Solving optimal continuous thrust rendezvous problems with generating functions

Chandeok Park, Daniel J. Scheeres, Vincent Guibout

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

The optimal control of a spacecraft as it transitions between specified states using continuous thrust in a fixed amount of time is studied using a recently developed technique based on Hamilton-Jacobi theory. Starting from the 1st order necessary conditions for optimally, we derive a Hamiltonian system for the state and adjoints with split boundary conditions. Then, recognizing the two point boundary value problem as a canonical transformation, we employ generating functions to find the optimal feedback control as well as the optimal trajectory. Though we formulate the optimal control problem in the context of the necessary conditions for optimality, our closed-loop solution also formally satisfies the sufficient conditions for optimally via the fundamental connection between the optimal cost function and generating functions. A solution procedure for these generating functions is posed and numerically tested on a non-linear optimal rendezvous problem in the vicinity of a circular orbit. Generating functions are developed as series expansions, and the optimal trajectories obtained from them are compared favorably with those of a numerical solution to the two point boundary value problem using a forward shooting method.

Original languageEnglish
Title of host publicationCollection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2005
Pages2332-2353
Number of pages22
Volume3
Publication statusPublished - 2005 Dec 1
EventAIAA Guidance, Navigation, and Control Conference 2005 - San Francisco, CA, United States
Duration: 2005 Aug 152005 Aug 18

Other

OtherAIAA Guidance, Navigation, and Control Conference 2005
CountryUnited States
CitySan Francisco, CA
Period05/8/1505/8/18

Fingerprint

Boundary value problems
Trajectories
Hamiltonians
Cost functions
Feedback control
Spacecraft
Orbits
Boundary conditions

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

Park, C., Scheeres, D. J., & Guibout, V. (2005). Solving optimal continuous thrust rendezvous problems with generating functions. In Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2005 (Vol. 3, pp. 2332-2353)
Park, Chandeok ; Scheeres, Daniel J. ; Guibout, Vincent. / Solving optimal continuous thrust rendezvous problems with generating functions. Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2005. Vol. 3 2005. pp. 2332-2353
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Park, C, Scheeres, DJ & Guibout, V 2005, Solving optimal continuous thrust rendezvous problems with generating functions. in Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2005. vol. 3, pp. 2332-2353, AIAA Guidance, Navigation, and Control Conference 2005, San Francisco, CA, United States, 05/8/15.

Solving optimal continuous thrust rendezvous problems with generating functions. / Park, Chandeok; Scheeres, Daniel J.; Guibout, Vincent.

Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2005. Vol. 3 2005. p. 2332-2353.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Park C, Scheeres DJ, Guibout V. Solving optimal continuous thrust rendezvous problems with generating functions. In Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2005. Vol. 3. 2005. p. 2332-2353