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Guidance for Hyperbolic Rendezvous

Guidance for Hyperbolic Rendezvous. Damon Landau April 30, 2005. Earth-Mars Cycler Mission. cycler. M4. taxi. M2. E1-M2 170 days. E3 flyby. E5. E1. E3. gravity assist. from Mars. Getting There. r = 477,000 km one-day transfer. lunar orbit. cycler frame. one hour before

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Guidance for Hyperbolic Rendezvous

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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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