Rendezvous Guidance Trajectories via Multiple-Subarc Sequential Gradient-Restoration Algorithm

Paper number

IAC-06-C1.7.03

Author

Dr. Angelo Miele, Rice University, United States

Coauthor

Mr. Marco Ciarcia, Rice University, United States

Year

2006

Abstract

In a previous paper (Ref. 1), we employed the single-subarc sequential gradient-restoration algorithm to optimize the rendezvous between a target spacecraft in a circular orbit at Space Station altitude and a chaser spacecraft with an initial separation distance and separation velocity in three dimensions.  The solutions achieved are characterized by two, three, or four subarcs depending on the performance index and the constraints.
In this paper, we employ the multiple-subarc sequential-gradient restoration algorithm to produce guidance trajectories implementable in real time via constant control components.  In other words, in this investigation we force the controls to behave as parameters in each subarc.  With the above understanding, we investigate four problems: (P1) minimum time, fuel free; (P2) minimum fuel, time free; (P3) minimum time, fuel given; (P4) minimum fuel, time given. 
Problem P1 results in a two-subarc solution, each subarc with constant controls: a max thrust accelerating subarc followed by a max thrust braking subarc.  Problem P2 results in a four-subarc solution, each subarc with constant controls: an initial coasting subarc, followed by a max thrust accelerating subarc, followed by another coasting subarc, followed by a max thrust braking subarc.  Problems P3 and P4 result in two, three, or four-subarc solutions depending on the performance index and the constraints, albeit with constant controls in each subarc.
For all of the problems studied, the performance index of the guidance trajectories approximates the performance index of the optimal trajectories of Ref. 1 within 1 percent.
Reference 1. A. MIELE, M. CIARCIÀ, and M. W. WEEKS, Rendezvous Optimal Trajectories via Single-Subarc Sequential Gradient-Restoration Algorithm, 57th International Astronautical Congress, Valencia, Spain, 2006.

Abstract document

IAC-06-C1.7.03.pdf

Manuscript document

IAC-06-C1.7.03.pdf (🔒 authorized access only).

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