Optimal Trajectories for Spacecraft Rendezvous
- 365 Downloads
The efficient execution of a rendezvous maneuver is an essential component of various types of space missions. This work describes the formulation and numerical investigation of the thrust function required to minimize the time or fuel required for the terminal phase of the rendezvous of two spacecraft. The particular rendezvous studied concerns a target spacecraft in a circular orbit and a chaser spacecraft with an initial separation distance and separation velocity in all three dimensions. First, the time-optimal rendezvous is investigated followed by the fuel-optimal rendezvous for three values of the max-thrust acceleration via the sequential gradient-restoration algorithm. Then, the time-optimal rendezvous for given fuel and the fuel-optimal rendezvous for given time are investigated. There are three controls, one determining the thrust magnitude and two determining the thrust direction in space.
The time-optimal case results in a two-subarc solution: a max-thrust accelerating subarc followed by a max-thrust braking subarc. The fuel-optimal case results in a four-subarc solution: an initial coasting subarc, followed by a max-thrust braking subarc, followed by another coasting subarc, followed by another max-thrust braking subarc. The time-optimal case with fuel given and the fuel-optimal case with time given result in two, three, or four-subarc solutions depending on the performance index and the constraints.
Regardless of the number of subarcs, the optimal thrust distribution requires the thrust magnitude to be at either the maximum value or zero. The coasting periods are finite in duration and their length increases as the time to rendezvous increases and/or as the max allowable thrust increases. Another finding is that, for the fuel-optimal rendezvous with the time unconstrained, the minimum fuel required is nearly constant and independent of the max available thrust. Yet another finding is that, depending on the performance index, constraints, and initial conditions, sometime the initial application of thrust must be delayed, resulting in an optimal rendezvous trajectory which starts with a coasting subarc.
KeywordsSpace trajectories Rendezvous Optimal control Calculus of variations Mayer problems Bolza problems Transformation techniques Sequential gradient-restoration algorithm
Unable to display preview. Download preview PDF.
- 1.Polites, M.E.: An assessment of the technology of automated rendezvous and capture in space. Technical Report TP-208528, NASA MSFC (1970) Google Scholar
- 2.Zimpfer, D., Tuohy, S.: Autonomous rendezvous, capture, and in-space assembly: past, present, and future. AIAA Paper 05-2523, 1st Space Exploration Conference: Continuing the Voyage of Discovery, Orlando, FL, 2005 Google Scholar
- 3.Ianni, J.D., Graves, J.D.: The human’s dismissing role in future on-orbit servicing missions. AIAA Paper 2001-4539, AIAA Space Conference and Exposition, Albuquerque, NM, 2001 Google Scholar
- 4.Matsumoto, S., Oda, M., Kawano, I.: Attitude dynamics and control of space cargo for reusable orbital logistic supply servicing. AIAA Paper 2002-4785, AIAA Guidance, Navigation, and Control Conference, Monterey, CA, 2002 Google Scholar
- 5.Defense Advanced Research Projects Agency (DARPA): Orbital Express space operation architecture. Website http://www.darpa.mil/tto/programs/oe.html
- 6.Air Force Research Laboratory (AFRL): XSS-11 Microsatellite. Website www.vs.afrl.af.mil/FactSheets/XSS11-MicroSatellite.pdf
- 7.Anonymous: Executive summary (introduction-CEV): NASA exploration system architecture study final report (DRAFT) (2005). Website http://www.spaceref.com/news/viewsr.html?pid=1967
- 8.Bailey, J.W.: NASA JSC Solicitation: commercial orbital transportation services (COTS) space flight demonstrations. NASA JSC Solicitation on spaceref.com. Website http://www.spaceref.com/news/viewsr.html?pid=18511
- 9.Dittmar, M.: Commercial avenues for space utilization. AIAA Paper 2003-6234, AIAA Space Conference and Exposition, Long Beach, CA, 2003 Google Scholar
- 10.Long, A., Hastings, D.: Catching the wave: a unique opportunity for the development of an on-orbit satellite servicing infrastructure. AIAA Paper 04-6051, AIAA Space Conference and Exhibition, San Diego, CA, 2004 Google Scholar
- 11.Pearson, D.J.: The glideslope approach. Adv. Astronaut. Sci. 69, 109–123 (1989), Paper AAS 89-162 (1989) Google Scholar
- 12.Fox, A.: Rendezvous Crew Training Handbook. Manual TD398B, Mission Operations Directorate, Training Division, NASA-MSFC (1998) Google Scholar
- 13.Jezewski, D.J., Brazzel, J.P., Jr., Prust, E.E., Brown, B.G., Mulder, T.A., Wissinger, D.B.: A survey of rendezvous trajectory planning. AAS Paper 91-505, AAS/AIAA Astrodynamics Conference, Durango, CO, pp. 1373–1396 (1991) Google Scholar
- 14.Pearson, D.J.: Baselining the Shuttle rendezvous technique. Informal Memorandum, Flight Design and Dynamics Division, NASA JSC (1990) Google Scholar
- 17.Thomson, W.T.: Introduction to Space Dynamics. Dover, New York, NY (1986) Google Scholar
- 18.Feshe, W.: Automated Rendezvous and Docking of Spacecraft. Cambridge University Press, Cambridge, MA (2003) Google Scholar
- 19.Bryson, A.E., Jr.: Control of Spacecraft and Aircraft. Princeton University Press, Princeton, NJ (1994) Google Scholar
- 23.Chiu, J.H.: Optimal multiple-impulse nonlinear orbital rendezvous. Ph.D. Thesis, University of Illinois at Urbana-Champaign (1984) Google Scholar
- 26.Guzman, J., Mailhe, L., Schiff, C., Hughes, S.: Primer vector optimization: survey of theory and some applications. Paper IAC-02-A. 6.09, 53rd International Astronautical Congress, Houston, TX, 2002 Google Scholar
- 29.Goldstein, A.A., Green, A.H., Johnson, A.T., Seidman, T.I.: Fuel optimization in orbital rendezvous. AIAA Paper 63-354, AIAA Guidance, Navigation, and Control Conference, Cambridge, MA, 1963 Google Scholar
- 30.Paiewonsky, B., Woodrow, P.J.: Three-dimensional time-optimal rendezvous. J. Spacecr. Rockets 3(11), 1577–1584 (1966) Google Scholar
- 32.Van Der Ha, J.C.: Analytical formulation for finite-thrust rendezvous trajectories. Paper IAF-88-308, 39th Congress of the International Astronautical Federation, Bangalore, India, 1988 Google Scholar
- 33.Carter, T.E., Brient, J.: Fuel-optimal rendezvous for linearized equations of motion. J. Guid. Control Dyn. 15(6), 1411–1416 (1992) Google Scholar
- 35.Clohessy, W.H., Wiltshire, R.S.: Terminal guidance system for satellite rendezvous. J. Aerosp. Sci. 27(9), 653–658 (1960) Google Scholar
- 41.Miele, A., Ciarcià, M., Weeks, M.W.: Guidance trajectories for spacecraft rendezvous. J. Optim. Theory Appl. 132(1) (2007) Google Scholar
- 42.Miele, A., Ciarcià, M., Weeks, M.W.: Rendezvous guidance trajectories via multiple-subarc sequential gradient-restoration algorithm. Paper IAC-06-C1.7.3, 57th International Astronautical Congress, Valencia, Spain, 2006 Google Scholar