satellite

• Extreme radiation environment in radiation belts limited use of conventional processors (i.e. state-machine-based and open loop ground control)

• “Free” hitchhiker ride provided no favors– No active processor– Unfavorable thermal environment (no heat for

10 hour period on spent rocket stage)– Random deployment tumble of up to 5rpm– Upper stage and RCS extreme plume

contamination• i.e. mounted beneath an RCS thruster module

IMEX Mission Summary


• Needed to deal with early deployment – Large angle (non-linear) spinup, detumbling, and sun acquisition maneuvers

• Developed simple state-machine based controller, Spinning Smallsat Detumbling and Sun Acquisition System [G. Mungas, D. Lawrence AIAA 2000-4143]

• Subsequently discovered other’s with similar design problem (i.e. Carnegie Mellon’s Helio-gyro experiment, MAX mission, etc.)

• Managed to develop concept for single module that can perform deployment operation as a small “slap-on” module.

IMEX GNC Design Theory

InertialSensor

Sun PresenceDiode

SpinupThruster

PrecessionThruster

SunCrossingDiode

y

x

z

InertialSensor

Sun PresenceDiode

SpinupThruster

PrecessionThruster

SunCrossingDiode

y

x

z


Spinning S/C Stability Theory

• Initial detumbling stabilization based on Lyapunov-like stability theory (not necessarily to single attractor) in one of two regions on body-mounted manifold 2222 HHHH zyx

MOMENTUM SPHERE2222 HHHH zyx

MOMENTUM SPHERE

ENERGY ELLIPSOID

TI

H

I

H

I

H

zz

z

yy

y

xx

x 2222

ENERGY ELLIPSOID

TI

H

I

H

I

H

zz

z

yy

y

xx

x 2222


Spinup Criteria

+ Z

2

Separatrix

Separatrix

- Z

+ X

- X

mins

0

• Spinup stabilization criteria and sizing of actuators based only on knowledge of spacecraft moment’s of inertia, worst case deployment tumble rate, and effective actuator torque

zzyyzz

xxxxyy

III

III

)(

)(tan

)costan(sin0min s

L

IF

spinup

tspinup

2

max )(

(2) Nutating Spin

z

x

zz

xx

y

y

th

zh

22

22221

2zzttzz IIIhh

2112 zzIT 2

22

22 zztt IIT

22

212 zztt

z

t III

IT

th zt

ztz

I

II

)(

th

th

y

x

h

h


Effective Torquing Efficiency

• Even with finite thrusting times over large spin angles, , effective applied torquing efficiency, torque remains high

xx

actuator

effective

y

x

2sin

2

torque (4)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 30 60 90 120 150 180

Torquing Angle ( in deg)

torq

ue


Denutation

• Simple denutation law applied in body frame.

• Implemented with low res. rate gyro or accelerometer.

th

y

y

x , Torque Axis, Precession Direction

DE

NU

TA

TIO

N

ZO

NE

Torque axis


Sun Acquisition I• Developed sensor/actuator candidate bang-bang control

hardware solution that should always close distance between inertial angular momentum vector, , and local sun vector, .

• Sun-seaking “Hardware” solution is based only on hemispherical slit photo-diode collocated with actuated transverse torquing axis

H

Optical Slit

x

y

zH

S

H

x

z

S

Inertial Frame Spacecraft Frame

S


Sun Acquisition II

• Define “Set” of normalized S/C properties (mass and thruster torque) that have sun-tracking solutions with acceptable tolerances on max nutation angle

;;xx

zz

xx

yy

I

I

I

I ;

22

ii

i

s

i I

;2

; ss

ii

tt

Normalized Parameters

Normalized Dynamics And Kinematics

zyxz

yxzy

xzyx

12

12

2

qtd

qd

zyx

zxy

yxz

xyz

~

0

0

0

0~


Sun Acquisition III

XX

ZZ

I

I

XX

YY

I

I

Major Axis Spinners

• 180° Acquisition

• Thruster On-Time = 1/12 s

• 5° Thruster steps

• 0° Initial nutation

Simulation Parameters

Spherically Symmetric


Sun Acquisition IV

Minor Axis Spinners

XX

ZZ

I

I

XX

YY

I

I

• 180° Acquisition

• Thruster On-Time = 1/12 s

• 5° Thruster steps

• 0° Initial nutation

Simulation Parameters

Spherically Symmetric

Not Realistic Mass Distributions


Detumbling/Sun Acquisition Summary

• Developed a simple hardware/control logic solution to a traditionally complex, non-linear spacecraft deployment problem. Solution (which can be packaged as add-on module to experiment) consists of:– Miniature shielded Photo-cell – sun acquisition– Spin-up and Precession Thruster + Fuel– Denutation sensor (MEMS rate gyro or accelerometer)– Simple state-machine + If/then control logic

• No requirement for S/C processor – Significant mission cost savings – flight qualifying software– Suitable for probes in high radiation environments – no

processor requirements. Measurements can be state-machine-based


• Develop low cost mission architecture for performing multi-node network Mars Aeronomy Explorer mission.

• Simultaneous spatial observations of electric/magnetic fields throughout magnetosphere and low altitude ion/neutrals composition

• Residual NAV/COM network• Package entire mission into a ~$500M cost cap

Group 1b : 4 Magnetometer Spacecraft, 100 x 10,000 km

Group 2 : 2 identical telecommunications spacecraft, 150 x 1,000 km

Group 3 : 2 identical spinner Spacecraft, 200 x 10,000 km

Group 1a : 2 Magnetometer Spacecraft, 250 x 30,000 km

MAX Mission Overview

SPINNERS in Highly Elliptic Orbits



MAX Constellation Spacecraft



MAX Spinners

• Adapt open loop ADCS architecture developed for the Laboratory of Atmospheric and Space Physics (LASP) SNOE spacecraft (~$15M mission including Pegasus launch) to the Mars environment.– SNOE (in sun synchronous orbit) was open loop

magnetorquer precessed ~1/day to track apparent solar motion.

– For open loop control, MAX spinner requires tracking RAAN precession of orbit normal vector within 1 with propulsive torque (no significant Mars magnetic field)

torqueth

h


MAX Orbital Precession• Maximum RAAN precession rate of <1.5/day

– Consistent with SNOE implementation approach

nRAAN Precession vs. Orbital Inclination for

Decaying 200x10,000 km Orbit

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 10 20 30 40 50 60 70 80 90

Orbital Inclination (deg)

Orb

ita

l Pre

ce

ss

ion

Ra

te

(de

g/d

ay

)

10,000 km

8,000 km

6,000 km

Apogee Altitude

mZ

n


Active Denutation

• Body frame denutation coupled control law– Restricts Precession torques to

a <50% duty cycle - ~25% for efficient fuel usage (see next slide)

• For MAX Spinner, applied torque momentum capability: – Vacuum arc thruster:

• Precession: >55/day• Min Angular Bit: 0.00002

– Milli-Newton N2H2 thruster:• Precession: >>100/day • Min Angular Bit: 0.0002

• Given <1.5/day Precession Requirement, Active Denutation Control is NOT a Significant Implementation Constraint

th

y

y

x , Torque Axis, Precession Direction D

EN

UT

AT

ION

Z

ON

E


Aerodynamic Drag Induced Nutation

Zz ˆ,ˆ

Yaeroˆ,

x

y

X

z

INERTIAL FRAME ( ZYX ˆ,ˆ,ˆ ) BODY FRAME ( zyx ˆ,ˆ,ˆ )

Zz ˆ,ˆ

Yaeroˆ,

x

y

z

0

cos)(

sin)(

z

zaerozxzt

tzy

zaerozyzt

ztx

h

thhII

IIh

thhII

IIh

)ˆsinˆcos( ytxtI

Ih zz

zz

aerott

22maxtan

zz

aerot

z

t

I

I

h

h

11

z

aero

z I

Figure 5. Calculating Nutation Excited by Constant Inertial Torque (close approximation of ~inertially fixed aerodynamic torque relative to spin rate)

Zz ˆ,ˆ

Yaeroˆ,

x

y

X

z

INERTIAL FRAME ( ZYX ˆ,ˆ,ˆ ) BODY FRAME ( zyx ˆ,ˆ,ˆ )

Zz ˆ,ˆ

Yaeroˆ,

x

y

z

0

cos)(

sin)(

z

zaerozxzt

tzy

zaerozyzt

ztx

h

thhII

IIh

thhII

IIh

)ˆsinˆcos( ytxtI

Ih zz

zz

aerott

22maxtan

zz

aerot

z

t

I

I

h

h

11

z

aero

z I


Zz ˆ,ˆ

Yaeroˆ,

x

y

X

z

ZYX ˆ,ˆ,ˆ zyx ˆ,ˆ,ˆ

Zz ˆ,ˆ

Yaeroˆ,

x

yz

NUTATION ANGLE,

0

cos)(

sin)(

z

zaerozxzt

tzy

zaerozyzt

ztx

h

thhII

IIh

thhII

IIh

Solution is )ˆsinˆcos( ytxtI

Ih zz

zz

aerott

22maxtan

zz

aerot

z

t

I

I

h

h

Valid for spin rates >> precession rates 11

z

aero

z I


Zz ˆ,ˆ

Yaeroˆ,

x

y

X

z

ZYX ˆ,ˆ,ˆ zyx ˆ,ˆ,ˆ

Zz ˆ,ˆ

Yaeroˆ,

x

yz

NUTATION ANGLE,

0

cos)(

sin)(

z

zaerozxzt

tzy

zaerozyzt

ztx

h

thhII

IIh

thhII

IIh

Solution is )ˆsinˆcos( ytxtI

Ih zz

zz

aerott

22maxtan

zz

aerot

z

t

I

I

h

h

Valid for spin rates >> precession rates 11

z

aero

z I



Aerodynamic Induced Disturbances

• Assuming 6 rpm, 10 cm Cp/Cg axial offset, 60 minute flight through worst case periapse (200x10,000km orbit), with MAX’s worst case aerodynamic profile– <0.007 Precession of – <0.000003 Excited Nutation

h


Attitude Determination with HCI’s

HCI Pointing

Roll Angle

HCI Mounting Angle

200 km altitude 1000 km altitude

Projected Horizon Plane Projected Horizon

122.36

126.84

47.46 56.56

Projected Horizon Plane

Figure 7. HCI Spin Angle Measurements for 1 Roll Angle Pointing Error as a Function of Altitude for a 45 HCI Mounting Angle.

HCI Pointing

Roll Angle

HCI Mounting Angle



122.36

126.84

47.46 56.56


HCI Pointing

Roll Angle

HCI Mounting Angle

HCI Pointing

Roll Angle

HCI Mounting Angle



122.36

126.84

47.46 56.56




122.36

126.84

47.46 56.56



HCI Pointing

Roll Angle

HCI Mounting Angle

-2000 -1000 0 1000 2000

-2000

-1500

-1000

-500

0

500

1000

1500

2000



-2000 -1000 0 1000 2000

-2000

-1500

-1000

-500

0

500

1000

1500

2000

122.36

126.84

47.46 56.56



HCI Pointing

Roll Angle

HCI Mounting Angle

-2000 -1000 0 1000 2000

-2000

-1500

-1000

-500

0

500

1000

1500

2000



-2000 -1000 0 1000 2000

-2000

-1500

-1000

-500

0

500

1000

1500

2000

122.36

126.84

47.46 56.56


HCI Pointing

Roll Angle

HCI Mounting Angle

HCI Pointing

Roll Angle

HCI Mounting Angle

-2000 -1000 0 1000 2000

-2000

-1500

-1000

-500

0

500

1000

1500

2000



-2000 -1000 0 1000 2000

-2000

-1500

-1000

-500

0

500

1000

1500

2000

122.36

126.84

47.46 56.56


-2000 -1000 0 1000 2000

-2000

-1500

-1000

-500

0

500

1000

1500

2000



-2000 -1000 0 1000 2000

-2000

-1500

-1000

-500

0

500

1000

1500

2000

122.36

126.84

47.46 56.56




HCI AD Sensitivity

• Over entire altitude range, HCI’s provide better than 0.1 degree instantaneous roll angle knowledge for a perfectly spherical Mars.


Filtering Body-fixed Measurement Errors

• Given extremely low disturbance environment, observed motion during a single pass is effectively due to body-fixed mounting errors.

h


Filtering w/ Elliptic Orbit• Similar geometric interpretation as circular orbit with low altitude arc to

remove estimation errors associated with body-fixed sensor errors

Orbital

Geometry

errh

h

errh

h

Sensor Design Constraint

Attitude Estimation

Arc (a)

Arc Traverse

Time

1deg/day RAAN

Precession over Arc

Peak Altitude

Nadir to Horizon Angle

(a)

Max Variation in a over Arc

(deg) (min) (deg) (km) (deg) (deg)0.0 0.0 0 0.000 200.0 70.8 0.0

10.0 2.4 15 0.002 205.0 70.6 0.2

20.0 4.8 29 0.003 220.1 69.9 0.9

30.0 7.3 44 0.005 245.4 68.8 2.040.0 9.8 59 0.007 281.1 67.5 3.450.0 12.4 74 0.009 327.6 65.8 5.060.0 15.0 90 0.010 385.4 63.9 6.970.0 17.7 106 0.012 454.8 61.9 8.980.0 20.5 123 0.014 536.6 59.7 11.190.0 23.5 141 0.016 631.6 57.5 13.3

100.0 26.6 160 0.018 740.6 55.2 15.6110.0 29.9 179 0.021 864.7 52.9 17.9120.0 33.4 200 0.023 1005.1 50.5 20.3

130.0 37.1 223 0.026 1163.0 48.2 22.6

140.0 41.2 247 0.029 1340.1 45.8 25.0

Number of Attitude

Measurements at 6rpm


Implementation Plan

torqueth

h

RAAN Precession

Pointing Requirement

Daily Permissible Tracking Error

Angular Momentum Vector Maneuver Starting Point

• ~Daily download of HCI vector• Filtered State Update• Upload of Daily Thruster Pulse Train

h


Hardware/Propellant Summary

• 2 x = ~10’s g.

• Spinup + precession thruster (10’s g)

• Nutation sensor (accelerometer or rate gyro) <10g.

• 0.5-1kg worst case propellant for 2 year mission + storage and plumbing

• Wiring to C&DH


Conclusions

• Proposed stable alternative open loop control architecture for low altitude velocity-vector-aligned mapping to within 1 for a low cost/low mass network spacecraft mission. Primary control error is orbital RAAN precession.

• HCI Attitude error estimates down near ~0.1 appear possible by triangulating in on h vector at different orbital locations

• Pointing control is very robust with >10-100 fold capability in daily momentum management and <1/1000 of minimum pointing error with thruster minimum impulse bits


Questions??

jet propulsion laboratory california institute of technology meeting no. 96 aerospace control and...

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