Conference PaperPDF Available

OREKIT: AN OPEN SOURCE LIBRARY FOR OPERATIONAL FLIGHT DYNAMICS APPLICATIONS

April 2010

Conference: ICATT 2010
At: ESAC - Madrid

Authors:

Luc Maisonobe

Thales Group

Pascal Parraud

CS GROUP, Toulouse France

The Orekit library is a space flight dynamics library developed since 2002 by CS. It was operationally used during the Jules Verne ATV mission. Since 2008, the library is freely available as an open-source product under the terms of the business-friendly Apache V2.0 license. Given the small size of the market and the still high need for advanced tailored solutions for space systems, the service based business model for added value is much more suited than the license based business model or its new version, the Software As a Service. There are several business models that can be used for economically sound open-source systems. Some are well suited for the space field and will be explained. Some are not adapted and the reasons for this will also been explained. Open-source is an approach that proved efficient in mainstream software industry. It does not always need a very large community as was once thought, but still needs some involvement. The return on investment increases for all contributors as the project expands and the risks decrease at the same time as more and more people use it. The model is attractive for both public entities, academics, industry and SMEs, bringing something to each one of them. It also increases the yield of public funding. OREKIT is an example of a successful open-source project initiated by private industry and operationally during ATV rendezvous. Since its inception, the OREKIT library was aimed both towards quick development for simple use cases and towards fine tuning for expert users. In order to fulfill the first goal, the programming interface provides high level features like attitude modes, automatic discrete events handling within propagation (ground station visibilities, eclipses, maneuver start/stop, altitude crossing, user defined event …), transparent handling of leap seconds, automatic transforms between all frames, transparent use of Earth Orientation Parameters and much more. In order to fulfill the second goal, several physical models are provided for many concepts (orbits, propagators, frames, events, attitudes, time scales, ephemerides …) and all of them can be extended naturally to add user specific models or change the behavior of the provided ones. Since many models offer similar user interfaces, it is possible to build applications that can be used both in a mission analysis configuration with fast models and in an operational configuration with accurate models with a single switch. The presentation will provide both a business view and a technical view of OREKIT. It will explain the benefits of open-source and business models. It will present an overview of the library features and available physical models. A focus on a few innovative concepts will be made, like for example discrete events, time scale handling, slave and master propagation modes, management of time-dependent frames, models switching or transparent handling of complex models that need lots of configuration data. Some examples of how the tool can be used in different operational contexts will be given. The roadmap for the future of the tool will be presented.

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Content uploaded by Luc Maisonobe

Content may be subject to copyright.

Orekit : an Open-source Library for Operational Flight Dynamics Applications







 !

"##$%&"'"#&$()

*$+,-#".$

/

1 OPEN-SOURCE FOR SPACE FLIGHT

DYNAMICS LIBRARY

1.1 Historical context

0++1##23  4  2  "   5

4#   66# %/1"    1

" 6##31 "    1

#21     3   73  1

21##6"4##6#31" 

84##"6"1 21

###3 # 6    1      1  2

#11  " 1 6#

1 464 2#"

9"#.61""#3

1  " 1   ### 6"1

6  ""    2  1  6"3  ###

66 7##1 28 "2  

"0 2#"#3  21 16" -1  #

64".64"6 



/1#.1""4#6

2"6#31  "  # 21  #

"1#""  #"3#8#31

"      "  2#"  ##2      2

7:-9;99:<   %/ 18 1 2



718"43166

11#3 6"61 #

"#16'

7## 1288 6#2 ++ "++(21

6  ""2 63    #

6 2#2  "#"

1 -13 6" 6 ++, 21 #3

16-1#36"2#2#4##

211 43"   "4#6#3

6    "  61 #  "#  "  131#  #"

#31$1 6" 2"7-=0

">43

01"  98?    ##2"    66

"#6"

1.2 Strategic choices and business model

0++)  1" 3" "8  985 

21# 1#"

23"1""""6# 

"#31646## 7-3&

  2  ##    83  #    66  "#

"  "4 63 #"

#23"2"4#6

/  1      """    ++(    13

#3  "" 98   6

6"

-1 "2 66" 861 6"#4

18        #3  @ A  "  ##2"    

66    44  #4      6

66 6"

1.2.1 License choice

#13    6  #    6  #31

"   6#    6  1    8

3#

4#  "  6  #   6  .

211 14" 21 6

"

"3#66"7211

"4#61"""7?".#"

&"#46#66#5

➢0 7   6#1"  "  1       BC3

6 #CD  #5 7?7;E  &    ""

"1#0"4#

6#"

➢0  7   6#1"  "  1        BCF8

6 #CD#5# 7?"""

1 # 7 &  """

"#

➢0 7    6#1"  "  1        BC&

"# CD  #5  1  7?    &  14    

"""13##7

G.6#    3  6 #  #    H  "

0.6#286 ##H

G  "  0  .6#    "#

#&E0-"761

12"1##23# 5

➢Bad example of the JAT I4  7" 

-#8  211    6'"  ++  

"" 2  "4#6"  1# .

#98?-1#12strong

copyleft license2111#"1"

"""4"#"#"113

1  #      ++(    4  1

"28

➢Orekit context:

◦  ""    1  8 21  3  "

"#    #   1  143  3

    ###  66

64J

◦"1#8131#

#"1#"1"J

◦  "#  1    "    4

"316"

7##    1  #"      1  1  761  +

BC"# CD  # 7   1 

64#2"# 82 1## 

1 " 898""211221

.6 31124 1343

16 311"7"66#1

986#1"3 #

-1###2#"#5

➢;  663    #      1  

"

➢;

➢/###12K"5

◦/"163

◦/"" 1216328

""6

◦/""6

◦/"    64  1  63  "

#164

9811312"5BC

"61CD

/498*2#") 1

I# ++(

1.2.2 Business model

96      661  1  64"    

2" 0"#2 "

4  #3     2    131   ##

"    4#4  -1      4

##16'.6""

1 8" 1    "

66#  -1  "#4   1  6#

  "  "  "  G  33

13    1     1  0  #    1

#"6#"3

7  "    1  6    "#  

6# " 4  "  66   

#-1"##"5

➢3##663

➢#    9%GL0-      6  #31

" 

➢36# 21"6

➢6"4#6

◦2"#

◦13

2 FROM BASIC TO EXPERT USE OF OREKIT

F?##2126##"#31" 

66#98

/?66198# 

"#4#0#3."'#

"

0"3"1"8"4#6

6#  "  " 6 "

.6

2.1 High level features for easy, fast

development

9864"#2#4#'"

#310    #### ""  

6  #31  "   #8      #

6663" ##"

"#I 61"  /1

.46664""

F?##      1  ##23  131  #4#  

64""613#53 5

•""

•1"#3

•663"

•#

•G16

Attitude modes

4#  6""  "  "    4##  1

-16#11#5

1BC# CD#2#85

➢&" =##" 63

➢-3="=9/63

➢9/."6#>"

1  BC6#.CD  #2  211    6#>  

# #25 23= 26

3"63

7##1"6## 13# "

111 6#1

 21#21;4

 6# " #  #2"

#6#.21# 131

#2#>"## 131

63"

Frames

/3>"1#16

2#311#8 

17 2        #    "3  1

  1  #8        6  J  1

    1      1    "

##23#  1

-1"1."4#

  #      1      

"6"  #2    1    "    

##  6""            

#  "6"  #2    1      6""  

14"# #12

"1 7-  3 21     ,+

"

7  #    6""      #  64""  

6###1G1"#

Orbit Propagation

98    "  8"    6""  

663    1      #8  86#

6631#663

96   66"  ##  663

1# 1"#"4"1#

"3  1     1  663  -1  663

   2 " "5 BC#4CD "

BCCD"

0  1     BC#4CD  "  1  1"#3    1

#66 6"6# 10?

21 2"## "#3 25 #6

42166"#1

6

0BCCD "1 1"#3   1    #6  

"#3"    1  663  #  "  #  1

63"11#612

  13121  ##"BC61"#CD-1

# 1663##21 1"#3

1#  #6 1BC1"#  6CD1" 16

1"#2####"##  1663

16-1"6#""

1  "6#3  2  1  #6#    1"#3

" "1 6#.6 21 

6" 16"163-1

6#  31#6 21" 4

""""13##6.6#"#

-16631"#1."6"6"

6;#>"61"###23"

 ."64  4#63

1

4  4  "      ##

6"  1663 ""321 ##"

BC4  "CD  9  3    #3  6#  

6""  4  "    4##   4

3#  4  4  4  "      "

1 2 494 """"1

6632##18161

  "  4  "  33      1  666

  G4         6""    

"4"    1  #  "3  1  663  21

"""

G4"works in both slave and master mode

#4"1"31"

 21 1 433"1# 1 1 #

  1  8"  1"In master mode

intermediary state corresponding to event time is

computed at the exact time event happens, no matter

step size

F1    4    33"        "  

##3 1663 #8 .6#133

1 "#21 4  6 4

    4  6##  663  1  663

21    #"  11#"    "  "3  

 # .6# -1  # "

  6#  6#  4  #333 3 " 

4# #6

Earth orientation parameters

7##  G1    4    66"  

6  "    "#  0G%  ++*  2

4  "  0G%  MM,    4  

4##    1  .3  G1      21  

2112133

9        4    .  21

1      1  4   1  

66#16"3"##

#""2131#431

  1  6#    1"#  1  1#  "

4"38

-11"#31136#""

4      3"            "

## 9.6 ##3

18 "#2?-131

6121#31" .6"

" 82 21 6  6#1" 

98?"8161

 2135 1 '68 6G1

"

Time scale

4##66":--70H--

"##""#4# -70#7"

"" 1#4##1"

  1    #  -1  4    1"#"

## #8#

-:#6"#1"#"6# J

21"821"?"1

1

2.2 Fine tuning for expert use

& "  ##  1  3"    1  #  

# 3 98    3  "      

"3#  66#21.6  3

 6

Force models

1   "#      #  6    6  #31

" #"7#36#1# "

"#    64""    98    1    ##  

""?"6# .""

4 6 "#  " 1

 # >"6# 6#.

7    .6#  "3  "  "  6    

161#16#."" 4#

#6#"# 21#3

416"#

…........

Events

G4"#6>#6

:31""461

66#    2  4  1"#      "

"34"

41 # 4 "#.#

31      1  3  664    

.#      @.A  "  & "  .3

@##A 4 #"3 

98?  4  1"#3  1    "  

      "  6  "3  1

663 1#"  6#6#   "31

6"336

Frames

:   2 "6" 1 "

"311#8 @6A

  1 .3 -1  

 # "6"-1 .# 21 2

"7- 3  21    1  ,+  

4#4""1# 141#"#



9  3       6"        

"6##     

1-1##2 .6#36#

16134  41#83

    1  6##.    1  ##  

211"" 2#31# 

…........

Time scale

G4   31 "" 98 #"

64"2"#6#2###

 " 6# 216 "01

6# 1"21"-70

Data

0  "    6#  3    98"

66#    #3     "  #"3    

>"216#311 

.3#"

3 ACKNOWLEDGEMENTS

F  181 /"> 1

66 1 6' "##239811

6##"

F  18  ##  1      98  "4#6

++,2112"1"4#4

16' F #  18  ##  1 211#6

"3"64316"

4 REFERENCES

 -  "  /  #4    

6E #8*""++

  #4  14 Stratégies et potentiels de l'open

source dans les entreprises et les administrations

françaises  ++M+  9609    96

F#"/++M

* E  E    1  "  H"   IERS

Conventions (2003)  0#  G1  %

"% 4

K Free Software Foundation, GNU General Public

License

165==22233=#=36#*+

"#1# I++)

$ G7  ;%  0;%07  0 Free Software

License Agreement6++,

165==222##=#=

N0N1#

, The BSD License

165==22263=#="#616

) 761+I ++K

165==222613=#=0G;G+

( E4"7##"# 2" %1"O'8

"-L#73++, Revisiting Spacetrack

Report #3, 2006 AIAA/AAS Astrodynamics Specialist

Conference

M G  O     4  #  ;P    H1"

FSolving Ordinary Differential Equations I.

Nonstiff Problems      6#

1#( 63#3 M()"

4""MM*

+     /">    

Building a community, an approach for

Space Flight Dynamics6++M

PAseos Simulates the Environment for Operating multiple Spacecraft

Preprint

Full-text available

Feb 2023

The next generation of spacecraft is anticipated to enable various new applications involving onboard processing, machine learning and decentralised operational scenarios. Even though many of these have been previously proposed and evaluated, the operational constraints of real mission scenarios are often either not considered or only rudimentary. Here, we present an open-source Python module called PASEOS that is capable of modelling operational scenarios involving one or multiple spacecraft. It considers several physical phenomena including thermal, power, bandwidth and communications constraints as well as the impact of radiation on spacecraft. PASEOS can be run both as a high-performance-oriented numerical simulation and/or in a real-time mode directly on edge hardware. We demonstrate these capabilities in three scenarios, one in real-time simulation on a Unibap iX-10 100 satellite processor, another in a simulation modelling an entire constellation performing tasks over several hours and one training a machine learning model in a decentralised setting. While we demonstrate tasks in Earth orbit, PASEOS is conceptually designed to allow deep space scenarios too. Our results show that PASEOS can model the described scenarios efficiently and thus provide insight into operational considerations. We show this in terms of runtime and overhead as well as by investigating the modelled temperature, battery status and communication windows of a constellation. By running PASEOS on an actual satellite processor, we showcase how PASEOS can be directly included in hardware demonstrators for future missions. Overall, we provide the first solution to holistically model the physical constraints spacecraft encounter in Earth orbit and beyond. The PASEOS module is available open-source online together with an extensive documentation to enable researchers to quickly incorporate it in their studies.

Physics‐Based Approach to Thermospheric Density Estimation Using CubeSat GPS Data

Article

Full-text available

Jan 2023
SPACE WEATHER

In Low Earth Orbit (LEO), atmospheric drag is the largest contributor to trajectory prediction error. The current thermospheric density model used in operations, the High Accuracy Satellite Drag Model (HASDM), applies corrections to an empirical density model every 3 hr using observations of 75+ calibration satellites. This work aims to improve global thermospheric density estimation by utilizing a physics‐based space environment model and precise GPS‐based orbit estimates of LEO CubeSats. The data assimilation approach presented here estimates drivers of the Thermosphere‐Ionosphere‐Electrodynamics General Circulation Model (TIE‐GCM) every 1.5 hr using CubeSat GPS information. In this work, Spire Global CubeSat data are used to demonstrate the method using only 10 satellites; the true strength of the method is its potential to exploit data already collected on large LEO constellations (hundreds of CubeSats). Precise Orbit Determination (POD) information from 10 CubeSats over 12 days is used to sense a global density field when Kp historical data show a minor and moderate geomagnetic storm in succession. This paper provides a direct comparison of estimated density, derived by our new method, to HASDM and Swarm mission derived density. A propagation analysis is also executed by comparing the CubeSat POD data to orbits propagated using our estimated density versus HASDM density. The analyses show that the estimated density is within 35% of HASDM during storm‐time conditions, and that the propagation using the estimated density yields an improvement of 26% over NRLMSISE‐00 compared to HASDM, while outperforming HASDM during the second storm peak.

AN ANALYSIS OF ORBITAL SEPARATION DISTANCES TO SUPPORT SPACE TRAFFIC MANAGEMENT

Conference Paper

Full-text available

Aug 2023

Large constellations are typically designed using sets of periodic orbits and satellite control boxes sized to ensure compatible phasing between co-orbital constellation planes to prevent conjunction events. This work investigates how control action for orbit maintenance influences the size of orbital control boxes. Simulation results are used to improve the fidelity of intrinsic (geometric) orbital capacity estimates and to understand factors that influence the number of admissible satellite locations in Low Earth Orbit. An analysis of orbital separation distances is performed as a function of control, propulsion, orbit, environmental, and S/C characteristics to define estimates for minimum orbital separation distances.

Optical transmittance based store and forward routing in satellite networks

Article

Jan 2023

Quantum computing will play a crucial part in our security infrastructure for the coming years. Quantum networks can consist of direct optical fiber or free-space links. With the use of satellite channels, we can create a quantum network with higher coverage than using optical fibers where the distances are limited due to the properties of the fiber. One of the highest drivers of cost for satellite networks, apart from the cost of the technology needed for such systems, are the costs of launching and maintaining said satellites. By minimizing the satellites needed for a well-functioning quantum network, we can decrease said network’s cost, thus enabling a cheaper quantum internet. In this paper, we present an optical transmittance-based routing algorithm with which it is possible to conduct successful quantum entanglement transfer between terrestrial nodes.

Quantum Algorithms Applied to Satellite Mission Planning for Earth Observation

Article

Full-text available

Jan 2023

Earth imaging satellites are a crucial part of our everyday lives that enable global tracking of industrial activities. Use cases span many applications, from weather forecasting to digital maps, carbon footprint tracking, and vegetation monitoring. However, there are limitations; satellites are difficult to manufacture, expensive to maintain, and tricky to launch into orbit. Therefore, satellites must be employed efficiently. This poses a challenge known as the satellite mission planning problem, which could be computationally prohibitive to solve on large scales. However, close-to-optimal algorithms, such as greedy reinforcement learning and optimization algorithms, can often provide satisfactory resolutions. This paper introduces a set of quantum algorithms to solve the mission planning problem and demonstrate an advantage over the classical algorithms implemented thus far. The problem is formulated as maximizing the number of high-priority tasks completed on real datasets containing thousands of tasks and multiple satellites. This work demonstrates that through solution-chaining and clustering, optimization and machine learning algorithms offer the greatest potential for optimal solutions. This paper notably illustrates that a hybridized quantum-enhanced reinforcement learning agent can achieve a completion percentage of 98.5% over high-priority tasks, significantly improving over the baseline greedy methods with a completion rate of 75.8%. The results presented in this work pave the way to quantum-enabled solutions in the space industry and, more generally, future mission planning problems across industries.

Empirical Parameterization of Broadband VLF Attenuation in the Earth‐Ionosphere Waveguide

Article

Full-text available

Apr 2023

The Earth‐ionosphere waveguide (EIW) determines the propagation of Very Low Frequency (VLF; ∼3−30 kHz) waves. Characterizing the waveguide is a longstanding challenge due to its large spatial scale and the complex variability of the lower ionosphere. Here we apply a novel linear basis function regression technique to characterize attenuation in the EIW using broadband measurements of lightning‐generated radio waves. The process begins with defining a basis function set, which ideally encompasses a feature set that can predict the variability seen in VLF attenuation properties. With this basis set defined, a system of linear equations is then constructed using sensor pair observations to eliminate the dependency on source amplitude in each observation. Using this formalism, an empirical attenuation model for broadband signals from lightning is constructed and the dependence on attenuation properties with the boundary conditions is explored. The empirically derived results show attenuation rates over ice that are 12 dB/Mm higher compared to paths over saltwater. Well‐known east/west attenuation rate asymmetry stemming from anisotropic reflection coefficients of the ionosphere is also demonstrated and investigated. For example, under a daytime ionosphere, westward‐propagating waves suffer up to 2.8 dB/Mm greater attenuation compared to eastward‐propagating waves. The trained model is used for propagation corrections in a global lightning locating system (LLS), but this technique can be expanded to further study VLF attenuation rates by employing different sets of basis functions.

SEMpy: a Python Open-Source Toolbox for Non-Keplerian Astrodynamics

Conference Paper

Jun 2021

Multi-Objective Optimization of an Intelligent Soil-Moisture-Monitoring Satellite Constellation

Article

Mar 2023

In early satellite mission design, requirements are not yet fixed, cost is sometimes negotiable, and designs are relatively unconstrained. During this period of design freedom, multi-objective optimization can provide a useful lens into the design space by showing theoretical performance limits and illuminating design tradeoffs. This work optimizes a radar constellation for a potential soil moisture mission. Several different optimization cases with different variables are considered and contrasted. The optimization of the instrument and constellation parameters is considered jointly and separately to better understand the effect of coupling on the optimization performance. A science-driven optimization based on soil moisture retrieval error is compared with a performance-metric-driven optimization. Pareto analysis and association rule mining are performed on the generated designs to provide insight into driving features. Design recommendations are made for several cost caps. Results show that optimization that considers the instrument and constellation design together find superior revisit metrics than treating instrument and constellation separately. The use of the science value metric as an optimization objective shows that while cost may always be increased to improve instrument and constellation performance, the difference in science value may be negligible. These findings can inform tradespace exploration studies for similar problems.

Quantum algorithms applied to satellite mission planning for Earth observation

Preprint

Full-text available

Feb 2023

Earth imaging satellites are a crucial part of our everyday lives that enable global tracking of industrial activities. Use cases span many applications, from weather forecasting to digital maps, carbon footprint tracking, and vegetation monitoring. However, there are also limitations; satellites are difficult to manufacture, expensive to maintain, and tricky to launch into orbit. Therefore, it is critical that satellites are employed efficiently. This poses a challenge known as the satellite mission planning problem, which could be computationally prohibitive to solve on large scales. However, close-to-optimal algorithms can often provide satisfactory resolutions, such as greedy reinforcement learning, and optimization algorithms. This paper introduces a set of quantum algorithms to solve the mission planning problem and demonstrate an advantage over the classical algorithms implemented thus far. The problem is formulated as maximizing the number of high-priority tasks completed on real datasets containing thousands of tasks and multiple satellites. This work demonstrates that through solution-chaining and clustering, optimization and machine learning algorithms offer the greatest potential for optimal solutions. Most notably, this paper illustrates that a hybridized quantum-enhanced reinforcement learning agent can achieve a completion percentage of 98.5% over high-priority tasks, which is a significant improvement over the baseline greedy methods with a completion rate of 63.6%. The results presented in this work pave the way to quantum-enabled solutions in the space industry and, more generally, future mission planning problems across industries.

Data-driven anomaly detection for resident space objects using autoencoder with binary classification

Conference Paper

Aug 2021

To detect anomaly for RSOs accurately and timely is critical to protect the long-term sustainability of space activities, including Space Situational Awareness (SSA) and Space Traffic Management (STM). In this paper, we explore a new data-driven framework based on deep autoencoder for RSOs' anomaly detection. A novel two-input autoencoder model is proposed to identify whether the tracks belong to the same orbit or not. An in-house simulation-based space catalog environment is used for experiments and analysis. We compare the proposed model with Principal Component Analysis (PCA) method in classification and the results show that the proposed method achieves higher accuracy in identifying whether two tracks are from the same orbits or not than the classical PCA method. Furthermore, the proposed method is also robust to noise data with high accuracy.

Solving ordinary differential equations. I: Nonstiff problems. 2nd revised ed., 3rd corrected printing

Article

Jan 2003

D Dennis
Gérard Mc Carthy
Petit

Dennis D. Mc Carthy and Gérard Petit, IERS Conventions (2003), International Earth Rotation and Reference Systems Service.

Software License Agreement

Sep 2006

Cnrs Cea
Cecill Inria
Free

CEA, CNRS, INRIA, CeCILL Free Software License Agreement, September 2006, http://www.cecill.info/licences/ Licence_CeCILL_V2-en.html.

Aug 2006

David A Vallado
Paul Crawford
Richard Hujsak
T S Kelso

David A. Vallado, Paul Crawford, Richard Hujsak, and T.S. Kelso, August 2006, Revisiting Spacetrack Report #3, 2006 AIAA/AAS Astrodynamics Specialist Conference.

OREKIT: AN OPEN SOURCE LIBRARY FOR OPERATIONAL FLIGHT DYNAMICS APPLICATIONS

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