The Trajectory Reconstruction Module

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2nd European Workshop on Astrodynamic Tools and Techniques

ESTEC, Noordwijk, 13-15 September 2004

© 2004 DEIMOS Space S.L. – www.deimos-space.com

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Tool

LOTNAVA Low-Thrust Interplanetary

Navigation Tool:

The Trajectory Reconstruction Module

Juan Luis Cano GonzálezMission Analysis DivisionDeimos Space S.L.

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Tool The LOTNAV ToolThe LOTNAV Tool

• The Low-Thrust Interplanetary Navigation Software Tool (LOTNAV) is a suite of software utilities that enables the mission analyst to address following tasks:– Regenerate and in some cases design low-thrust

interplanetary trajectories– Define a profile of observables for trajectory estimation– Perform a trajectory estimation covariance analysis– Simulate the GNC performance by means of a Monte Carlo– Interface with some low-thrust trajectory optimisation

tools• LOTNAV has been developed by Deimos Space under

contract with ESA/ESOC

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Tool LOTNAV’s CapabilitiesLOTNAV’s Capabilities

•Trajectory Generation Module

Trajectory Reconstruction UtilityTrajectory Graphical Exploit. UtilityTrajectory Sectioning UtilityMinor Body Propagation Utility•Measurements Generation Module

Measurements Generation UtilityMeasurements Graphical Exploit. Utility

•Covariance Analysis ModulePartial Derivatives Computation UtilityCovariance Analysis UtilityCovariance Graphical Exploit. Utility

•Simulation ModuleMonte Carlo Simulation UtilityStatistical Analysis UtilityMonte Carlo Graphical Exploit. Utility

•Re-optimisation Module

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Tool LOTNAV’s CapabilitiesLOTNAV’s Capabilities

UtilitiesSub-window

DataSub-windowCommand

buttons

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Tool LOTNAV Use SchemeLOTNAV Use Scheme

Low-thrust Trajectory Definition

CovarianceAnalysisModule

CovarianceEvolution

TrajectoryGeneration

Module

MeasurementsGeneration

Module

MeasurementsProfile

SystemUncertainties

SimulationModule

SimulationProfile

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Tool Trajectory Reconstruction ModuleTrajectory Reconstruction Module

• It allows preparing and analysing the trajectory profile of use for the navigation activities

• Its main core is formed by the Trajectory Reconstruction Utility

• The rest of the utilities are minor service packages• The main purpose is to recreate the best possible

representation of a low-thrust mission profile such to be of use in the navigation studies

• The tool allows solving following problems:– Initial value problems– Multiple point boundary value problems in two degrees of

approximation

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Tool Measurements Generation ModuleMeasurements Generation Module

• The tool allows simulating a number of measurement systems to generate a set of observables for trajectory determination

• A very flexible measurements scheduler is available to define the observables profile

• Available measurement systems are:

• Radiometric range • LOS to celestial objects

• Doppler • On-board accelerometers

• Differential one-way range • Radar to target

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Tool Covariance Analysis ModuleCovariance Analysis Module

• A covariance analysis can be carried out on the trajectory estimation process to ascertain the expected accuracy in the determination of the spacecraft state

• A Square Root Information Filter is utilised• Uncertainties can be assumed in:

– S/C state– Central body gravitational field – Third bodies gravity constant– Ephemerides of celestial bodies– Solar radiation pressure forces– Performance of the low-thrust propulsion system– Atmospheric forces– Ground tracking stations– Measurements systems

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Tool Simulation ModuleSimulation Module

• A Monte Carlo simulation can be performed on the low-

thrust mission GNC

• Guidance is assumed to be done by means of a Linear

Quadratic controller acting on the low-thrust definition

(thrust modulus and thrust angles)

• The trajectory determination is performed with batch

measurements along proposed time intervals

• Guidance is performed after trajectory determination

solving the associated Ricatti equation and computing

the updates to the controls

• Statistics on the computed simulations are extracted an

compared, whenever possible, to the results of the

covariance analysis

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Tool ReRe--Optimisation ModuleOptimisation Module

• Whenever trajectory dispersion is large to be corrected

by means of the LQ controller, trajectory re-

optimisation is required

• Interfaces have been prepared between LOTNAV and

DITAN (developed by Politecnico di Milano under ESA

contract) to allow performing re-optimisation

• New trajectory computed by DITAN is read by LOTNAV

to proceed with navigation analyses

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Tool Trajectory Generation Utility: BVP Solver (1)Trajectory Generation Utility: BVP Solver (1)

• The Bounday Value Problem solver makes use of a

direct optimisation algorithm (based on a penalty

function approach) to obtain the low-thurst solution for

a given trajectory profile

• Trajectory profiles are defined by:

– Some initial conditions

– Sequence of celestial bodies to visit

– Sequence of coast-thrust arcs in the trajectory

– Some final conditions

• The cost function is the final mass at the target

• The constraints are added to the cost function by

means of a penalty function

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• Trajectory is solved by:

– Propagating forward and backward from an encounter

event with a celestial body

– Imposing the matching of the trajectory branches by

appropriately modifying the optimisation variables at the

same time as optimising the cost function

Departure event

Flyby event i-1

Flyby event i

Arrival event Phase i

Phase n Phase 1

... ...

+ix

−ix

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• Optimisation variables can be:– The initial conditions (departure excess velocity)– The swingby conditions (arrival velocity & impact vector)– The arrival conditions (arrival excess velocity)– The event epochs (departure date, arrival date, swingby

dates, thrust switch dates)– The thrust direction law for each thrust arc (parameterised

by means of quadratic functions in the two angles)• Constraints are:

– Matching of the segments for each phase– Arcs duration– Minimum swingby heights– Some initial/final conditions– Maximum change in the event times

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• Initial conditions can be:

– Initial state about a central body plus a chemical burn

– Escape from a given large body after a chemical burn

– Launch from Earth using one of the available launcher

models (Ariane 5, Soyuz, Atlas, Delta, Zenit, HII)

• Final conditions can be:

– Final state about a central body after a chemical burn

– Flyby of a celestial body with no further destination

– Arrival to a given orbit about a large body

– Rendezvous with a small body

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• Trajectory Generation Utility:– BVP Solver: DS1 trajectory example

• Trajectory structure: Earth-TC-Braille-CTC-Borrelly (2 Phases)• NSTAR engine• Launch on Delta II 7326• 27 optimisation variables• 14 equality constraints• 9 inequality constraints

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• Trajectory Generation Utility:– BVP Solver: BepiColombo trajectory example

• Trajectory structure: E-CTC-V1-C-V2-4×TC-M (3 Phases)• Engine with 170 mN/340 mN and 3200 s• Launch with Soyuz• 49 optimisation variables• 21 equality constraints• 24 inequality constraints

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• Trajectory Generation Utility:– BVP Solver: SOLO trajectory example

• Trajectory structure: E1-CTC-V1-CTC-E2-TCTC-V2 (3 phases)• Engine dependent on available power• Soyuz launch• 53 optimisation variables• 22 equality constraints• 32 inequality constraints

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Tool ConclusionConclusion

• Summary

– A flexible tool is available to the mission analyst for trajectory definition and navigation assessment of interplanetary missions

– Development is currently under finalisation

– Trajectory Generation Module has been deeply tested

– Navigation modules are currenly under final verification

– Final Presentation takes place in September

– Potential application to Solar Orbiter, LISA, BepiColombo and other ESA missions

The Trajectory Reconstruction Module

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