Systematic Design of Optimal Low-Thrust Transfers for the Three-Body Problem
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Systematic Design of Optimal Low-Thrust Transfers for the Three-Body Problem Shankar Kulumani1
· Taeyoung Lee1
© American Astronautical Society 2019
Abstract 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 Poincar´e 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. Keywords Three body problem · Reachability · Optimal control
Introduction Designing spacecraft trajectories is a classic and ongoing topic of research. There has been significant research into the design of orbital transfers for space vehicles. Optimal expenditure of onboard propellant is critical to allowing a mission to continue for a longer period of time or to enable the launch of a less massive spacecraft. Electric propulsion systems offer a much greater specific impulse than chemical systems. As a result, the greatly increased efficiency allows for greater payload mass or extended duration missions. However, these electric propulsion systems typically have much Shankar Kulumani
[email protected] Taeyoung Lee [email protected] 1
Department of Mechanical & Aerospace Engineering, George Washington University, 800 22nd St NW, Washington, DC 20052, USA
The Journal of the Astronautical Sciences
less thrust than their chemical counterparts and therefore orbital maneuvers have a much longer time of flight. In spite of this drawback, a wide variety of missions, such as communication and deep space probes, have utilized the unique benefits of low thrust electric propulsion to great effect [3]. Recent developments in miniature electric propulsion and small satellites now offer the potential for new research opportunities [6, 9]. The potential for more demanding missions places an even greater importance on the mission design to ensure that optimal trajectories satisfy mission requirements [6, 7, 14, 25]. There has been extensive research focused on the optimal control of spacecraft orbital transfers in the three-body problem [8, 14, 22, 25]. Within the three-body problem, a spacecrafts feasible region of motion is constrained by its energy, or Jacobi integral. The addition of low-thrust propulsion offers the potential of reduced transfer transit times and the ability to depart from the free motion trajectory to allow for increased transfer opportunities. Frequently, insight into the problem or intuition on the part of the designer is req
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