Integrated Orbit and Attitude Control for a Nanosatellite with Power

Constraints

Bo NaaszMatthew BerryHye-Young Kim

Chris Hall

13th Annual AAS/AIAA Space Flight Mechanics Meeting

February 9-13, 2003, Ponce, Puerto Rico

Virginia Tech Department of Aerospace & Ocean

Engineering

AAS 03-100

Overview

• ION-F and HokieSat• Orbit & Attitude Coupling• Dynamics• Control• Simulation/Software• Results

Ionospheric Observation Nanosatellite Formation (ION-F)

• Three of 10 student-built spacecraft in AFOSR/DARPA University Nanosatellite Program, also sponsored by NASA Goddard Space Flight Center

• Three-satellite stack will launch from Shuttle Hitchhiker Experiment Launcher System

• Mission goals– Formation flying demonstration– Distributed ionospheric measurements

HokieSat• 18.25 inch major diameter• Hexagonal footprint• 12 inches tall• 39 lbs (~18 kg)

ION-F

USUSat

Dawgstar

HokieSat DCS Hardware• Orbit control

– UW/Primex Pulsed Plasma Thrusters (PPT)• Impulse bit per thruster: 56 N• No radial thrust• Paired thrusters cannot fire simultaneously

• Attitude control– Magnetic torque coils

• Interact with Earth’s magnetic field• Provide < 5 x 10-5 N-m Torque

– PPTs for limited yaw steering

Pulsed Plasma Thruster

V

1

2

34

V

1

2

3

V

1

2

34

PPT layout

Maneuver Modes

• “Normal” mode– Slew as required to point thrusters– Negligible thrust torque– 180 degree slews required

• “Sideways” mode– Allow thrust torque– Frequent control interruption– No slews required

V

1

4

3

2

V1 4

32

Sources of Orbit-Attitude CouplingNatural dynamics:

• Attitude dependent orbit perturbations– Atmospheric drag– Solar radiation pressure

• Orbit dependent attitude perturbations– Magnetic field variation– Gravity gradient torque

• Dynamical coupling (very weak)

Guidance Navigation & Control (GNC) System:

• Actuator induced disturbances– Non-coupled thrusters– Thruster disturbance torques

• Shared resources– Actuators – Sensors– Others

• Subsystem inter-dependencies– Drag/SRP control– Thruster pointing

Dynamics• Orbit

– Two body motion– Control forces from thrusters– Perfect state knowledge

• Attitude– External torques from gravity gradient,

thrusters– Control torques from magnetic torque coils– Perfect state knowledge

Orbit Control

*

*

*

*

*

* Gains vary with trig functions of true anomaly to minimize error growth

Mean motion control:

Elemental Lyapunov Control:

Thrust On/Off Logic

Normal mode

Fire PPT 2&35

1

4

3

2

b2

b1

If

Then

Else

Thrust On/Off Logic (cont’d)Sideways mode

Fire PPT 1

Fire PPT 2&3

Fire PPT 4

b2

b1

1

4

3

2

Pointing requirement independent of desired thrust direction

Attitude Control

• LQR• Torque perpendicular to magnetic field

direction only• Desired attitude set by maneuvering

mode and desired thrust direction• Assume torque is throttleable, with a

maximum of ~ 5 x 10-5 N-m Torque

Simulation• Reference orbit:

– Semi-major axis: 6770 km– Circular (e 0)– Inclination: 52

• Spacecraft initial conditions:– 700m leader follower– 700m same ground track

• Propagation:– 1 second time step– Runge-Kutta integration for Orbit

and Attitude• Software

– written in C++ – Prototype of flight code– 4 processes

• Orbit determination• Orbit control• Attitude determination• Attitude control

Leader Follower Formation

Same Ground Track Formation

Results – Leader Follower, Normal Mode

0 5 10 15-0.2

0

0.2

0.4

0.6

0.8

[Orbit Number]

[km

]

Position Error - S20010

r1

r2

r3

0 5 10 150

50

100

150

200

[Orbit Number]

[de

gre

es

]

Angle Error

0 5 10 15-2

-1

0

1

2x 10

-6

[Orbit Number]

[N m

]

Applied Torque

g1

g2

g3

0 5 10 15-1.5

-1

-0.5

0

0.5

1

x 10-4

[Orbit Number]

[N]

Applied Thrust

T1

T2

T3

Results – Same Ground Track, Normal Mode

0 5 10 15-4

-3

-2

-1

0

1

[Orbit Number]

[km

]Position Error - S20020

r1

r2

r3

0 5 10 150

50

100

150

200

[Orbit Number]

[de

gre

es

]

Angle Error

0 5 10 15-2

-1

0

1

2x 10

-6

[Orbit Number]

[N m

]

Applied Torque

g1

g2

g3

0 5 10 15-1.5

-1

-0.5

0

0.5

1

x 10-4

[Orbit Number]

[N]

Applied Thrust

T1

T2

T3

Results – Same Ground Track, Sideways Mode

0 5 10 15-0.2

0

0.2

0.4

0.6

0.8

[Orbit Number]

[km

]

Position Error - S21020

r1

r2

r3

0 5 10 150

2

4

6

8

10

[Orbit Number]

[de

gre

es

]

Angle Error

0 5 10 15-1

-0.5

0

0.5

1x 10

-7

[Orbit Number]

[N m

]

Applied Torque

g1

g2

g3

0 5 10 15-1.5

-1

-0.5

0

0.5

1

x 10-4

[Orbit Number]

[N]

Applied Thrust

T1

T2

T3

Summary

Future Work

• Orbit-attitude coupling issues are real for HokieSat– Induced disturbances– Subsystem independences

• “Normal” maneuvering mode– May be sufficient for simple maneuvers– Fails for more complex maneuvers (insufficient torque, power)

• “Sideways” maneuvering mode – Successful for all attempted maneuvers– Thrust in +/- velocity direction, one out of plane direction (no slews)

• Estimation (GPS)• Orbit perturbations (mean element feedback)• Nanosat Cross Link Transceiver (NCLT) issues

Normal mode clipSideways mode clip

Questions?

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Choosing the control

we get:

Use LaSalle’s Invariance Principle to prove global

asymptotic stability under this control law

• Control orbital 6DOF as two systems– First System:

• First five elements (size, shape, orientation of orbit)

Orbital Control

We want:

Combing these equations (with =1)

And solving for a

For uncontrolled spacecraft,

And the relative dynamics are:

Orbit Control

– Second system (a feedback phasing maneuver):

• Sixth element (angular position within the orbit)

Orbit Dynamics

f and G given by Gauss’ Form of LPEu includes external forces from control, perturbations

Attitude Dynamics

ge includes external torques from magnetic control, gravity gradient, thrusters

0 5 10 15-0.2

0

0.2

0.4

0.6

0.8

[Orbit Number]

[km

]

Position Error - S21110

r1

r2

r3

0 5 10 150

2

4

6

8

10

[Orbit Number]

[de

gre

es

]

Angle Error

0 5 10 15-1.5

-1

-0.5

0

0.5

1x 10

-7

[Orbit Number]

[N m

]

Applied Torque

g1

g2

g3

0 5 10 15-1.5

-1

-0.5

0

0.5

1

x 10-4

[Orbit Number]

[N]

Applied Thrust

T1

T2

T3

Results – Leader Follower, Sideways Mode, Eclipse

0 200 400-800

-600

-400

-200

0

200

[Orbit Number]

[km

]Position Error - S21002

r1

r2

r3

0 100 200 300-400

-300

-200

-100

0

100

[Orbit Number]

[km

]

Position Error - S21003

r1

r2

r3

0 500 1000-400

-300

-200

-100

0

100

[Orbit Number]

[km

]

Position Error - S21013

r1

r2

r3

0 500 1000-1500

-1000

-500

0

500

[Orbit Number]

[km

]

Position Error - S21102

r1

r2

r3

Spacecraft Formation Flying

Very Large Array – New Mexico27 dishes, 25-m diameter =

resolution of a 36km antenna

TechSat21 – Air Force radar formation. Increase

geolocation accuracy from 5-10 km to ~10m

Multiple spacecraft in formation provide• Unlimited effective aperture • Improved reliability • Reduced life cycle cost • Inherent adaptability

Problem StatementControl the motion of formation-flying spacecraft using integrated nonlinear orbit and attitude feedback control laws to achieve a predefined target orbit.

Sample formations: • Leader follower• Same ground track

Constraints:• No radial thrust • Magnetic torque• No simultaneous orbit & attitude control• Eclipse constraints

− maneuvering spacecraft− target orbit− leader spacecraft