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

2. Damon Landau2 Earth-Mars Cycler Mission E5 E3 E1 M4 M2 E1-M2 170 days gravity assist E3 flyby from Mars cycler taxi

3. April 30, 2005Damon Landau3 Getting There cycler V ∞ =5 km/s taxi V ∞ =5 km/s r = 477,000 km one-day transfer lunar orbit Earth one hour before rendezvous  V = 284 m/s  V from LEO = 4.30 km/s cycler frame

4. April 30, 2005Damon Landau4 Relative Motion Earth cycler taxi

5. April 30, 2005Damon Landau5 Guidance Algorithm taxi cycler docking axis x,y frame r,  frame

6. April 30, 2005Damon Landau6 Rendezvous Begin thrusting after 23 hours. Design for 1/2-hour settling time,  = 2, v f = 0.1 m/s  dock = 180°  V = 294 m/s (ideal  V = 284 m/s)  f = 0.238 m, v f = 0.146 m/s time to rendezvous = 4.1 hours Earth centered cycler centered taxi mass = 50 mt

7. April 30, 2005Damon Landau7 Rendezvous Begin thrusting after 23 hours. Design for 1/2-hour settling time,  = 2, v f = 0.1 m/s  dock = 0°  V = 1,837 m/s  f = 0.600 m, v f = 0.264 m/s time to rendezvous = 3.8 hours Earth centered cycler centered taxi mass = 50 mt

8. April 30, 2005Damon Landau8 Departure Error  V error of 50 m/s from LEO Begin thrusting after 23 hours. Design for 1/2-hour settling time,  = 2, v f = 0.1 m/s  dock = 180°  V = 6,572 m/s  f = 0.291 m, v f = 0.141 m/s time to rendezvous = 5.3 hours Earth centered cycler centered taxi mass = 50 mt

9. April 30, 2005Damon Landau9 Lower Gains Begin thrusting after 23 hours. Design for 1/2-hour settling time,  = 0.8, v f = 0.1 m/s  f = 0.002 m, v f = 83.8 m/s Rendezvous speed is too fast Will the speed approach zero? cycler centered 1 st loop GES, but not practical  f = 1 cm, v f = 1.6 cm/s

10. April 30, 2005Damon Landau10 Future (Fun)Work 3-D analysis Limit controls to thruster capabilities Include navigational errors Failure analysis Optimize for  V and time Conclusions Hyperbolic rendezvous is possible with a relatively simple controller. The  V and time for rendezvous can be similar to the ideal case. Poor choice of docking axis significantly increases  V. The state near  = 0 is more important than the response as t  ∞.

11. April 30, 2005Damon Landau11 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.