Optimal thrust design of a mission to Apophis based on a homotopy method

Xiaoli Bai, James D. Turner, John L. Junkins

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

7 Scopus citations


A novel homotopy method for solving optimal thrust direction control problems through Pontryagin's principle is presented. The homotopy method enforces the satisfaction of the dynamic equation constraints along the homotopy path, yielding an algorithm that is robust to the high nonlinearity of both dynamic equation constraints and performance criteria. The homotopy approach extends the convergence domain of the initial guess of the unknown boundary conditions when compared to the sequential quadratic programming method. The homotopy algorithm is applied to an Earth to Apophis mission analysis. A hybrid impulsive and low thrust propulsion strategy is studied. Through simulation results, we prove that if we use a 0.05N constant thrust and choose the time of flight from 250 days to 300 days, the launch window for the Earth to Apophis mission can span a full year from April 2012 to April 2013 for a standard launch vehicle.

Original languageEnglish (US)
Title of host publicationSpaceflight Mechanics 2009 - Advances in the Astronautical Sciences
Subtitle of host publicationProceedings of the 19th AAS/AIAA Space Flight Mechanics Meeting
Number of pages13
StatePublished - 2009
Externally publishedYes
Event19th AAS/AIAA Space Flight Mechanics Meeting - Savannah, GA, United States
Duration: Feb 8 2009Feb 12 2009

Publication series

NameAdvances in the Astronautical Sciences
ISSN (Print)0065-3438


Other19th AAS/AIAA Space Flight Mechanics Meeting
Country/TerritoryUnited States
CitySavannah, GA

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science


Dive into the research topics of 'Optimal thrust design of a mission to Apophis based on a homotopy method'. Together they form a unique fingerprint.

Cite this