Optimal Maneuvers Around Binary Asteroids Using Particle Swarm Optimization and Machine Learning
Abstract
Designing optimal transfer trajectories and reference orbit tracking in binary asteroid systems is both challenging and computationally expensive. This paper proposes a method of bypassing the high computational overhead by leveraging a collection of known techniques. Indeed, the proposed framework is based on the combination of artificial intelligence techniques, such as the particle swarm optimization and neural networks, along with the inverse dynamics and the B-splines approximation of the trajectory. The real irregular shapes of the asteroids are considered in the free dynamics of the system, which are obtained via the mutual polyhedral model. The gravitational accelerations of the single asteroids acting on the spacecraft are approximated by using two single-layer neural networks trained via an extreme learning machine. By using a combination of these techniques, the computational time of the whole optimization is decreased from hours to minutes. The proposed approach is applied to the optimal trajectory design around the binary asteroid system, 1999 KW4, showing the feasibility of the proposed optimization approach, reducing the computational effort and time, and increasing the reliability of the obtained results. It is shown through a Monte Carlo analysis that our optimization strategy yields more accurate solutions than other optimization algorithms, such as the interior point and sequential quadratic programming methods, when a random initial guess is provided. Finally, the proposed optimization approach can be used in combination with other techniques to provide a feasible and reliable initial guess for a better solution refinement.t
References
[1] , “The Hayabusa Mission-Its Seven Years Flight,” 2011 Symposium on VLSI Circuits-Digest of Technical Papers, IEEE, New York, 2011, pp. 2–5, https://ieeexplore.ieee.org/document/5985987.
[2] , “Hayabusa2 Mission Overview,” Space Science Reviews, Vol. 208, Nos. 1–4, 2017, pp. 3–16. https://doi.org/10.1007/s11214-017-0377-1
[3] , “OSIRIS-REx: Sample Return from Asteroid (101955) Bennu,” Space Science Reviews, Vol. 212, Nos. 1–2, 2017, pp. 925–984. https://doi.org/10.1007/s11214-017-0405-1
[4] , “Near Earth Asteroid (NEA) Scout Solar Sail Contingency Trajectory Design and Analysis,” 2018 Space Flight Mechanics Meeting, AIAA Paper 2018-0199, 2018. https://doi.org/10.2514/6.2018-0199
[5] , “Lucy: Navigating a Jupiter Trojan Tour,” AIAA/AAS Astrodynamics Specialist Meeting, AAS Paper 17-632, Univelt, Inc., Escondido, CA, Aug. 2017, https://ntrs.nasa.gov/citations/20170008008 [retrieved 17 May 2023].
[6] , “The ESA Hera Mission: Detailed Characterization of the DART Impact Outcome and of the Binary Asteroid (65803) Didymos,” Planetary Science Journal, Vol. 3, No. 7, 2022, Paper 160. https://doi.org/10.3847/PSJ/ac6f52
[7] , “Double Asteroid Redirection Test (DART) Phase D Mission Design & Navigation Analysis,” 7th IAA Planetary Defense Conference (PDC), United Nations Office of Outer Space Affairs (UNOOSA), 2021, p. 251, https://dataverse.jpl.nasa.gov/file.xhtml?fileId=72733&version=1.0 [retrieved 16 Jan. 2023].
[8] , “Stable Regions of Motion Around a Binary Asteroid System,” Journal of Guidance, Control, and Dynamics, Vol. 42, No. 11, 2019, pp. 2521–2531. https://doi.org/10.2514/1.G004217
[9] , “Trajectory Design About Binary Asteroids Through Coupled Three-Body Problems,” Spaceflight Mechanics, Univelt, Inc., Escondido, CA, 2014, pp. 2093–2110, https://hdl.handle.net/11311/809727 [retrieved 23 June 2022].
[10] , “A Comparative Reliability Analysis of Ballistic Deployments on Binary Asteroids,” Acta Astronautica, Vol. 156, March 2019, pp. 308–316. https://doi.org/10.1016/j.actaastro.2018.03.020
[11] , “Ballistic Landing Design on Binary Asteroids: The AIM Case Study,” Advances in Space Research, Vol. 62, No. 8, 2018, pp. 2245–2260. https://doi.org/10.1016/j.asr.2017.11.033
[12] , “Opportunities for Ballistic Soft Landing in Binary Asteroids,” Journal of Guidance, Control, and Dynamics, Vol. 40, No. 6, 2017, pp. 1390–1402. https://doi.org/10.2514/1.G002181
[13] , “Image-Based Meta-Reinforcement Learning for Autonomous Guidance of an Asteroid Impactor,” Journal of Guidance, Control, and Dynamics, Vol. 45, No. 11, 2022, pp. 2013–2028. https://doi.org/10.2514/6.2022-2270
[14] , “Bounded Trajectory Design and Self-Adaptive Maintenance Control Near Non-Synchronized Binary Systems Comprised of Small Irregular Bodies,” Acta Astronautica, Vol. 152, Nov. 2018, pp. 768–781. https://doi.org/10.1016/j.actaastro.2018.09.028
[15] , “Impact of Solar Radiation Pressure Modeling on Orbital Dynamics in the Vicinity of Binary Asteroids,” Acta Astronautica, Vol. 165, Dec. 2019, pp. 167–183. https://doi.org/10.1016/j.actaastro.2019.09.003
[16] , “Solar-Sail Orbital Motion About Asteroids and Binary Asteroid Systems,” Journal of Guidance, Control, and Dynamics, Vol. 41, No. 9, 2018, pp. 1947–1962. https://doi.org/10.2514/1.G003235
[17] , “Stationkeeping Analysis for Solar Sailing the L4 Region of Binary Asteroid Systems,” Journal of Guidance, Control, and Dynamics, Vol. 42, No. 6, 2019, pp. 1306–1318. https://doi.org/10.2514/1.G003994
[18] , “Solar-Photon Sail Hovering Orbits About Single and Binary Asteroids,” Advances in Space Research, Vol. 63, No. 11, 2019, pp. 3691–3705. https://doi.org/10.1016/j.asr.2019.02.021
[19] , “Global Mapping of Asteroids by Frozen Orbits: The Case of 216 Kleopatra,” Acta Astronautica, Vol. 161, Aug. 2019, pp. 101–107. https://doi.org/10.1016/j.actaastro.2019.05.026
[20] , “Adaptive and Supertwisting Adaptive Spacecraft Orbit Control Around Asteroids,” Journal of Aerospace Engineering, Vol. 32, No. 4, 2019, Paper 04019042. https://doi.org/10.1061/(ASCE)AS.1943-5525.0001043
[21] , “Closed-Loop Control of Close Orbits Around Asteroids,” Journal of Guidance, Control, and Dynamics, Vol. 38, No. 5, 2015, pp. 854–860. https://doi.org/10.2514/1.G000158
[22] , “Iterative-Learning-Control-Based Tracking for Asteroid Close-Proximity Operations,” Journal of Guidance, Control, and Dynamics, Vol. 42, No. 5, 2019, pp. 1195–1203. https://doi.org/10.2514/1.G003884
[23] , “Direct Adaptive Control of Spacecraft Near Asteroids,” Acta Astronautica, Vol. 202, Jan. 2023, pp. 197–213. https://doi.org/10.1016/j.actaastro.2022.10.014
[24] , “Tracking Reference Orbits Around Asteroids with Unknown Gravitational Parameters Using a Nonlinear Adaptive Controller,” AIAA SciTech 2020 Forum, AIAA Paper 2020-0226, 2020. https://doi.org/10.2514/6.2020-0226
[25] , “Trajectory Tracking Near Small Bodies Using Only Attitude Control,” Journal of Guidance, Control, and Dynamics, Vol. 42, No. 1, 2019, pp. 109–122. https://doi.org/10.2514/1.G003653
[26] , “Optimal Reference Orbit Tracking Around Asteroids via Particle Swarm Optimization and Inverse Dynamics Technique,” 31st AAS/AIAA Space Flight Mechanics Meeting, AAS Paper 21-260, Univelt, Inc., Escondido, CA, 2021, https://www.researchgate.net/profile/Andrea-Dambrosio-4/publication/349044019_Optimal_reference_orbit_tracking_around_asteroids_via_Particle_Swarm_Optimization_and_inverse_dynamics_technique/links/602c117d4585158939ad488d/Optimal-reference-orbit-tracking-around-asteroids-via-Particle-Swarm-Optimization-and-inverse-dynamics-technique.pdf [retrieved 15 March 2021].
[27] , “Mutual Potential of Homogeneous Polyhedra,” Celestial Mechanics and Dynamical Astronomy, Vol. 91, No. 3, 2005, pp. 337–349. https://doi.org/10.1007/s10569-004-4621-0
[28] , “Simulation of the Full Two Rigid Body Problem Using Polyhedral Mutual Potential and Potential Derivatives Approach,” Celestial Mechanics and Dynamical Astronomy, Vol. 96, No. 3, 2006, pp. 317–339. https://doi.org/10.1007/s10569-006-9045-6
[29] , “Particle Swarm Optimization,” Proceedings of the ICNN’95-International Conference on Neural Networks, Vol. 4, IEEE, New York, 1995, pp. 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
[30] , “Exterior Gravitation of a Polyhedron Derived and Compared with Harmonic and Mascon Gravitation Representations of Asteroid 4769 Castalia,” Celestial Mechanics and Dynamical Astronomy, Vol. 65, No. 3, 1996, pp. 313–344. https://doi.org/10.1007/BF00053511
[31] , “Real-Time Optimal Control for Irregular Asteroid Landings Using Deep Neural Networks,” Acta Astronautica, Vol. 170, May 2020, pp. 66–79. https://doi.org/10.1016/j.actaastro.2019.11.039
[32] , “Extreme Learning Machine: Theory and Applications,” Neurocomputing, Vol. 70, Nos. 1–3, 2006, pp. 489–501. https://doi.org/10.1016/j.neucom.2005.12.126
[33] , “Modelling Irregular Small Bodies Gravity Field via Extreme Learning Machines,” 27th AAS/AIAA Spaceflight Mechanics Meeting, AAS Paper 17-469, Univelt, Inc., Escondido, CA, 2017, https://www.researchgate.net/publication/316655907 [retrieved 20 April 2021].
[34] , “Modeling Irregular Small Bodies Gravity Field via Extreme Learning Machines and Bayesian Optimization,” Advances in Space Research, Vol. 67, No. 1, 2020, pp. 617–638.
[35] , “A Perspective on Methods for Trajectory Optimization,” AIAA/AAS Astrodynamics Specialist Conference and Exhibit, AIAA Paper 2002-4727, 2002. https://doi.org/10.2514/6.2002-4727
[36] , “Flatness and Defect of Non-Linear Systems: Introductory Theory and Examples,” International Journal of Control, Vol. 61, No. 6, 1995, pp. 1327–1361. https://doi.org/10.1080/00207179508921959
[37] , “Design of Algorithms for Satellite Slew Manoeuver by Flatness and Collocation,” 2007 American Control Conference, IEEE, New York, 2007, pp. 3168–3173. https://doi.org/10.1109/ACC.2007.4282459
[38] , “On Calculating with B-Splines,” Journal of Approximation theory, Vol. 6, No. 1, 1972, pp. 50–62. https://doi.org/10.1016/0021-9045(72)90080-9
[39] , Orbital Motion in Strongly Perturbed Environments: Applications to Asteroid, Comet and Planetary Satellite Orbiters, Springer, Berlin, 2016, pp. 55–57. https://doi.org/10.1007/978-3-642-03256-1
[40] , “A Fast and Accurate Online Sequential Learning Algorithm for Feedforward Networks,” IEEE Transactions on Neural Networks, Vol. 17, No. 6, 2006, pp. 1411–1423. https://doi.org/10.1109/TNN.2006.880583
[41] , “Particle Swarm Optimization Applied to Space Trajectories,” Journal of Guidance, Control, and Dynamics, Vol. 33, No. 5, 2010, pp. 1429–1441. https://doi.org/10.2514/1.48475
[42] , “Low-Cost Transfer Between Asteroids with Distant Orbits Using Multiple Gravity Assists,” Advances in Space Research, Vol. 56, No. 5, 2015, pp. 837–847. https://doi.org/10.1016/j.asr.2015.05.013
[43] , “Analysis of Some Global Optimization Algorithms for Space Trajectory Design,” Journal of Spacecraft and Rockets, Vol. 47, No. 2, 2010, pp. 334–344. https://doi.org/10.2514/1.45742
[44] , “Particle Swarm Optimization for Time-Optimal Spacecraft Reorientation with Keep-Out Cones,” Journal of Guidance, Control, and Dynamics, Vol. 39, No. 2, 2016, pp. 312–325. https://doi.org/10.2514/1.G001228
[45] , “Optimal Finite-Thrust Rendezvous Trajectories Found via Particle Swarm Algorithm,” Journal of Spacecraft and Rockets, Vol. 50, No. 6, 2013, pp. 1222–1234. https://doi.org/10.2514/1.A32402
[46] , “Particle Swarm Optimization of Multiple-Burn Rendezvous Trajectories,” Journal of Guidance, Control, and Dynamics, Vol. 35, No. 4, 2012, pp. 1192–1207. https://doi.org/10.2514/1.55592
[47] , “Particle Swarm Optimization Applied to Ascent Phase Launch Vehicle Trajectory Optimization Problem,” Procedia Computer Science, Vol. 54, Jan. 2015, pp. 516–522. https://doi.org/10.1016/j.procs.2015.06.059
[48] , “Trajectory Planning of Free-Floating Space Robot Using Particle Swarm Optimization (PSO),” Acta Astronautica, Vol. 112, July 2015, pp. 77–88. https://doi.org/10.1016/j.actaastro.2015.03.008
[49] , “UPSO: A Unified Particle Swarm Optimization Scheme,” Lecture Series on Computer and Computational Science, International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2004), Vol. 1, Taylor and Francis, Philadelphia, PA, 2004, pp. 868–873. https://doi.org/10.1201/9780429081385
[50] , “PSO-Based Soft Lunar Landing with Hazard Avoidance: Analysis and Experimentation,” Aerospace, Vol. 8, No. 7, 2021, Paper 195. https://doi.org/10.3390/aerospace8070195
[51] , “Time-Suboptimal Satellite Formation Maneuvers Using Inverse Dynamics and Differential Evolution,” Journal of Guidance, Control, and Dynamics, Vol. 41, No. 5, 2018, pp. 1108–1121. https://doi.org/10.2514/1.G003110