Improved shaping approach to the preliminary design of low-thrust trajectories

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Abstract

This paper presents a general framework for the development of shape-based approaches to low-thrust trajectory design. A novel shaping method, based on a three-dimensional description of the trajectory in spherical coordinates, is developed within this general framework. Both the exponential sinusoid and the inverse polynomial shaping are demonstrated to be particular two-dimensional cases of the spherical one. The pseudoequinoctial shaping is revisited within the new framework, and the nonosculating nature of the pseudoequinoctial elements is analyzed. A two step approach is introduced to solve the time of flight constraint, related to the design of low-thrust arcs with boundary constraints for both spherical and pseudoequinoctial shaping. The solution derived from the shaping approach is improved with a feedback linear-quadratic controller and compared against a direct collocation method based on finite elements in time. The new shaping approach and the combination of shaping and linear-quadratic controller are tested on three case studies: a mission to Mars, a mission to asteroid 1989ML, a mission to comet Tempel-1, and a mission to Neptune.
Original languageEnglish
Pages (from-to)128-147
Number of pages20
JournalJournal of Guidance, Control and Dynamics
Volume34
Issue number1
DOIs
Publication statusPublished - 1 Jan 2011

Keywords

  • shaping approach
  • trajectories
  • spherical coordinates
  • Mars
  • Neptune
  • Space exploration

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