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Guidance for Hyperbolic Rendezvous in Earth-Mars Cycler Missions

This comprehensive guide by Damon Landau explores hyperbolic rendezvous techniques for Earth-Mars cycler missions, detailing the trajectory design, thrusting strategies, docking procedures, error analysis, and optimization methods. The paper discusses algorithmic guidance, control strategies, departure errors, and future work considerations for achieving efficient and accurate rendezvous in cycler missions.

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Guidance for Hyperbolic Rendezvous in Earth-Mars Cycler Missions

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  1. Guidance for Hyperbolic Rendezvous Damon Landau April 30, 2005

  2. Earth-Mars Cycler Mission cycler M4 taxi M2 E1-M2 170 days E3 flyby E5 E1 E3 gravity assist from Mars Damon Landau

  3. Getting There r = 477,000 km one-day transfer lunar orbit cycler frame one hour before rendezvous DV = 284 m/s taxi V∞=5 km/s cycler V∞=5 km/s Earth DV from LEO = 4.30 km/s Damon Landau

  4. cycler taxi Earth Relative Motion Damon Landau

  5. docking axis cycler taxi Guidance Algorithm x,y frame r,q frame Damon Landau

  6. Rendezvous taxi mass = 50 mt • Begin thrusting after 23 hours. • Design for 1/2-hour settling time, z= 2, vf = 0.1 m/s • fdock = 180° • DV = 294 m/s (ideal DV = 284 m/s) • rf = 0.238 m, vf = 0.146 m/s • time to rendezvous = 4.1 hours cycler centered Earth centered Damon Landau

  7. Rendezvous taxi mass = 50 mt • Begin thrusting after 23 hours. • Design for 1/2-hour settling time, z= 2, vf = 0.1 m/s • fdock = 0° • DV = 1,837 m/s • rf = 0.600 m, vf = 0.264 m/s • time to rendezvous = 3.8 hours cycler centered Earth centered Damon Landau

  8. Departure Error taxi mass = 50 mt • DV error of 50 m/s from LEO • Begin thrusting after 23 hours. • Design for 1/2-hour settling time, z= 2, vf = 0.1 m/s • fdock = 180° • DV = 6,572 m/s • rf = 0.291 m, vf = 0.141 m/s • time to rendezvous = 5.3 hours cycler centered Earth centered Damon Landau

  9. Lower Gains cycler centered • Begin thrusting after 23 hours. • Design for 1/2-hour settling time, z= 0.8, vf = 0.1 m/s • rf = 0.002 m, vf = 83.8 m/s • Rendezvous speed is too fast • Will the speed approach zero? 1st loop GES, but not practical rf = 1 cm, vf = 1.6 cm/s Damon Landau

  10. Future (Fun)Work 3-D analysis Limit controls to thruster capabilities Include navigational errors Failure analysis Optimize for DV and time Conclusions Hyperbolic rendezvous is possible with a relatively simple controller. The DV and time for rendezvous can be similar to the ideal case. Poor choice of docking axis significantly increases DV. The state near r = 0 is more important than the response as t  ∞. Damon Landau

  11. References • Byrnes, D. V., Longuski, J. M., and Aldrin, B., “Cycler Orbit Between Earth and Mars,” Journal of Spacecraft and Rockets, Vol. 30, No. 3, May-June 1993, pp. 334-336. • Kluever, C. A., “Feedback Control for Spacecraft Rendezvous and Docking,” Journal of Guidance, Control, and Dynamics, Vol. 22, No. 4, July-August 1999, pp.609-611. • McConaghy, T. T., Landau, D. F., Yam, C. H., and Longuski, J. M., “A Notable Two-Synodic-Period Earth-Mars Cycler,” to appear in Journal of Spacecraft and Rockets. • Penzo, P. A., and Nock, K. T., “Hyperbolic Rendezvous for Earth-Mars Cycler Missions,” Paper AAS 02-162, AAS/AIAA Space Flight Mechanics Meeting, San Antonio, TX, Jan. 27-30, 2002, pp. 763-772. • Prussing, J. E., and Conway, B. A., Orbital Mechanics, New York, Oxford University Press, 1993. • Shaohua, Y., Akiba, R., and Matsuo, H., “Control of Omni-Directional Rendezvous Trajectories,” Acta Astronautica, Vol. 32, No.2, 1994, pp. 83-87. • Wang, P. K. C., “Non-linear guidance laws for automatic orbital rendezvous,” International Journal of Control, Vol. 42, No. 3, 1985, pp. 651-670. Damon Landau

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