Systematic Design of Optimal Low-Thrust Transfers for the Three-Body Problem

  • Shankar KulumaniEmail author
  • Taeyoung Lee


We develop a computational approach for the design of continuous low thrust transfers in the planar circular restricted three-body problem. The use of low thrust propulsion allows the spacecraft to depart from the natural dynamics and enables a wider range of transfers. We generate the reachable set of the spacecraft and use this to determine transfer opportunities, analogous to the intersection of control-free invariant manifolds. The reachable set is developed on a lower dimensional Poincaré section and used to design transfer trajectories. This is solved numerically as a discrete optimal control problem using a variational integrator, which preserves the geometric structure of the motion in the three-body problem. We demonstrate our approach with two numerical simulations of transfers in the Earth-Moon three-body system.


Three body problem Reachability Optimal control 



This research has been supported in part by NSF under the grants CMMI-1243000 (transferred from 1029551), CMMI-1335008, and CNS-1337722. The authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest, or non-financial interest in the subject matter or materials discussed in this manuscript.


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Copyright information

© American Astronautical Society 2019

Authors and Affiliations

  1. 1.Department of Mechanical & Aerospace EngineeringGeorge Washington UniversityWashingtonUSA

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