Control of Spacecraft Swarms Oct 01

8/11/2019 Control of Spacecraft Swarms Oct 01

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Advanced Space Propulsion LaboratoryAdvanced Space Propulsion LaboratoryAdvanced Space Propulsion LaboratoryAdvanced Space Propulsion Laboratory

Control of Spacecraft Swarms UsingCoulomb Forces

Lyon B. KingGordon G. Parker

Jer-Hong Chong

Satwik Deshmukh

Department of Mechanical Engineering

This research made possible through funding from the

NASA Institute for Advanced Concepts


2/21


Motivation: Coulomb Clusters

How to build a tractor beam

Without gravitons

Ions in 1/r2 confining potential

form stable crystal formations

What would charged spacecraft

do in a gravity potential?

Laser-cooled trapped ion research at NIST


3/21


Presentation Overview

Introduction to formation flying

Space-based imaging and interferometry

Formation propulsion requirements

Spacecraft charging as control force

Coulomb force metrics

Coulomb formation orbital dynamics


4/21


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Interferometry Basics

Spatial frequencies in the image are given by u,v points

Each unique physical separation yields amplitude at one u,v point

(x1,y1)

(x2,y2) d

Two Spacecraft

In physical plane

y

x (u1,v1) u

v

Single amplitude

In Fourier plane

u = x2-x1/

v = y2-y1/

Inverting Spatial Frequency Spatial Amplitude Image

To perform the inversion we need to fill the u,v plane


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3 Spacecraft

7 Spacecraft

9 Spacecraft

11 Spacecraft

5 Spacecraft

Physical

Plane

Fourier

Plane Finite apertures can fill-in

Holes in u-v plane

Consider single aperture

As array of sub-apertures

(xi, yi)

Kong, E.M., Optimal Trajectories and Orbit Design for Separated

Spacecraft Interferometry, Masters Thesis, MIT Dept. of Aeronautics

and Astronautics, November, 1998.

Cornwell, T.J., A Novel Principle for Optimization of the Instantaneous

Fourier Plane Coverage of Correlation Arrays, IEEE Trans. On Antennas

and Propagation, Vol. 36, No. 8, 1165-1167.


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Interferometry for Formations

(xi, yi)

(xj, yj)d

All separations (u,v points) less

Than d are covered by a single aperture

Separations (u,v points) greater than d

Must come from separated spacecraft

> d

Implication:

To provide seamless u,v coverage spacecraft must fly

within close proximity (~ d) of each other


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Formation Flying Introduction

Optimal imaging configurations yield non-optimal orbital trajectories

Inertial Orbit

Non-inertial Orbit

Non-inertial Orbit

Rigid Formation

Requires constant thrust

Good imaging properties

Time-varying position

About center satellite

Family of inertial orbits

Dynamic Formation

Thrust only for error correction

Complicated imaging


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Propulsion Requirements

For rigid formation: 0... ===== yyx &&&&&&

zmF

xmF

z

x

2

23

=

= Fx ~ 16 NFz ~ 6 N

m = 100 kg

x, z ~ 10 m

zzm

F

xym

F

yxxm

F

z

y

x

2

2

2

23

+=

+=

=

&&

&&&

&&&

Hills Equations for Formation

= angular velocity (for GEO =7.3x10-5 rad/sec)Figure reprinted from Kong, E.M., Optimal Trajectories and Orbit Design for SeparatedSpacecraft Interferometry, Masters Thesis, MIT Dept. of Aeronauticsand Astronautics, November, 1998.


10/21


Coulomb Control Forces

Engineering throttleable thrusters for 10 N is tough Current candidates (FEEP, Colloid) exhaust contaminants

Collisions are of paramount concern

Is there a better way to control the formation? YES!Maybe!

10-6

10-5

10-4

10-3

Coulomb

Force(N)

70605040302010

Spacecraft Separation (m)

6 kV8 kV10 kV

If the plasma Debye length is larger

than spacecraft separation, Coulomb

forces could be used

12

d

Spacecraft 1 at

Voltage Vsc1

Spacecraft 2 at

Voltage Vsc2

Vsc1 = Vsc2Spacecraft radius = 1 m

GEO plasma conditions

=

d

scsc

o

d

d

VVrrF

exp4

2

2121

2,1


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Electron emission drives Vscpositive

Ion emission drives Vsc negative

Spacecraft potential control is naturally stable

Spacecraft Charge Control

+ +

+

+

Vcontrol

Vspacecraft

V

xVplasma (Gods ground)

V


Vspacecraft

Vcontrol+

+

+

V


Vcontrol

Vspacecraft

+ +

When Vsc = Vcontrol the emission

Current is returned (Icontrol

= 0)

Vcontrol

+


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r4

2exp

2r4I

C

I

dt

dV

0

2

1

2

1

2

control

sc

+

==

phw

i

iBi

eB

sc

e

eBe Ie

m

Tken

Tk

eV

m

Tken

1-m-radius spacecraft charging analysis

for average GEO plasma environment

0

500

1000

1500

2000

2500

3000

0.00001 0.0001 0.001 0.01 0.1

Time (sec)

SpacecraftPotential

(Volts)

P = 0.1 W

P = 1 WP = 10 W

controlcontrol V

PI =


14/21


1

2

22

22

control

TotaloCoulomb

Id

PrF

=

sp

TotalThruster

gI

PF

2

=

d

FCoulomb

FCoulomb

1

2

FThruster

FThruster

Coulomb

Control

Thruster

Control

Coulomb vs. Electric Propulsion

103

104

105

106

107

FCoulomb

/FThrusteratequivalentp

ower

70605040302010

Spacecraft Separation (m)

1 mWatt

10 mWatts100 mWatts1000 mWatts

Comparison of Coulomb Control for 1-m-radius

Spacecraft in average GEO plasma with FEEP

Thruster technology (Isp = 10,000 sec, = 0.65)


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0.0280.0500.1860.00683TOTAL PROPULSION

SYSTEM MASS (kg)

0.0240.0050.0970.0068INERT MASS (kg)

0.11250.2160.370.22MASS/POWER

RATIO (kg/W)

0.2090.0210.2610.031INPUT POWER (W)

0.0040.0450.0890.00003

(using H2

for

Ion source)

MASS OF FUEL FOR

10 YEARS (kg)

0.650.650.0260.65EFFICIENCY

1000010005001 x 107SPECIFIC

IMPULSE (sec)

FEEPCOLLOID

THRUSTER

MICROPPTCOULOMB

CONTROL

MEANS OF

CONTROL

Mission design parameters for two-spacecraft flying in

20-m formation (located on Hills z-axis)

gm

FIsp

&=


16/21


Coulomb Orbit Dynamics

Do formations exist for forces acting only along position vectors?

Figure reprinted from Kong, E.M., Optimal Trajectories and Orbit Design for Separated

Spacecraft Interferometry, Masters Thesis, MIT Dept. of Aeronautics

and Astronautics, November, 1998.

x

z

y

x

z

y

x

z

y

Along-track

leader-follower

Zenith-nadir

Coulomb tether Z-axis stack

3-spacecraft formations considered

3 canonical orientations

Hills equations for relative motion

GEO orbit with 10-m separation


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3-Spacecraft Orbital Analysis

Equilibrium solutions to Hills equations

o

scsc

sc

osc

qrV

r

qV

4

4

1

=

=

x

z

y

x z

y

x z

y

Along-trackleader-follower

Zenith-nadirCoulomb tether

Z-axis stack

02

1

0

1

20

1

2

Parameter Vscr is like equivalent charge:


18/21

x

y

z

10 m

10 m

Spacecraft 1

Spacecraft 3

Spacecraft 2

Spacecraft 4

Spacecraft 0

4 collector + 1 combiner

Imaging configuration


19/21


5-Spacecraft Formation

1

2

3

4

0 Special case of 3-spacecraft z stack

Vehicle 2 and 4 remain neutral

Solution Family 1


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1

2

3

4

0

5-Spacecraft Formation

Solution Family 2

Spacecraft 1 & 3

Spacecraft 0 All 5 Spacecraft charged

Minimum Vscr identified


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Phase I Summary

Conclusions

Coulomb forces comparable with best thrusters

Continuous force dither/variation is possible

Required charge control demonstrated as early as 1979 (SCATHA)

Rich family of orbital solutions possible

Particularly suited to Fizeau interferometry (visible GEO imager?)

Coulomb control works best where thrusters work worst => synergistic control

Coulomb control can help with collision avoidance

Even if Coulomb is not used for control

natural charging will be significant perturbation that must be addressed!

On-going tasks

Examine formations for stability

Develop dynamic simulation

Formulate control laws

Search for more complicated formation solutions

Perform vehicle sizing analysis for canonical mission

Control of Spacecraft Swarms Oct 01

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