Improved Collocation Methods to Optimize Low-Thrust, Low-Energy Transfers in the Earth-Moon System

Abstract

Modern and near-future Solar Electric Propulsion capabilities enable many new missions that were inconceivable using chemical propulsion systems. Many of these involve highly complex trajectories that are very challenging to design. New tools are needed that effectively utilize the rapidly growing parallel processing capabilities of modern computers. This research improves Gauss-Lobatto collocation methods, which are known to perform very well for low-thrust trajectory optimization, by formulating them as massively parallel processes. The parallelized elements of the problem formulation execute up to 11 times faster, depending on what force model is used and when evaluated by themselves. When accounting for the operations of the nonlinear programming solver, this translates to up to 3.7 times faster performance for solving a complete trajectory optimization problem, again depending on the force model that is used. The remaining barriers to further performance improvements, and the conditions upon which these depend, are clearly identified.

The implemented methods are combined into an optimization tool named Maverick. More general improvements to the formulation of the Gauss-Lobatto collocation methods are also developed and included in Maverick, which permit a more flexible use of these optimization schemes and enable them to find more complex solutions. One example of this is Maverick's ability to autonomously introduce gravity assists into trajectories, which greatly increases the utility and convergence radius of these methods.

In order to demonstrate the benefit of this work, three applications are studied. The first are transfers between halo-like orbits in the Earth-Moon system, which shows this is likely an unattractive region for missions like the New Worlds Observer. The second application investigates stabilization maneuvers in lunar distant retrograde orbits. This work demonstrates the feasibility of these stabilization transfers for a variety of sample return missions, such as the upcoming Asteroid Redirect Mission. The final application discussed is a series of multi-body low-thrust transfers from the Earth to the Moon that efficiently utilize highly variable dynamics to reduce propellant consumption, which is relevant for a variety of future mission concepts. These are computed for a wide range of flight times, showing that reductions up to 45% of the transfer time can be achieved with a propellant consumption as little as 0.5% of the total spacecraft mass. Up to 90% of the flight time can be eliminated for a propellant cost of 4% of the total spacecraft mass, or up to 83% for a propellant cost of less than 2%. The developed algorithm seamlessly transitions its solutions from full low-thrust, low-energy trajectories to the 'pure' low-thrust trajectories that define the shortest transfer trajectories, validating its robust performance. Beyond these quantifiable results, these examples illustrate the complexity of the solutions that can be identified with these improved implementations of Gauss-Lobatto collocation methods, with many instances where the optimization method autonomously introduces powered gravity assists, an unusual capability that has the potential for useful application to many other trajectory optimization problems.