ASTRA (Automatic Swing-by TRAjectories) is a MATLAB-based toolbox for optimally build multi-gravity assist (MGA) trajectories. This has been built as a result of Andrea Bellome's Ph.D. thesis [1]. ASTRA is based on Dynamic Programming (DP) to optimize MGA trajectories, both in single-objective (SODP) and multi-objective (MODP).
To cite this folder please use the references [1] and [2].
To work with ASTRA, one can simply clone the repository in the local machine:
git clone "https://github.com/andreabellome/astra"To run a full exploration of MGA trajectories, the following system requirements are recommended:
- CPU six-core from 2.6 GHz to 3.6 GHz
- RAM minimum 16 GB
- Any version of MATLAB>2021b
- A compiler for C functions should be used. You can use the minGW
Lighter requirements will be required in future releases, as ASTRA will be able to optimize one launch year at a time, and even one date at a time. The price will be the computational time.
To use the repository, one finds different test scripts. These are listed here:
- Test script 1: st1_astra_main.m, to optimize MGA missions. Refer to this section.
- Test script 2: st2_astra_main_saturn_system.m, to optimized MGA missions using custom constraints and different planetary systems. Refer to this section.
This script allows to optimize ASTRA using both SODP (single-objective dynamic programming) and MODP (multi-objective dynamic programming). This section provides a breakdown of the minimal input parameters needed.
The following script is used to add ASTRA and to build mex functions (namely the Lambert solver and the defects function).
clearDeleteAdd;Then one proceeds to select appropriate input parameters.
%% --> input section
% --> clear INPUT and define new ones
try clear INPUT; catch; end; clc;
% --> sequence to be optimized
INPUT.idcentral = 1;
seq = [ 3 2 3 3 5 ]; res = [ 2 1 3 ];
%%%%%%%%%% multi-rev. options %%%%%%%%%%
maxrev = 0; % --> max. number of revolutions (round number)
chosenRevs = differentRuns_v2(seq, maxrev); % --> generate successive runs
[INPUT.chosenRevs, INPUT.res] = processResonances(chosenRevs, res); % --> process the resonances options
[INPUT.chosenRevs] = maxRevOuterPlanets(seq, INPUT.chosenRevs); % --> only zero revs. on outer planets
%%%%%%%%%% multi-rev. options %%%%%%%%%%
%%%%%%%%%% set departing options %%%%%%%%%%
t0 = date2mjd2000([2023 1 1 0 0 0]); % --> initial date range (MJD2000)
tf = t0 + 1*365.25; % --> final date range (MJD2000)
dt = 2.5; % --> step size (days)
INPUT.depOpts = [t0 tf dt];
%%%%%%%%%% set departing options %%%%%%%%%%
%%%%%%%%%% set options %%%%%%%%%%
INPUT.opt = 2; % --> (1) is for SODP, (2) is for MODP, (3) is for DATES, (4) is for YEARS - MODP
INPUT.vInfOpts = [3 5]; % --> min/max departing infinity velocities (km/s)
INPUT.dsmOpts = [1 Inf]; % --> max defect DSM, and total DSMs (km/s)
INPUT.plot = [0 0]; % --> plot(1) for Pareto front, plot(2) for best traj. DV
INPUT.parallel = true; % --> put true for parallel, false otherwise
INPUT.tstep = dt; % --> step size for Time of flight
%%%%%%%%%% set options %%%%%%%%%%Things to notice are:
INPUT.idcentralallows to select the system. In this example,INPUT.idcentral = 1means that Solar System is selected. Other options are: 5 for Jupiter system, 6 for Saturn system and 7 for Uranus system. See also constants.m for knowing about the IDs of the bodies.maxRevOuterPlanetswill prune options with more than one rev. on legs towards outer planets (i.e., from Jupiter on). This to prevent the mission duration to increase a lot.resis a list of integers with[ N, M, LEG_ID ], whereNandMare the object and spacecraft revolutions, respectively, andLEG_IDis the number of the leg at which the resonance is.INPUT.optselects the type of optimization.1is for SODP2is for MODP3is for SODP run each launch date. If the user selects a launch window greater or equal than 1 year, this option is selected automatically.4is for MODP run each launch year. If the user selects a launch window greater or equal than 3 year, this option is selected automatically.
The options defined above allow for an MGA trajectory search of Earth-Venus-Earth-Earth-Jupiter mission in year 2023 using MODP (INPUT.opt=2). There is a specified 2:1 resonance on the Earth-Earth leg, i.e., res = [2 1 3].
ASTRA main engine can then be run using:
%% --> optimize using ASTRA
% --> launch ASTRA optimization
OUTPUT = ASTRA_DP(seq, INPUT);Results are saved in a structure called OUTPUT.
If needed, one can then post-process the results, extracting the desired trajectory from the Pareto front, plotting the Pareto front itself and the selected path.
%% --> extract desired path and plot
close all; clc;
% --> extract path from Pareto front
[path, revs, res] = pathfromPF(OUTPUT);
% --> plot the Pareto front
figPareto = plotPareto(OUTPUT(1).ovPF);
% --> plot the path
[figECI, STRUC, figSYN, figRSC, figVSC] = plotPath(path, INPUT.idcentral);
% --> save the output
generateOutputTXT(path, INPUT.idcentral, './results');The plot of the Pareto front is the following:
The plot of the optimal trajectory in inertial and Earth-Sun synodic frame is the following:
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The function plotPath.m also allows to plot the evolutions of spacecraft distance and velocity with respect to central body:
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The function generateOutputTXT.m creates a .txt file in a folder called ./results that has all the info of the trajectory. This is reported here:
_/_/_/ _/_/_/ _/_/_/_/_/ _/_/_/ _/_/_/
_/ _/ _/ _/ _/ _/ _/ _/
_/_/_/_/ _/_/ _/ _/_/_/ _/_/_/_/
_/ _/ _/ _/ _/ _/ _/ _/
_/ _/ _/_/_/ _/ _/ _/ _/ _/
- ASTRA solution -
--------------------------------------------------------------
Departing body : Earth
Distance from the central body : 1.0000 AU
--------------------------------------------------------------
Arrival body : Jupiter
Distance from the central body : 5.2026 AU
Departing C3 : 11.1821 km^2/s^2
Departing infinity velocity : 3.3440 km/s
Arrival infinity velocity : 5.5560 km/s
Total cost (DSMs) : 0.2297 km/s
Total cost : 9.1297 km/s
Time of flight : 6.5995 years
--------------------------------------------------------------
MGA Details :
Swing-by sequence : -E--V--E--E--J-
Departing date : [2023 6 5 0 0 0]
Arrival date : [2030 1 9 11 32 29]
Time of flight per leg : 175 days
325 days
730.4809 days
1180 days
DSMs magnitudes : 0 km/s
0 km/s
0.0025302 km/s
0 km/s
0.22717 km/s
Infinity velocities :
Earth - Venus : 3.344 - 5.5398 km/s
Venus - Earth : 5.5423 - 9.3649 km/s
Earth - Earth : 9.3649 - 9.3667 km/s
Earth - Jupiter : 9.5899 - 5.556 km/s
State at departure/arrival (km and km/s) :
Earth : [-41536210.28622 -145973470.626 0 25.22061812303 -7.815385638442 -1.511901456476]
Venus : [-68483058.5096 82679154.4959 5068735.73872 -31.9673430837 -19.9046273943 1.44904973131]
Venus : [-68483058.5096 82679154.4959 5068735.73872 -31.8207835326 -24.8436384232 -0.473867544232]
Earth : [136074658.5919 60926320.94723 0 -20.73484901584 22.55369065354 1.423799578027]
Earth : [136074658.5919 60926320.94723 0 -21.90609082435 27.19379108781 1.468331664356]
Earth : [136074658.5919 60926320.94723 0 -21.90609082435 27.19379108781 1.468331664356]
Earth : [136074658.5919 60926320.94723 0 -19.36823020848 33.54168925672 -2.256209104279]
Jupiter : [-590948699.8079 -555350715.9192 15543181.54531 5.830113194957 -4.241447010639 0.3662016507624]
Encounter dates :
Earth : [2023 6 5 0 0 0]
Venus : [2023 11 27 0 0 0]
Earth : [2024 10 17 0 0 0]
Earth : [2026 10 17 11 32 29]
Jupiter : [2030 1 9 11 32 29]
Transfer types :
Earth - Venus : outbound - outbound
Venus - Earth : outbound - inbound
Earth - Earth : inbound - inbound
Earth - Jupiter : inbound - inbound
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Finally, one can further refine the solution around a specified trajectory, to further reduce the defects that might arise:
%% --> futher refine around the optimal DV-solution
INPUT.t0days = 10; % --> days around current solution departing epoch
INPUT.tofdays = 15; % --> days around current solution TOFs
INPUT.dt = 0.5; % --> step size (days)
INPUT.revs = revs;
INPUT.res = res;
% --> further refine using ASTRA
OUTPUTref = refineUsingASTRApath(path, INPUT);If one wants to set up specific constraints for a custom optimization scenario, it can write as follows:
% --> specify custom bounds for TOFs and VINFs
INPUT.TOF_LIM = [[30 60]; [20 40]; [20 40]];
% INPUT.vInfLim = [ [0 XXX]; [0 XXX]; [0 XXX]; [0 XXX]; [0 XXX]]; % --> PL1, PL2, PL3, ... where the matrix INPUT.TOF_LIM refers to lower and upper bounds for TOFs per MGA leg, while the matrix INPUT.vInfLim refers to lower and upper bounds for infinity velocity at each fly-by body.
With the current setup:
%% --> input section
% --> clear INPUT and define new ones
try clear INPUT; catch; end; clc;
% --> sequence to be optimized
INPUT.idcentral = 6; % --> central body (Sun in this case)
seq = [ 5 4 4 3 ]; res = [ 13 7 2 ];
%%%%%%%%%% multi-rev. options %%%%%%%%%%
maxrev = 3; % --> max. number of revolutions (round number)
chosenRevs = differentRuns_v2(seq, maxrev); % --> generate successive runs
[INPUT.chosenRevs, INPUT.res] = processResonances(chosenRevs, res); % --> process the resonances options
[INPUT.chosenRevs] = maxRevOuterPlanets(seq, INPUT.chosenRevs, INPUT.idcentral); % --> only zero revs. on outer planets
%%%%%%%%%% multi-rev. options %%%%%%%%%%
%%%%%%%%%% set departing options %%%%%%%%%%
t0 = date2mjd2000([2023 1 1 0 0 0]); % --> initial date range (MJD2000)
tf = t0 + 0.5*365.25; % --> final date range (MJD2000)
dt = 0.1; % --> step size (days)
INPUT.depOpts = [t0 tf dt];
%%%%%%%%%% set departing options %%%%%%%%%%
%%%%%%%%%% set options %%%%%%%%%%
INPUT.opt = 2; % --> (1) is for SODP, (2) is for MODP, (3) is for DATES, (4) is for YEARS - MODP
INPUT.vInfOpts = [0 2]; % --> min/max departing infinity velocities (km/s)
INPUT.dsmOpts = [1 Inf]; % --> max defect DSM, and total DSMs (km/s)
INPUT.plot = [1 1]; % --> plot(1) for Pareto front, plot(2) for best traj. DV
INPUT.parallel = true; % --> put true for parallel, false otherwise
INPUT.tstep = dt; % --> step size for Time of flight
%%%%%%%%%% set options %%%%%%%%%%
% --> specify custom bounds for TOFs and VINFs
INPUT.TOF_LIM = [[30 60]; [20 40]; [20 40]];
%% --> optimize using ASTRA
% --> launch ASTRA optimization
OUTPUT = ASTRA_DP(seq, INPUT);one has the following resulting trajectories:
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where the MGA mission is around Saturn, flying-by Titan-Rhea-Rhea-Dione, with a 13:7 resonance on the Rhea-Rhea leg.
The corresponding output is reported here:
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- ASTRA solution -
--------------------------------------------------------------
Departing body : Titan
Distance from the central body : 20.9828 Rs
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Arrival body : Dione
Distance from the central body : 6.4809 Rs
Departing C3 : 2.4048 km^2/s^2
Departing infinity velocity : 1.5508 km/s
Arrival infinity velocity : 1.7465 km/s
Total cost (DSMs) : 0.7016 km/s
Total cost : 3.9988 km/s
Time of flight : 0.3065 years
--------------------------------------------------------------
MGA Details :
Swing-by sequence : -T--R--R--D-
Departing date : [2023 6 24 19 11 59]
Arrival date : [2023 10 14 17 51 0]
Time of flight per leg : 31.6 days
58.7438 days
21.6 days
DSMs magnitudes : 0 km/s
0 km/s
0 km/s
0.70157 km/s
Infinity velocities :
Titan - Rhea : 1.5508 - 3.4391 km/s
Rhea - Rhea : 3.4391 - 3.4391 km/s
Rhea - Dione : 3.2324 - 1.7465 km/s
State at departure/arrival (km and km/s) :
Titan : [230777.07612 1199878.4264 0 -3.9470736019 0.76717345853 0]
Rhea : [424287.5053 -312766.6167 0 8.215458564 5.523455913 0]
Rhea : [424287.5053 -312766.6167 0 8.174753313 5.428292303 0]
Rhea : [424287.5053 -312766.6167 0 8.174753313 5.428292303 0]
Rhea : [424287.5053 -312766.6167 0 7.602562939 4.866499723 0]
Dione : [-233098.6853 -296804.2178 0 9.251156872 -7.279494237 0]
Encounter dates :
Jupiter : [2023 6 24 19 11 59]
Mars : [2023 7 26 9 35 59]
Mars : [2023 9 23 3 27 0]
Earth : [2023 10 14 17 51 0]
Transfer types :
Titan - Rhea : outbound - outbound
Rhea - Rhea : outbound - outbound
Rhea - Dione : outbound - outbound
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Currently, only invited developers can contribute to the repository.
The work is under license CC BY-NC-SA 4.0, that is an Attribution Non-Commercial license.
[1] Bellome, A., “Trajectory design of multi-target missions via graph transcription and dynamic programming,” Ph.D. thesis, Cranfield University, 2023. https://dspace.lib.cranfield.ac.uk/items/711f45c8-e6e4-4f27-909d-94170df400e3
[2] Bellome, A., et al. "Multiobjective design of gravity-assist trajectories via graph transcription and dynamic programming." Journal of Spacecraft and Rockets 60.5 (2023): 1381-1399. https://doi.org/10.2514/1.A35472.