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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