LOTNAV. A Low-Thrust Interplanetary Navigation Tool: The Trajectory Reconstruction Module

Transcription

1 LOTNAV A Low-Thrust Interplanetary Navigation Tool: The Trajectory Reconstruction Module Juan Luis Cano González Mission Analysis Division Deimos Space S.L. -1-

2 The 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 -2-

3 Trajectory Generation Module LOTNAV s Capabilities Trajectory Reconstruction Utility Trajectory Graphical Exploit. Utility Trajectory Sectioning Utility Minor Body Propagation Utility Measurements Generation Module Measurements Generation Utility Measurements Graphical Exploit. Utility Covariance Analysis Module Partial Derivatives Computation Utility Covariance Analysis Utility Covariance Graphical Exploit. Utility Simulation Module Monte Carlo Simulation Utility Statistical Analysis Utility Monte Carlo Graphical Exploit. Utility Re-optimisation Module -3-

4 Utilities Sub-window Command buttons LOTNAV s Capabilities Data Sub-window -4-

5 Trajectory Generation Module Measurements Generation Module Measurements Profile LOTNAV Use Scheme Low-thrust Trajectory Definition Covariance Analysis Module System Uncertainties Simulation Module Covariance Evolution Simulation Profile -5-

6 Trajectory 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 -6-

7 Measurements 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 Doppler Differential one-way range LOS to celestial objects On-board accelerometers Radar to target -7-

8 Covariance 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 -8-

9 Simulation Module A Monte Carlo simulation can be performed on the lowthrust 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 -9-

10 Re-Optimisation Module Whenever trajectory dispersion is large to be corrected by means of the LQ controller, trajectory reoptimisation 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 -10-

11 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 -11-

12 Trajectory Generation Utility: BVP Solver (2) 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 Phase 1... Flyby event i-1 Phase i x i + x i Flyby event i... Phase n Arrival event -12-

13 Optimisation variables can be: Trajectory Generation Utility: BVP Solver (3) 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 -13-

14 Initial conditions can be: Trajectory Generation Utility: BVP Solver (4) 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 -14-

15 Trajectory Generation Utility: BVP Solver (5) -15-

16 Trajectory Generation Utility: BVP Solver (6) Trajectory Generation Utility: BVP Solver: DS1 trajectory example Trajectory structure: Earth-TC-Braille-CTC-Borrelly (2 Phases) NSTAR engine Launch on Delta II optimisation variables 14 equality constraints 9 inequality constraints -16-

17 Trajectory Generation Utility: BVP Solver (7) 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 -17-

18 Trajectory Generation Utility: BVP Solver (8) 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 -18-

19 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 Conclusion Navigation modules are currenly under final verification Final Presentation takes place in September Potential application to Solar Orbiter, LISA, BepiColombo and other ESA missions -19-