Speaker
Ravishankar Mathur
(Emergent Space Technologies, Inc.)
Description
The NASA CubeQuest Challenge offers a launch on the 2018 Exploration Mission 1 (EM1) to competing teams who can demonstrate a high probability of success for a 6U CubeSat design. The selected competitors will have their CubeSat disposed into a high-energy lunar flyby trajectory soon after EM1 launch. If the CubeSat remains ballistic, the lunar flyby will eject it from the Earth-Moon system, reaching a distance of 4 million km in 2 months. The trajectory design goal of the Challenge is a thrust profile that will allow the CubeSat to enter a stable lunar orbit (with prescribed orbit size bounds), and maintain that orbit for 28 days, all within 1 year of disposal. Due to EM1 safety considerations, high-thrust chemical propulsion is not allowed, which eliminates the possibility of direct lunar orbit injection during the lunar flyby. This limits competitor teams to using low-thrust propulsion and designing trajectories that take advantage of the natural Earth-Moon-Sun system dynamics.
In this paper, we examine the incremental and iterative process of designing and optimizing a low-thrust trajectory that achieves and maintains lunar orbit within the prescribed 1 year. We start by exploring the post-disposal dynamics of the Earth-Moon-Sun system, and determine the general transfer trajectory types that remain in the vicinity of the Earth-Moon system. Next, we design a transfer trajectory using multiple unconstrained impulsive maneuvers, and look for minimum Delta-V solutions where the individual Delta-V magnitudes would be attainable in realistic time with thrust levels on the order of 1 mN. Finally, we convert the impulsive maneuvers to finite-burn maneuvers and re-optimize to maintain a continuous trajectory while minimizing total thrust duration. In doing so, we incorporate the need to perform periodic tracking and orbit determination as a constraint on the maximum continuous thrust time, and discuss the impact of this constraint on the optimal trajectory.
This is a particularly difficult trajectory design problem due to a highly nonlinear dynamical system (Earth-Moon-Sun) and a milli-newton thrust propulsion system. We discuss the use of Earth-Sun L1 dynamics to transition from an Earth-departing trajectory to a lunar arrival trajectory. We use a multiple-shooting method to match these trajectories, and show how this greatly aids in optimization convergence. We also discuss the benefits of using a stable lunar distant retrograde orbit (DROs) as an intermediate target before spiraling the CubeSat down into its final low lunar orbit. Finally, we address the design of the lunar spiral-down phase and final lunar orbit itself, including orbit stability and visibility from ground stations.
We use the NASA GSFC General Mission Analysis Tool (GMAT), combined with the VF13ad optimizer, for trajectory design and optimization. GMAT allows us to set up the trajectory design problem using impulsive propulsion, then easily transfer that solution to finite-burn propulsion. Additionally, the ease with which the VF13ad optimizer can be used from GMAT allows us to transition from a feasible to an optimal solution with minimal changes to the problem setup.
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Primary author
Ravishankar Mathur
(Emergent Space Technologies, Inc.)
