Robust Trajectory Design in Highly Perturbed Environments Leveraging Continuation Methods

Research is proposed to investigate continuation methods to improve the robustness of trajectory design algorithms for spacecraft in highly perturbed dynamical environments, such as near asteroids and comets, where many traditional methods that are often used and taken for granted simply do not work. The continuation is achieved through establishing homotopies between some simple models, for which solutions are easy to obtain, and the full models. We will investigate how sensitivities of the trajectory to the homotopy parameters can be used to systematically and effectively automate the homotopy continuation, improving the robustness of the algorithms. We will also investigate adaptive fidelity models and alternative interpolation-based gravity models, as well as a number of techniques developed by the investigators to speed up the dynamics evaluations. Almost every legacy trajectory design software code used by NASA (e.g., Malto, Copernicus, EMTG, GMAT, etc.) is faced by the dilemma that hard problems simply don�t converge without a good initial guess. The gradient-based localized optimization methods used in these software tools require initial guesses that are close to the final solutions. The common practice of using solutions based on simplified models as initial guesses often do not yield convergence if the full problem is solved directly, especially in highly perturbed dynamical environments. In the proposed method, instead of taking a full step from the simple model to the full model, we systematically take smaller steps, and judiciously introduce incremental perturbations. This method is amenable to automation and yields robustness in convergence. The proposed research will greatly benefit NASA and the space trajectory design community in designing high-fidelity trajectories with true ephemerides and force fields.

The proposed robust trajectory design techniques and tool are significant for NASA in supporting its committed ambition of robotic and human space flight. Expected NASA applications are in the area of interplanetary mission design, missions to asteroids and comets, planetary moon tours, atmospheric entry, aerobraking, launch vehicle trajectory optimization, etc., all of which can benefit from the improved robustness in convergence as a result of the continuation methods. Existing NASA software packages such as the open-source GMAT (General Mission Analysis Tool), Copernicus, Malto, etc., can all be enhanced through wrappers or plugin implementing the proposed methods.

The proposed technology can find applications at other government agencies and commercial entities that deal with spacecraft trajectory design and launch vehicle analysis, such as the Air Force, Missile Defense Agency, Orbital Science Corporation, Boeing, SpaceX, etc. Potential applications can also be found in engineering and mathematical software market such as Analytical Graphics, Inc. and Mathworks, Inc. The benefit of the continuation methods goes beyond the spacecraft trajectory design because it can also improve the robustness of numerical optimal control solvers, which are used in a great deal of industries such as the automobile manufacturing, oil production, chemical plants, etc.

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