caa a22 4500 463169948 CHVBK 20180406164810.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s10957-007-9166-4 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9166-4 Optimal Trajectories for Spacecraft Rendezvous [Elektronische Daten] [A. Miele, M. Weeks, M. Ciarcià] 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. Springer Science+Business Media, LLC, 2007 Space trajectories nationallicence Rendezvous nationallicence Optimal control nationallicence Calculus of variations nationallicence Mayer problems nationallicence Bolza problems nationallicence Transformation techniques nationallicence Sequential gradient-restoration algorithm nationallicence Miele A. Aero-Astronautics Group, Rice University, Houston, TX, USA aut Weeks M. Aeroscience and Flight Mechanics Division, NASA-Johnson Space Center, Houston, TX, USA aut Ciarcià M. Aero-Astronautics Group, Rice University, Houston, TX, USA aut Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/3(2007-03-01), 353-376 0022-3239 132:3<353 2007 132 10957 https://doi.org/10.1007/s10957-007-9166-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9166-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Miele A. Aero-Astronautics Group, Rice University, Houston, TX, USA aut NATIONALLICENCE 700 1- Weeks M. Aeroscience and Flight Mechanics Division, NASA-Johnson Space Center, Houston, TX, USA aut NATIONALLICENCE 700 1- Ciarcià M. Aero-Astronautics Group, Rice University, Houston, TX, USA aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/3(2007-03-01), 353-376 0022-3239 132:3<353 2007 132 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer