Sanny omar esa_presentation_no_video

1. Sanny Omar, PhD
University of Florida
ADAMUS lab
ESA Presentation
1
A Drag Device and Control Algorithm for
Spacecraft Attitude Stabilization and De-Orbit
Point Targeting using Aerodynamic Drag

2. Outline
Research objectives
Drag De-Orbit Device (D3) hardware and
attitude stability
Guidance trajectory generation algorithm
Navigation and trajectory tracking algorithms
D3 CubeSat mission
Conclusions and future work
2

3. Research Overview and Objectives
Most Low Earth Orbit (LEO) spacecraft do not have thrusters and
re-enter atmosphere in random locations at uncertain times
Objects pose a risk to persons, property, or other satellites
Skylab de-orbit over Australia is an example
Has become a larger concern with the recent increase in small satellites
Retractable drag de-orbit device (D3) to expedite de-orbit and
facilitate orbital maneuvering, collision avoidance, and re-entry
point targeting
“Targeting Algorithm” which utilizes aerodynamic drag modulation
to lead a satellite to a desired de-orbit location
Guidance trajectory generation, navigation, and guidance tracking
components
2U CubeSat to test the drag device and control algorithms in orbit
3

4. D3 Hardware and
Attitude Stability
4

5. Drag De-Orbit Device (D3) Overview
 Drag De-Orbit Device (D3) attaches to
existing CubeSats to facilitate de-orbit
of a 12U, 15 kg satellite in 25 years
from a 700 km circular orbit
 .5 𝑚2
drag area
 D3 is retractable and facilitates re-entry
point targeting, orbital maneuvering,
and collision avoidance
D3 Installed on CubeSat
5
Orbit Lifetime vs. Initial Circular Orbit Altitude with D3 and in Max Drag without D3

6. Drag De-Orbit Device (D3) Design
Consists of four retractable, independently
actuated tape spring booms
4 cm wide and up to 3.7 m long
Inclined at 20 degree angle relative to x-y plane
Boom angle provides passive aerodynamic
attitude stability
Booms collectively deployed or retracted to
modulate drag for orbital maneuvering
Swarm maintenance and controlled re-entry
capabilities
Two opposing booms can be partially
retracted while other two remain fully
deployed for gravity gradient stabilization
Embedded magnetorquers used for detumble
and damping steady state attitude oscillations
x
z
y
6

7. D3 Interfacing
 D3 adapter stage houses magnetorquers and interfaces
with standard CubeSat structure
 Each D3 deployer requires two wires for motor and four
wires for rotary encoder that measures boom
deployment
 24 wire ribbon cable for deployers
 6 wire ribbon cable for magnetorquers
7
x
y
z

8. Deployer Uses Motor to Drive Boom
8

9. Maximizing Miss Distances using Aerodynamic Drag for 400 and 600 km Circular Orbits
400 km orbit 600 km orbit
9
 Product of orbit lifetime and surface area unchanged before and after drag device deployment
 If collision risk directly related to cross-sectional area, drag device may not reduce collision risk
 Ability to maneuver away from impending collisions makes D3 a more appealing de-orbit mechanism than
static sails

10. Power-limited BDot De-Tumble Law
 Conventional B-Dot: 𝝁 𝑑𝑒𝑠 = −𝐾 𝑩
𝑩 =
𝑩2 − 𝑩1
Δ𝑡
𝝉 𝑚𝑎𝑔 = 𝝁 × 𝑩
 If 𝑩 is large, achieving 𝝁 𝑑𝑒𝑠 might
require excessive power
𝝁 = 𝐼𝐴𝑛 𝒏
𝑃 = 𝐼𝑉 = 𝐼2 𝑅
 Scale magnitude of 𝝁 𝑑𝑒𝑠 such the
required power ≤ 𝑃𝑚𝑎𝑥
 Required 𝑃𝑟𝑒𝑞 calculated
 If P𝑟𝑒𝑞 ≥ 𝑃𝑚𝑎𝑥
 𝝁 𝑑𝑒𝑠 = 𝝁 𝑑𝑒𝑠0
𝑃 𝑚𝑎𝑥
𝑃𝑟𝑒𝑞
10

11. Attitude Simulation
 Spacecraft z-axis should align with LVLH
y-axis (along-track) while spacecraft x-axis
aligned with LVLH x-axis (radial)
 Less than 5 degree pointing error in ISS
orbit
 Magnetorquers utilized for rate damping
and ensuring gravity gradient stabilization
with x-axis zenith instead of nadir pointing
11
x
y
z

12. Simulation Results Continued
12

13. Re-Entry Point
Targeting Algorithm
13

14. Algorithms Overview
“Targeting Algorithm” has three components
Guidance Trajectory Generation Algorithm
Computes the ballistic coefficient (Cb) over time profile and corresponding
trajectory that a satellite must follow to de-orbit in a desired location
Navigation Algorithm with Kalman Filtering
Given noisy GPS measurements, estimates the position and velocity of the
spacecraft relative to the guidance trajectory
Guidance Trajectory Tracking Algorithm
Based on the relative position and velocity, computes the ballistic coefficient that
spacecraft must maintain to return to the guidance trajectory
Continues LQR-based full state feedback
14

15. Orbit Simulation Framework
State is cartesian position (𝒓) and velocity (𝒗) relative to Earth Centered
Inertial (ECI) frame
ECI frame defined as aligned with ECEF frame at epoch
Equations of motions written in state space form and numerically integrated
using MATLAB ode113 or in-house RKF7(8) numerical integrator
𝒓
𝒗
=
𝒗
∑𝑭
𝑚
Earth gravitational and aerodynamic forces included in simulator
Relativity, solar gravity, lunar gravity, tidal effects, solar pressure, variable
winds, and precession/nutation of Earth’s rotation axis ignored
Accuracy sufficient for guidance trajectory generation
15

16. Guidance Trajectory Generation Algorithm
 Given a numerically propagated decay trajectory, it is possible to analytically estimate the Cb
profile needed to de-orbit in a desired location 𝐶 𝑏 =
𝐶 𝑑 𝐴
2𝑚
 Shrinking horizon with drag-work enforcement guidance generation strategy
 Trajectory propagated with analytical Cb profile. First tg seconds comprises first part of guidance trajectory
 tg is 1/10 of orbit life on each step
 𝐶 𝑏 varied during 𝑡 𝑔 seconds of propagation to ensure total work done by drag matches analytical solution
 New Cb profile analytically calculated, orbit propagated, and first tg seconds of resulting trajectory appended to
guidance
 Procedure continues until trajectory found that yields low enough guidance error or less than certain amount (1
day) of orbit life remaining
16

17. Guidance Trajectory Generation Analytical Solution
 Must control de-orbit latitude and longitude at given geocentric altitude
 Final time free
 Control parameters are
 tswap = time until ballistic coefficient is changed
 Cb1 = ballistic coefficient from t0 to tswap
 Cb2 = ballistic coefficient from tswap to tterm
 Spacecraft maintains some predetermined drag profile after tterm
 Given enough time, variation of these parameters is sufficient to target any de-
orbit point with latitude below the orbit inclination
 Analytical Solution Assumptions
 Circular orbit around spherical Earth
 Density is a function of semi major axis
 If density is a function of altitude in a circular orbit around a spherical Earth, density is also a function of
semi major axis
 De-Orbit point is before aerodynamic forces exceed gravitational forces (above 70 km altitude)
 orbital elements still valid
 Shrinking horizon strategy eliminates errors resulting from these assumptions
17

18. Analytical Mapping from Initial to Final State
Fundamental building block of analytical solution
If a satellite with Cb1 takes time t1 to achieve some change in semi major axis
and experiences a change in argument of latitude ∆𝑢1 during this time
𝑢 = 𝜔 + 𝜃 , then for a satellite with the same initial conditions and Cb2
𝑡2 =
𝐶 𝑏1 𝑡1
𝐶 𝑏2
∆𝑢2=
𝐶 𝑏1∆𝑢1
𝐶 𝑏2
The average rate of change of right ascension Ω for a given change in semi
major axis is independent of ballistic coefficient
ΔΩ = Ω𝑡
Ballistic coefficient is defined as 𝐶 𝑏 =(drag_coefficient*drag_area)/(2*mass)
18

19. Characterizing New Trajectory Based on Old Trajectory
 Divide trajectories into four phases from same initial
to final semi major axes
 Cb values are unchanging in each phase
 Time and changes in orbital elements during each
phase in the new trajectory calculated based on
corresponding phase in old trajectory and analytical
relations
 Final time and orbital elements based on initial
conditions and sum of changes during each phase
𝑡𝑓 = 𝑡𝑖𝑛𝑖𝑡 +
𝑖=1
4
𝐶 𝑏𝑖0Δ𝑡𝑖0
𝐶 𝑏𝑖
𝑢 𝑓 = 𝑢𝑖𝑛𝑖𝑡 +
𝑖=1
4
𝐶 𝑏𝑖0Δ𝑢𝑖0
𝐶 𝑏𝑖
Ω 𝑓 = Ω𝑖𝑛𝑖𝑡 +
𝑖=1
4
ΔΩ𝑖0
Δ𝑡𝑖0
Δ𝑡𝑖
𝜔 𝑓 = 𝑒𝑓 = 0
𝑖 𝑓 = 𝑖𝑖𝑛𝑖𝑡
 Time and orbital elements of the new spacecraft at de-
orbit point can be calculated and used to calculate de-
orbit latitude and longitude. 19

20. Analytical Guidance Trajectory Solution
 Given initial trajectory propagated with some Cb1, Cb2, and
tswap
 Orbit life and argument of latitude increases (Δ𝑡 𝑑, Δ𝑢 𝑑)
required for proper targeting calculated
 Argument of latitude at target latitude calculated
 Required increase in argument of latitude (Δ𝑢 𝑑) calculated
 Any Δ𝑢 𝑑 + 2𝜋𝑛 acceptable
 Spacecraft lat-long calculated where spacecraft passes over target
latitude
 Required life increase calculated (longitude 𝜆 positive east)
Δ𝜆 = 𝜆 𝑑 − 𝜆 𝑎
Δ𝑡 𝑑 = −
Δ𝜆
2𝜋
𝑇⨁
 𝑇⨁ =86,164 s = sidereal day
 Total required orbit life and argument of latitude change
Δ𝑡𝑡 = Δ𝑡𝑡0 + Δ𝑡 𝑑, Δ𝑢 𝑡 = Δ𝑢 𝑡0 + Δ𝑢 𝑑
z
Life
increase
required
Target
Actual de-
orbit
20

21. Calculating New Control Parameters
Control parameters to achieve desired
Δ𝑢 𝑡 and Δ𝑡𝑡
𝐶 𝑏2 =
𝐶 𝑏20 Δ𝑡20Δ𝑢10 − Δ𝑡10Δ𝑢20
Δ𝑡𝑡Δ𝑢10 − Δ𝑡10Δ𝑢 𝑡
𝐶 𝑏1 =
𝐶 𝑏10 Δ𝑡10Δ𝑢20 − Δ𝑡20Δ𝑢10
Δ𝑡𝑡Δ𝑢20 − Δ𝑡20Δ𝑢 𝑡
𝑡 𝑠𝑤𝑎𝑝 =
Δ𝑡10 𝐶 𝑏10
𝐶 𝑏1
Compute control solution for multiple
initial values of tswap to explore full
control space
Select solution with maximum remaining
orbit lifetime controllability
21

22. Ensuring Feasible Parameter Ranges
 Can analytically calculate 𝑢10, 𝑢20, Δ𝑡10, Δ𝑡20 given a numerically propagated trajectory
and initial 𝐶 𝑏10, 𝐶 𝑏20 and 𝑡 𝑠𝑤𝑎𝑝
 For a given required total change in argument of latitude (Δ𝑢 𝑡), the feasible Δ𝑡𝑡 values
can be calculated based on min and max Cb values
 For Δ𝑡𝑡 𝑚𝑎𝑥
for given Δ𝑢 𝑡 need largest Cb2 and smallest Cb1
 Want to spend as long as possible in higher orbit with longer period
Δ𝑡𝑡 𝑚𝑎𝑥
= min
𝐶 𝑏20 Δ𝑡20Δ𝑢10 − Δ𝑡10Δ𝑢20 + 𝐶 𝑏 𝑚𝑎𝑥
Δ𝑡10Δ𝑢 𝑡
𝐶 𝑏 𝑚𝑎𝑥
Δ𝑢10
,
𝐶 𝑏10 Δ𝑡10Δ𝑢20 − Δ𝑡20Δ𝑢10 + 𝐶 𝑏 𝑚𝑖𝑛
Δ𝑡20Δ𝑢 𝑡
𝐶 𝑏 𝑚𝑖𝑛
Δ𝑢20
Δ𝑡𝑡 𝑚𝑖𝑛
= max
𝐶 𝑏20 Δ𝑡20Δ𝑢10 − Δ𝑡10Δ𝑢20 + 𝐶 𝑏 𝑚𝑖𝑛
Δ𝑡10Δ𝑢 𝑡
𝐶 𝑏 𝑚𝑖𝑛
Δ𝑢10
,
𝐶 𝑏10 Δ𝑡10Δ𝑢20 − Δ𝑡20Δ𝑢10 + 𝐶 𝑏 𝑚𝑎𝑥
Δ𝑡20Δ𝑢 𝑡
𝐶 𝑏 𝑚𝑎𝑥
Δ𝑢20
 If desired Δ𝑡𝑡 not is feasible range, pick closest achievable Δ𝑡𝑡
22

23. Drag-Work Enforcement Method
 During orbit propagation, total work done by aerodynamic drag
(per unit mass) is a state variable in addition to ECI position
and velocity
𝑊𝑑 = 𝑎 𝑑 𝑣
 Desired work done by drag at each point in new trajectory can
be calculated prior to trajectory propagation
 During propagation of new trajectory sections that will be used
in guidance trajectory (first 𝑡 𝑔 seconds), satellite 𝐶 𝑏 iteratively
varied until actual 𝑊𝑑 equals desired 𝑊𝑑 𝑑𝑒𝑠
from analytical
solution
 𝐶 𝑏 updated and trajectory section re-run until 𝑊𝑑 = 𝑊𝑑 𝑑𝑒𝑠
achieved
 Update law: 𝐶 𝑏 𝑢𝑝
= 𝐶 𝑏 𝑜𝑙𝑑
𝑊 𝑑 𝑑𝑒𝑠
𝑊 𝑑
First 𝑡 𝑔 seconds of
guidance propagated
with 𝐶 𝑏
Drag work 𝑊𝑑 at 𝑡 𝑔
calculated
𝑊𝑑 compared to
desired drag work
𝑊𝑑 𝑑𝑒𝑠
𝐶 𝑏 updated based on
difference between 𝑊𝑑 and
𝑊𝑑 𝑑𝑒𝑠
Init 𝐶 𝑏 from
analytical
solution
𝑊𝑑 − 𝑊𝑑 𝑑𝑒𝑠
above threshold
Remainder of
trajectory
propagated𝑊𝑑 − 𝑊𝑑 𝑑𝑒𝑠
below
threshold
23

24. Full State Feedback Guidance Tracking using Schweighart Sedgwick Relative Motion
Equations
Tracker ensures spacecraft follows guidance trajectory despite drag
uncertainties
SS Equations provide linear approximation of 𝒓 𝑟𝑒𝑙 over time in LVLH
frame
Like Clohessy-Wiltshire equations but include J2 effects
Approximation based on circular orbit assumption
𝒓 𝑟𝑒𝑙 = 𝒓 𝑠𝑐 − 𝒓 𝑔𝑢𝑖𝑑 =
𝛿𝑥
𝛿𝑦
𝛿𝑧
Linear Quadratic Regulator (LQR) full state feedback law based on SS
dynamics used to regulate 𝒓 𝑟𝑒𝑙 to zero
24

25. Schweighart Sedwick Relative Motion Equations with Differential Drag
𝛿 𝑥
𝛿 𝑦
𝛿 𝑥
𝛿 𝑦
=
0 0 1 0
0 0 0 1
𝑏
0
0
0
0
−𝑎
𝑎
0
𝛿𝑥
𝛿𝑦
𝛿 𝑥
𝛿 𝑦
+
0
0
0
−𝜌𝑣2
𝐶 𝑏 𝑠𝑐
− 𝐶 𝑏 𝑔𝑢𝑖𝑑
𝛿 𝑧 = −𝑛2 𝛿𝑧 (𝑢𝑛𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝑙𝑒𝑑)
𝑎 = 2𝑛𝑐, 𝑏 = 5𝑐2 − 2 𝑛2, 𝑐 = 1 +
3𝐽2 𝑅 𝑒
2
8𝑎2
1 + 3cos(2𝑖) , 𝑛 =
𝜇
𝑎3
25

26. Full State Feedback Control
𝐶 𝑏 𝑠𝑐
= 𝐶 𝑏 𝑔𝑢𝑖𝑑
− 𝐾𝒙
𝐾 = 𝑙𝑞𝑟(𝐴, 𝐵, 𝑄, 𝑅, 0)
System of form 𝒙 = 𝐴𝒙 + 𝐵𝑢
𝒙 is relative position and velocity, 𝑢 = Δ𝐶 𝑏 = 𝐶 𝑏 𝑠𝑐
− 𝐶 𝑏 𝑔𝑢𝑖𝑑
R is a 1x1 control weighting matrix
Q is a 4x4 error penalty matrix
Gain value K minimizes cost functional 𝐽 = 0
∞
(𝒙 𝑡 𝑄𝒙 + 𝑢 𝑡 𝑅𝑢) 𝑑𝑡
26

27. Tracker with Constant Drag Bias Error of 1.5
Actuator running .12% of the time or 1.2 seconds for every 1000
seconds of orbit
Simulations assume 4 minutes needed to go from Cbmin to Cbmax
27

28. Tracking Simulation Results with Drag
Errors
To simulate drag error, density multiplied
by error factor consisting of
Bias error
Period errors at frequencies of
26 days (synodic period)
1 day (Earth’s solar day)
5400 seconds (roughly one orbital period)
Noise free tracking example
28

29. Discrete Time Extended Kalman Filter for LQR Guidance Trajectory
Tracking
 State will be relative position and velocity
 Measurement 𝑧 = relative position and velocity derived from GPS measurement and guidance state
𝑧𝑖 = 𝐺𝑥𝑖, 𝑥𝑖 ≈ Φ𝑖 𝑥𝑖−1
𝐺 = 𝐼 4𝑥4, Φ𝑖 = 𝑒(𝐴−𝐵𝐾)𝑡
𝑊 = measurement noise covariance
𝑄 = Process noise covariance
Λ = Fading term
f represents numerical propagation from ti to ti-1
𝑥1
−
and 𝑃𝑖
−
are a-priori state and state error covariance estimates
𝑥𝑖
−
= 𝑓(𝑡𝑖, 𝑡𝑖−1, 𝑥𝑖−1
+
)
𝑃𝑖
−
= Φ𝑖 𝑃𝑖−1
+
Φ𝑖
𝑇
+ 𝑄
𝑆 = 𝐺𝑃𝑖
−
𝐺 𝑇 + 𝑊
𝐾𝑖 = 𝑃𝑖 𝐺 𝑇
𝑆 −1
𝑥𝑖
+
= 𝑥𝑖
−
+ 𝐾𝑖 𝑧𝑖 − 𝐺𝑥𝑖
−
𝑃𝑖
+
= 𝐼 − 𝐾𝑖 𝐺 𝑃𝑖Λ
29

30. Kalman Filter with Measurement Noise, Bias, and Density Error
Motor runs 3.5% of the time assuming 240 seconds for full
deployment
5% actuator deadband
Truly a “worst case”
Tracking to 90 km altitude
30

31. Monte Carlo Simulations
Variable Range Probability Distribution
Semi Major Axis [6698, 6718] km Uniform
True Anomaly [0, 360] degrees Uniform
Eccentricity [0, .004] Uniform
Right Ascension [0, 360] degrees Uniform
Argument of the Periapsis [0, 360] degrees Uniform
Inclination [1, 97] degrees Uniform
Impact Latitude [0, max(inclination, 180-
inclination)-. 1] degrees
Uniform
Impact Longitude [-180, 180] degrees Uniform
Cbmax [.033, .067] Uniform
Cbmin [.0053, .027] Uniform
epoch [11/1/2003, 11/1/2014] Uniform
31
1,000 guidance trajectory generation and tracking simulations were conducted for the randomly varying
simulation parameters in the table above.

32. Monte Carlo Simulations
1000 guidance and tracking simulations with
randomized initial conditions run to 120 km geodetic
altitude
997 guidance cases below 25 km error threshold, all
guidance errors below 106 km
All tracking errors below 6 km
32

33.  Trajectory simulated to ground with terminal ballistic coefficient
and initial mean orbital elements: 𝑎 = 6418, 𝑒 = 0, 𝑖 = 𝑖0, 𝜔 =
0, 𝑢 = 0, Ω = 0
 Argument of latitude increase Δ𝑢 needed to achieve target
latitude calculated
 RAAN increase ΔΩ equal to longitude difference between target
location and point beneath the orbital plane at desired 𝑢
 Initial conditions updated with Δ𝑢 and ΔΩ and trajectory
propagated again
 May update with smaller percentage of Δ𝑢 to aid
convergence
 When initial conditions found that lead to desired impact
location, DEO point is the trajectory state at 100 km geocentric
altitude
 Target DEO point with guidance trajectory generation algorithm
and adjust final 𝐶 𝑏 to ensure landing on ground target
Ω decrease,
𝑢 increase
Target
Actual
impact
Initial conditions
Propagate to
ground
Compute Δ𝑢 and ΔΩ
needed for desired
ground impact Extract DEO point if
errors below threshold
Update initial
conditions with
Δ𝑢 and ΔΩ
33
De-Orbit Point Point Selection Algorithm

34. D3 CubeSat Mission
34

35. Spacecraft Design CAD Model
ISIS Turnstile antenna system
SkyFox piPATCH GPS antenna
SkyFox piNav-NG GPS
Clyde Space CPUT UTRX
half duplex radio
D3 control board
Clyde Space 20 Whr battery
D3 system
D3 adapter stage
Clyde Space standard 1U structure
DHV Technologies solar cell
Clyde Space 3rd generation 1U
EPS
35
Magnetorquer Brackets

36. Final Version of D3, Adapter, and CubeSat Structure
36

37. CAD Models Views
37

38. Ongoing/Future Work
Targeting a ground impact point using
aerodynamic drag
Desired re-entry point at 100 km altitude
selected through iterative simulations to ground
D3 flexible body attitude dynamics analysis
Implementation of ground targeting
algorithm on MISTRAL and IPERDRONE
satellites using IRENE heat shield as drag
device
Completion and launch of D3 CubeSat
Flight of D3 unit on Ames TechEdSat
CubeSat
38

39. Conclusions
Targeting a re-entry point using solely aerodynamic drag is possible
Guidance trajectory generation
Guidance trajectory tracking
Navigation
Algorithm reliability demonstrated via Monte Carlo simulations and case
studies
Have developed a retractable Drag De-orbit Device (D3) to provide
attitude stability and facilitate aerodynamic re-entry point targeting
D3 CubeSat in development at UF to test drag device and algorithms
Collaborations with NASAAmes and the Italian Aerospace Research
Centre (CIRA) to use hardware and algorithms for re-entry point and
ground targeting
39

40. Questions?
40

41. Backup Slides
41

42. Background Info
42

43. Drag Devices
 IRENE [1]
 In development
 Planned flights on MISTRAL and
IPERDRONE satellites
 Can modulate area
 Serves as re-entry heat shield
 Cylde Space AEOLDOS module [2]
 No sale option seen
 Single deploy
 ExoBrake [3]
 Multiple flights on CubeSats
 Goal is to perform guided re-entry
 iDod [4]
 Inflatable device, not retractable
 CubeSail [5]
 Single-deploy sail used for drag and solar
sailing
 Freedom Drag Sail [6]
 Built by JAXA
 Successful ISS launch and de-orbit
43

44. Targeted Re-Entry Algorithms
Dutta’s Algorithm [3]
Orbit initial conditions and satellite’s ballistic coefficient range provided to Post2
numerical optimizer
Post2 calculates 7 discrete Cb changes to get satellite close to desired de-orbit
location
Undesirable for onboard use
Computationally intensive and no convergence guarantee
Virgili’s Algorithm [7]
Analytical solution used to compute guidance directly without any orbit
propagation
Assumes circular orbit, exponential density, J2 as only perturbation
Guidance trajectories are not very accurate
Patera’s Algorithm [8]
Change ballistic coefficient during final de-orbit phase to reduce casualty risk
44

45. Contributions
Aerodynamic re-entry point targeting algorithms
Guidance trajectory generation algorithm capable of running onboard a small
satellite
Uses high fidelity force model
Robust tracking algorithm to follow guidance trajectory
Robust and reliable drag De-Orbit Device (D3) hardware implementation
Capable of changing Cb while providing attitude stability
Will be used to perform re-entry point targeting algorithms on-orbit
45

46. Old PADDLES Drag Device
Origami drag sail
Rotating shaft unfurls sail
Design issues
Does not provide passive
aerodynamic attitude stability
Difficult to determine exact sail
geometry
Deployment mechanism
sometimes snags
46

47. Attitude Dynamics
47

48. Attitude Simulation Framework
 Numerically integrate equations of motion in state space
form
 Simultaneous attitude and orbit propagation in ECI (Earth
Centered Inertial) frame
𝒙 = 𝒓 𝑻
𝒗 𝑻
𝒒 𝑻
𝝎 𝑻 𝑇
𝒙 = 𝒗 𝑻 𝒗 𝑻 𝒒 𝑻 𝝎 𝑻 𝑇
 𝒒 is quaternion that describes rotation from ECI frame to
body frame. Rotation of ECI frame about 𝒆 by 𝜃 yields
body frame.
𝒒 =
𝒆 sin 𝜃/2
cos 𝜃/2
= 𝑞1 𝑞2 𝑞3 𝑞4
𝑇
𝒒 =
1
2
𝑞4 −𝑞3 𝑞2 𝑞1
𝑞3 𝑞4 −𝑞1 𝑞2
−𝑞2 𝑞1 𝑞4 𝑞3
−𝑞1 −𝑞2 −𝑞3 𝑞4
𝜔 𝑥
𝜔 𝑦
𝜔 𝑧
0
𝝎 = 𝑰−𝟏 𝑻 𝒏𝒆𝒕 − 𝝎 × 𝑰𝝎
𝒗 =
𝑭 𝒏𝒆𝒕
𝑚 48
Variable Definition
𝒙 State vector
𝒓 ECI position
𝒗 ECI velocity
𝒒 Attitude
quaternion
𝝎 Angular velocity
𝑰 Sat moment of
inertia tensor
𝑻 𝒏𝒆𝒕 Net torque
𝑭 𝒏𝒆𝒕 Net force
𝑚 Satellite mass

49. Magnetic Torques
Running a current through a wire generates a magnetic
field
A loop of wire, also known as a solenoid or
magnetorquer, impersonates a bar magnetic with
magnetic moment 𝝁
𝝁 = 𝐼𝐴𝑛 𝒏 (𝐴𝑚𝑝 ∗ 𝑚𝑒𝑡𝑒𝑟2)
 𝐼 is current in wire, 𝐴 is loop area, 𝑛 is number of loops in
magnetorquer, 𝒏 is magnetorquer normal unit vector
Including a ferromagnetic material inside the loop increases
the magnetic moment
A dipole magnet wants to align with the ambient
magnetic field B (Tesla)
Alignment torque is
𝑻 = 𝝁 × 𝑩 (𝑁𝑒𝑤𝑡𝑜𝑛 ∗ 𝑚𝑒𝑡𝑒𝑟)
49

50. Gravity Gradient Torques
 Caused by differing values of gravitational attraction on different parts of
orbiting object
𝑀 𝑥 =
3𝜇 𝑒 𝑅 𝑦 𝑅 𝑧
𝑅5
𝐼𝑧𝑧 − 𝐼 𝑦𝑦
𝑀 𝑦 =
3𝜇 𝑒 𝑅 𝑥 𝑅 𝑧
𝑅5
𝐼 𝑥𝑥 − 𝐼𝑧𝑧
𝑀𝑧 =
3𝜇 𝑒 𝑅 𝑥 𝑅 𝑦
𝑅5
𝐼 𝑦𝑦 − 𝐼 𝑥𝑥
𝑴 =
3𝜇 𝑒
𝑅3
𝑹 × 𝑰 𝑹
 𝑴 = 𝑀 𝑥 𝑀 𝑦 𝑀𝑧
𝑇 is the gravity gradient torque in the satellite body
frame (Newton*meter)
 𝑹 = 𝑅 𝑥 𝑅 𝑦 𝑅 𝑧
𝑇 is the vector from the center of the Earth to the
satellite center of mass expressed in the satellite body frame (km). 𝑅 = 𝑹 .
 𝑰 is satellite moment of inertia tensor
R
𝜃
50

51. Aerodynamic Torques
Mean free path between particles is large, so fluid assumption not
valid
Panel methods can be used to compute the aerodynamic force and
torque acting on each panel and sum to get total effect on satellite
Can assume specular reflection for simplicity where each particle collides
elastically with panel (kinetic energy conserved) and bounces of at the same
angle
Drag force on each panel is 𝑭 𝒅 = −2𝜌𝐴𝑣⊥ 𝒗⊥ (𝑁𝑒𝑤𝑡𝑜𝑛𝑠)
Force acts at geometric center of panel, normal to panel
Torque generated by this force is 𝑻 𝒅 = 𝒓 × 𝑭 𝒅 (𝑁𝑒𝑤𝑡𝑜𝑛 ∗ 𝑚𝑒𝑡𝑒𝑟)
 𝒓 from satellite center of mass to panel center of pressure
𝒗∞
𝑭 𝒅
𝒗⊥
51

52. Attitude Stabilization Procedure
 Desired attitude: z-axis ram aligned, x-axis zenith
pointing
 Run BDot de-tumble controller until satellite angular
velocity below specified threshold
 Partially deploy all booms to 1 m and continue BDot
with fixed magnetic moment vector superimposed
along satellite x-axis
 Causes x-axis to pull toward Earth magnetic field vector
 When magnetic field most zenith pointing, fully
deploy +x and –x booms, deploy +y and –y booms
half way, and remove fixed magnetic moment vector
 Orbit propagated in advance to determine when magnetic
field is most zenith pointing
 Continue BDot until attitude stabilizes with
oscillations damped
x
y
z
52

53. Simulation Setup
2U, 2 kg, D3 equipped CubeSat simulated in
ISS orbit
52 degree inclination, 400 km circular orbit
To compute appropriate time for final boom
deployment, primary simulation paused and
forecast made of magnetic field over the next
orbit
Boom deployment when magnetic field most
zenith pointing for proper gravity gradient
stabilization
Final attitude displayed with respect to Local
Vertical Local Horizontal (LVLH) frame
x-axis aligned with zenith vector, z-axis aligned
with orbit angular momentum
53

54. Simulation Results
 BDot running until 𝑡 = 10,000 𝑠 with
gain of -5
 All booms deployed to 1 𝑚 and Bdot
continues running with the addition of
fixed magnetic moment vector
.015 0 0 𝑇 𝐴𝑚2 until 𝑡 = 20,000 𝑠
(5.56 hrs)
 Magnetic field forecast for one orbit.
Magnetic field will be most zenith
pointing at 𝑡 = 20,800 𝑠
 At 𝑡 = 20,800 𝑠, +𝑦 and −𝑦 booms
deployed to 1.85 m and +𝑥 and −𝑥 booms
deployed to 3.7 m. Fixed magnetic
moment removed
 BDot continues for remainder of
simulation and boom deployment does not
change
54

55. Orbit Simulation
Environment
55

56. Modeling Earth’s Gravity
 Gravitational acceleration in ECEF frame is gradient of potential function
𝑈 =
𝜇 𝑒
𝑅 𝑒
𝑛=0
∞
𝑚=0
𝑛
𝐶 𝑛𝑚 𝑉𝑛𝑚 + 𝑆 𝑛𝑚 𝑊𝑛𝑚
 Gravitational coefficients 𝐶 and 𝑆 given by EGM2008 gravity model
 Coefficients through degree and order 10 utilized
 𝑉 and 𝑊 given by recurrence relations
𝑉00 =
𝑅 𝑒
𝑟
, 𝑊00 = 0
𝑉𝑚𝑚 = 2𝑚 − 1
𝑥𝑅 𝑒
𝑟2
𝑉 𝑚−1,𝑚−1 −
𝑦𝑅 𝑒
𝑟2
𝑊 𝑚−1,𝑚−1
𝑊𝑚𝑚 = 2𝑚 − 1
𝑥𝑅 𝑒
𝑟2
𝑊 𝑚−1,𝑚−1 +
𝑦𝑅 𝑒
𝑟2
𝑉 𝑚−1,𝑚−1
𝑉𝑛𝑚 =
2𝑛 − 1
𝑛 − 𝑚
𝑧𝑅 𝑒
𝑟2
𝑉𝑛−1,𝑚 −
𝑛 + 𝑚 − 1
𝑛 − 𝑚
𝑅 𝑒
2
𝑟
𝑉𝑛−2,𝑚
𝑊𝑛𝑚 =
2𝑛 − 1
𝑛 − 𝑚
𝑧𝑅 𝑒
𝑟2
𝑊𝑛−1,𝑚 −
𝑛 + 𝑚 − 1
𝑛 − 𝑚
𝑅 𝑒
2
𝑟
𝑊𝑛−2,𝑚
56

57. Aerodynamic Model
Aerodynamic drag acceleration given by
𝒂 𝒅 = −
1
2𝑚
𝐶 𝑑 𝐴𝜌𝑣∞ 𝒗∞ = −𝐶 𝑏 𝜌𝑣∞ 𝒗∞
𝐶 𝑏 =
𝐶 𝑑 𝐴
2𝑚
𝒗∞ = 𝒗 − 𝝎 𝒆 × 𝒓
Density and drag coefficient most difficult to
predict
Factor of 100 difference between min and max
density
High fidelity density model critical
Drag coefficient will vary between two for a
sphere and four for a flat plate assuming
specular reflection
57
𝒗∞
𝑭 𝒅
𝒗⊥

58. Density Variability
58
Density changes
significantly based on
both location and time
High fidelity
NRLMSISE-00
density model
necessary to capture
these variations

59. Propagator Validation
 Simulation from same initial conditions
conducted in MATLAB and in STK
HPOP environment
 Epoch June 6, 2010, 0000 UTC
 Initial osculating elements:
𝑎, 𝑒, Ω, 𝜔, 𝜃, 𝑖 =
(6778 𝑘𝑚, 0, 50 𝑜
, 400
, 10 𝑜
, 70 𝑜
)
 Orbit discrepancies primarily due to
differences in drag modeling
 Resulting along-track errors and can be
corrected via 𝐶 𝑏 modulation
 MATLAB 𝐶 𝑏 = .11
𝑚2
𝑘𝑔
 STK HPOP 𝐶 𝑏 = .1155
𝑚2
𝑘𝑔
 Algorithms can use STK propagator
directly if desired
59

60. Targeting Algorithm
Proofs and Details
60

61. Proving the Analytical Relation Between Cb changes and Orbit Behavior
 Gauss variation of parameters for semi major axis is
𝑑𝑎
𝑑𝑡
=
2
𝑛 1 − 𝑒2
𝑒 sin 𝜃 𝐹𝑅 +
𝑝
𝑟
𝐹𝑠
 For a circular orbit around a spherical Earth, 𝑒 = 0, 𝑝 = 𝑎 1 − 𝑒2
= 𝑟, and 𝐹𝑠 = 𝑎 𝑑
𝑑𝑎
𝑑𝑡
=
2𝑎 𝑑
𝑛
𝑛 =
𝜇
𝑎3
 In a non-rotating atmosphere
𝑎 𝑑 = −𝐶 𝑏 𝜌𝑣2
𝐶 𝑏 =
𝐶 𝑑 𝐴
2𝑚
 Making some substitutions
−
𝜇
𝑎3
1
2𝐶 𝑏 𝜌𝑣2
𝑑𝑎 = 𝑑𝑡
61

62. Proof Continued
𝑣 =
𝜇
𝑎
Substituting into last equation on previous page yields
−
𝑑𝑎
2 𝜇𝑎𝐶 𝑏 𝜌
= 𝑑𝑡
Integrate both sides of equation, assume density is a function of semi major
axis, and multiply by 𝐶 𝑏
∆𝑡𝐶 𝑏 =
𝑎0
𝑎 𝑓
−
𝑑𝑎
2 𝜇𝑎𝜌
∆𝑡𝐶 𝑏 = 𝐺 𝑎 𝑓 − 𝐺(𝑎0)
∆𝑡𝐶 𝑏 is constant for fixed initial and final 𝑎 so
∆𝑡2 =
𝐶 𝑏1∆𝑡1
𝐶 𝑏2
62

63. Proof Continued
 In a circular orbit
𝑛 =
𝑑𝜃
𝑑𝑡
=
𝑑𝑢
𝑑𝑡
𝑑𝑎
𝑑𝑡
= −2 𝜇𝑎𝐶 𝑏 𝜌
 Multiply 𝑛 =
𝑑𝑢
𝑑𝑡
by inverse of
𝑑𝑎
𝑑𝑡
and substitute formula for 𝑛
𝑑𝑢
𝑑𝑎
= −
𝑛
2 𝜇𝑎𝐶 𝑏 𝜌
= −
1
2𝑎2 𝐶 𝑏 𝜌
 Multiply both sides by 𝐶 𝑏 𝑑𝑎 and integrate
∆𝑢𝐶 𝑏 =
𝑎0
𝑎 𝑓 𝑑𝑎
2𝑎2 𝜌
= 𝑃 𝑎 𝑓 − 𝑃 𝑎0
 ∆𝑢𝐶 𝑏 is constant for fixed initial and final 𝑎 so
∆𝑢2=
𝐶 𝑏1∆𝑢1
𝐶 𝑏2
63

64. Control Parameters Formula Proof
 Subscript 1 indicates parameter between 𝑡0 and 𝑡 𝑠𝑤𝑎𝑝. Subscript 2 indicates parameter between 𝑡 𝑠𝑤𝑎𝑝
and 𝑡𝑡𝑒𝑟𝑚. Subscript 0 indicates parameter from old numerically propagated trajectory
 If swap point occurs at same semi major axis in old and new trajectories, the following relations hold
∆𝑢1 + ∆𝑢2 = ∆𝑢 𝑡
∆𝑡1 + ∆𝑡2 = ∆𝑡𝑡
∆𝑢1 =
∆𝑢10 𝐶 𝑏10
𝐶 𝑏1
∆𝑢2 =
∆𝑢20 𝐶 𝑏20
𝐶 𝑏2
∆𝑡1 =
∆𝑡10 𝐶 𝑏10
𝐶 𝑏1
∆𝑡2 =
∆𝑡20 𝐶 𝑏20
𝐶 𝑏2
64

65. Proof Continued
∆𝑢 𝑡 = ∆𝑢1 + ∆𝑢2 =
∆𝑢10 𝐶 𝑏10
𝐶 𝑏1
+
∆𝑢20 𝐶 𝑏20
𝐶 𝑏2
 Solve for 𝐶 𝑏1
𝐶 𝑏1 =
∆𝑢10 𝐶 𝑏10 𝐶 𝑏2
∆𝑢 𝑡 𝐶 𝑏2 − ∆𝑢20 𝐶 𝑏20
∆𝑡𝑡 = Δ𝑡1 + Δ𝑡2 =
∆𝑡10 𝐶 𝑏10
𝐶 𝑏1
+
∆𝑡20 𝐶 𝑏20
𝐶 𝑏2
 Substitute equation for 𝐶 𝑏1 and solve for 𝐶 𝑏2
∆𝑡𝑡 =
∆𝑡10 𝐶 𝑏10 ∆𝑢 𝑡 𝐶 𝑏2 − ∆𝑢20 𝐶 𝑏20
∆𝑢10 𝐶 𝑏10 𝐶 𝑏2
+
∆𝑡20 𝐶 𝑏20
𝐶 𝑏2
𝐶 𝑏2 =
𝐶 𝑏20 ∆𝑡20∆𝑢10 − ∆𝑡10∆𝑢20
∆𝑡𝑡 ∆𝑢10 − ∆𝑡10 ∆𝑢 𝑡
 Update 𝑡 𝑠𝑤𝑎𝑝 to ensure that 𝐶 𝑏 change occurs at same semi major axis in both trajectories
𝑡 𝑠 𝑛𝑒𝑤
=
Δ𝑡10 𝐶 𝑏10
𝐶 𝑏1
65

66. Single Stage Targeting Algorithm Used on TES6 ExoBrake
Increase in argument of latitude Δu needed to de-orbit at target latitude
calculated
Any Δ𝑢 + 2𝑛𝜋 also yields proper latitude if 𝑛 is an integer
Change 𝐶 𝑏1 to achieve desired total 𝑢 = 𝑢0 + Δ𝑢
 𝐶 𝑏1 𝑛𝑒𝑤
= 𝐶 𝑏1
𝑢0
𝑢0+Δ𝑢
Ex: 𝑢0 = 100 𝑟𝑎𝑑, Δ𝑢 = 1 𝑟𝑎𝑑, 𝐶 𝑏1 = 10, 𝐶 𝑏1 𝑛𝑒𝑤
= 10 ∗
100
101
= 9.9
Can analytically estimate new de-orbit time and change in orbital elements at
de-orbit point using this 𝐶 𝑏 value and the analytical relations
Test all candidate Δ𝑢 values and select the one that yields lowest total error
Propagate trajectory with corresponding 𝐶 𝑏1 value
Repeat estimation process until trajectory found that converges to desired
location
66

67. Analytical Drag-Work Calculation
 Work done by drag identical between old and new
trajectories at end of each phase
 Same final orbital energy
 Phase start and end times from analytical theory
 For new trajectory at time Δ𝑡 beyond phase endpoint
with some 𝐶 𝑏, the time after the phase start in the initial
trajectory (Δ𝑡0) with the same energy state is
Δ𝑡0 =
𝐶 𝑏
𝐶 𝑏0
Δ𝑡
 Desired work done by drag 𝑊𝑑 𝑑𝑒𝑠
is equal to work
done by drag in old trajectory at Δ𝑡0 beyond phase start
 𝐶 𝑏0 = old trajectory ballistic coefficient during phase
 Note that old trajectory has been numerically propagated
and 𝑊𝑑 is known at all points
67

68. Sensitivity Analysis
 Investigates effects of changes in drag profile on de-orbit location
 An error in estimated drag force of .25% puts satellite on the other side of Earth
 Closed loop control necessary
 Changes in density profile between numerical propagations can cause analytical and numerical solutions to
diverge
 System less sensitive when orbit life is shorter
300 km circular orbit with 1976 standard atmosphere,
Cb10=.025, Cb20=.01, ts0=150,000 s
270 km circular orbit with 1976 standard atmosphere,
Cb10=.025, Cb20=.01, ts0=150,000 s
68

69. Guidance Trajectory
Tracking
69

70. Q and R Selection Strategy
𝑄 =
0 0 0 0
0 1 0 0
0
0
0
0
0
0
0
0
 With this Q matrix, system only cares about minimizing error in the along-track direction
 Minimizing along track error requires also minimizing radial error as well as error rates in the long run
 Temporary increases in radial error and error rates allowed if they lead to faster minimization of along-track error
 1 by 4 gain matrix K0 first calculated with R0 = 10000
 𝛿𝑦𝑠𝑎𝑡 specified such that controller guaranteed to saturate at 𝛿𝑦 = 𝛿𝑦𝑠𝑎𝑡
 Calculate second element in K required to ensure saturation at 𝛿𝑦𝑠𝑎𝑡
𝐾2 𝑟𝑒𝑞 =
𝐶 𝑏𝑚𝑎𝑥 − 𝐶 𝑏𝑚𝑖𝑛
𝛿𝑦𝑠𝑎𝑡
 R required to achieve this gain given based on 𝑅0 and second element of K0 𝐾0(2)
𝑅 =
𝐾0 2
𝐾2 𝑟𝑒𝑞
2
𝑅0
 LQR gain K re-evaluated with new R
 Gain periodically updated as density changes
70

71. Handling Saturation
If requested 𝐶 𝑏 below min 𝐶 𝑏, set 𝐶 𝑏 = 𝐶 𝑏 𝑚𝑖𝑛
If requested 𝐶 𝑏 above max 𝐶 𝑏, set 𝐶 𝑏 = 𝐶 𝑏 𝑚𝑎𝑥
71

72. Noise Model
Noise based on PiNav-NG GPS Unit
Periodic bias error and Gaussian random noise on
position and velocity measurements
Position error = [.001; -.005; .002]*sin(2*pi*time/5400) +
randn(3,1)*.005 km
Velocity error = [.00005; -.00005;
.00005/2]*sin(2*pi*time/5400) +randn(3,1)*.00005 km/s
72
Error estimate from
manufacturer

73. Simulation with Navigation Errors
Navigation errors due to measurement noise have significant effects if
not filtered
Actuator running 84% of the time
73

74. Kalman Filtering for Measurement Noise Cancellation
Kalman filter implemented to remove measurement noise
Motor running .43% of the time
74

75. Re-Entry Safety Analysis
Effects of GNC errors and system uncertainties on ground impact point
characterized via Monte Carlo simulations and Inputs’ Statistics method
Safety box cross-track dimension only affected by cross-track GNC
errors
Remaining variables affect the safety box along-track dimension
75

76. D3 CubeSat and
Mission Design
76

77. D3 Control Board Pin Header Interface
77

78. D3 Board Components and External Connections
 External Wiring
 USB Power and Data Line
 Ribbon cable containing
 16 wires for 4 motors and 4 encoders
 2 wires for ground and 5V for all encoders
 6 wires for 3 magnetorquer circuits
 Components
 2 quad half h-bridge motor driver chips (SN754410)
 2 quad half h-bridge chips to drive 3 magnetorquers
 Can use 3 low voltage DRV8837DSGR chips if using 3.3 V bus for
magnetorquers
 Possibly 1 IMU chip (TDK ICM-20948)
 Beagle Bone Black Indsutrial high performance processor
 1 Watchdog timer
 1 30-minute countdown timer
 RBF Pin
 Antenna deployment controller
78

79. Desired Processor
Beaglebone Black Industrial Version
Significant flight heritage
1 Watt power use in low power
mode
May be possible to use less power if
HDMI and ethernet ports removed
Fits on D3 control board
79

80. CubeSat Mission Requirements
Success Level and Description Demonstration Verification Criteria
Required: D3 CubeSat ejects from
deployer
Prerequisite.  Track CubeSat with radar.
 Confirmation of launch from vehicle.
Required: Ground systems make
contact with CubeSat
Prerequisite. Make radio contact.
D3 booms are used to change the cross-
wind area of the CubeSat
Boom can operate in LEO.  Commanded motor position
telemetry.
 Track CubeSat with radar and look
for drag changes.
D3 stabilizes attitude of CubeSat Booms and magnetorquers can be used
to stabilize attitude in LEO.
 Commanded motor position
telemetry.
 Magnetometer telemetry.
D3 device is used to actuate a desired
maneuver
D3 can be used to actuate a desired
maneuver.
JSpOC radar data and CubeSat GPS data.
D3 device is used to deorbit within a
desired interval
Ability of D3 to deorbit a CubeSat as
desired.
JSpOC radar data and CubeSat GPS data.
Maximum: d3 deorbits to within
1300km of a desired target interface
point at 90km altitude.
Ability of D3 to deorbit the CubeSat to a
safe location.
Track CubeSat with radar.
80

81. Hardware Configuration
Component Mass (g) Avg Power User (mW) Cost (USD)
Clyde Space 3rd Generation EPS 86 160 4900
Clyde Space 20 WHr Battery 256 0 2700
Clyde Space CPUT UTRX Half Duplex Radio 90 250 RX, 4000TX, 333 avg with 30 min daily TX 8850
ISISpace Turnstile Antenna System 30 0 6891
D3 Deployers 1100 200 avg (20% duty cycle), 16400 peak 2000
D3 Magnetorquers 101 Variable, max 1000 during de-tumble 100
Beaglebone Black Master CubeSat and D3
Micro-controller
24 1000 100
DHV Technologies Custom Solar Panels
(four 2U side panels, one 1U top panel)
400 total 4240 max gen. for 2U panels and 2120 max. gen.
for 1U panel
26000
1U Clyde Space Structure 200 0 3550
D3 Adapter Stage 200 0 200
SkyFox piNav-NG GPS Unit 100 139 9624
SkyFox piPATCH GPS Antenna 25 100 2238
Totals 2612 1932 average continuous use 67153
81

82. Robot Operating System (ROS) Implementation
• ROS allows multiple
software “Nodes” to run
simultaneously on
BeagleBone Black
• Nodes communicate
with each other via data
publications to “topics”
• Nodes written in c++
with speed or hardware
interfacing needed
• Python otherwise
82

83. Telemetry and Commands List
Ground Station Commands Spacecraft Telemetry
Reset microcontroller Battery voltage
Update software Solar panel voltages
Update F10.7 and Ap solar and geomagnetic indices
for density forecasting
Boom deployment levels
Target desired de-orbit location GPS position and velocity estimates
Change operation mode (normal, debug, bare-bones) Magnetometer readings
Manual boom deployment profile Motor and magnetorquer usage history
Request telemetry Any relevant error codes
Guidance update Current guidance trajectory
LQR and BDOT gain updates Temperatures
83

84. Disposal Plan
All components expected to burn on re-entry
Verified through analysis in-house and at KSC
84

85. Operations Flowchart-from ConOps
Provides a plan for the sequence of spacecraft operations necessary to
meet the mission requirements
85
Uplink desired
de-orbit
location and
updated F10.7
and Ap indices

86. References
[1] R. Fortezza, R. Savino, and G. Russo, “MISTRAL (AIR-LAUNCHEABLE MICRO-SA℡LITE WITH
REENTRY CAPABILITY) A small spacecraft to carry out several missions in LEO,” 2013.
[2] P. Harkness, M. McRobb, P. Lützkendorf, R. Milligan, A. Feeney, and C. Clark, “Development status of
AEOLDOS – A deorbit module for small satellites,” Advances in Space Research, vol. 54, no. 1, pp. 82–91, Jul. 2014.
[3] S. Dutta, A. Bowes, A. M. Dwyer Cianciolo, C. Glass, and R. W. Powell, “Guidance Scheme for Modulation
of Drag Devices to Enable Return from Low Earth Orbit,” in AIAA Atmospheric Flight Mechanics Conference, 2017,
p. 0467.
[4] D. C. Maessen, E. D. van Breukelen, B. T. C. Zandbergen, and O. K. Bergsma, “Development of a Generic
Inflatable De-Orbit Device for CubeSats.” .
[5] N. Adeli and V. Lappas, “Deployment System for CubeSail nano-Solar Sail Mission,” presented at the
SmallSat 2010, Logan, UT.
[6] “Re-Entry: FREEDOM Drag Sail CubeSat – Spaceflight101.” .
[7] J. Virgili and P. Roberts, “Atmospheric Interface Reentry Point Targeting Using Aerodynamic Drag
Control,” Journal of Guidance, Control, and Dynamics, vol. 38, no. 3, pp. 1–11, 2015.
[8] R. Patera, “Drag Modulation as a Means of Mitigating Casualty Risk for Random Reentry,” in AIAA
Atmospheric Flight Mechanics Conference and Exhibit, American Institute of Aeronautics and Astronautics.
[9] F. Marcos, B. Bowman, and R. Sheehan, “Accuracy of Earth’s thermospheric neutral density models,” in
Proceedings of the AIAA/AAS Astrodynamics Specialist Conference, Keystone, CO, 2006.
[10] W. L. Hankey, Re-Entry Aerodynamics. American Institute of Aeronautics and Astronautics, 1988.
[11] A. W. Koenig, T. Guffanti, and S. D’Amico, “New State Transition Matrices for Spacecraft Relative Motion
in Perturbed Orbits,” Journal of Guidance, Control, and Dynamics, 2017.
86