{"project":{"acronym":"","projectId":88588,"title":"A Numerical Method to Generate Reference Trajectories for Optimization Methods to Support Low-Thrust Mission Design","primaryTaxonomyNodes":[{"taxonomyNodeId":10956,"taxonomyRootId":8816,"parentNodeId":10955,"level":3,"code":"TX15.2.1","title":"Trajectory Design and Analysis","definition":"Trajectory design and analysis technologies support the design, optimization, analysis, and reconstruction of space vehicle and air vehicle flight trajectories. ","exampleTechnologies":"1. Trajectory Design and Optimization. Includes design and optimization of space vehicle and air vehicle trajectories. Includes definition of the envelope of acceptable trajectories given the capabilities of the vehicle, and determination of the optimal trajectory. For space vehicles, includes ascent; orbital targeting, orbital maintenance, and on-orbit rendezvous; interplanetary trajectories; theoretical astrodynamics; low-thrust design and optimization; planetary moon tour design; three-body orbit modeling and design; and entry through landing. For air vehicles, includes takeoff, mission execution or cruise, and approach/landing. 2. Trajectory Reconstruction. Technologies that enhance post-flight and on-board procedures that use real-time, telemetered or recorded flight data to determine as-flown estimates of vehicle performance (propulsion, aerodynamics, GN&C, etc.) and encountered environment characteristics (atmosphere, gravity, etc.). 3. End-to-end mission design and optimization of space vehicles and air vehicles. Involves integrating trajectory solutions from the various phases of flight to optimize the overall mission in terms of duration, mass, propellant, flexibilities, and requirements for associated subsystems, such as lighting, communications, power, propulsion, etc. Helps evaluate interactions and trades between other disciplines (aero, propulsion, structures, GN&C, etc.) and identifies/establishes subsystem performance and requirements.","hasChildren":false,"hasInteriorContent":true}],"startTrl":2,"currentTrl":3,"endTrl":3,"benefits":"The improved initial guesses generated by this method will produce superior locally optimal trajectories, which could entail fuel or time savings for spacecraft. Therefore, mission design strategies produced by this study could yield innovative trajectories that would reduce mission cost and increase scientific return. Furthermore, this research will yield methods for understanding the stability of low-thrust enabled periodic orbits. The potential of low-thrust spacecraft has only begun to be realized. Investment in astrodynamics research will expand the space attainable by these spacecraft, opening up new regions of space for science and exploration by NASA and its partners.","description":"The recent success of missions employing low thrust propulsion systems has demonstrated the promise this technology holds for a wide array of future applications, from asteroid tours, to missions to Mars. Low-thrust spacecraft motion is governed by a sensitive system of nonlinear differential equations, and this makes finding desirable trajectories challenging. Current low-thrust trajectory design methods rely heavily on optimization techniques to obtain feasible trajectories. These techniques require an initial guess for the spacecraft trajectory and this guess heavily impacts the final optimized trajectory. Many locally optimal trajectories are available and a precise initial guess can lead to the most desirable locally, or even globally, optimal trajectory. Despite the importance of a good initial guess in low-thrust trajectory design, relatively few comprehensive methods exist for creating these guesses. A method for generating a wide array of initial guesses and selecting one that best fits a set of preferred criteria is desirable because it would expand the range of possible low-thrust trajectories. One tool that shows promise for developing initial guesses for low-thrust trajectories is the theory of invariant manifolds. In astrodynamics, invariant manifolds can be thought of as structures that show the natural flow of gravitational forces about a periodic orbit. The manifolds of low-thrust periodic orbits are likely helpful for producing a range of detailed initial guesses for low-thrust trajectories. The proposed investigation will study how the manifolds of low-thrust periodic orbits can be used to produce improved initial guesses for low-thrust spacecraft trajectories. The study will begin by computing low-thrust periodic orbits and obtaining the manifolds of these orbits. Following this, a variety of visualization methods will be employed to understand manifold behavior, these include Poincare maps and three-dimensional plots. The intuition gained from these visualizations will be used to develop a scheme for categorizing manifold behavior. Understanding gained from visualization and categorization will be applied to low-thrust mission design. A number of realistic mission scenarios will be tested, including polesitting orbits and transfers from the Earth-Moon system to other bodies. It is important to note that a spacecraft can leverage the manifolds of a low-thrust periodic orbit without entering the orbit. Therefore, a low-thrust periodic orbit does not need to be the final destination of a spacecraft in order for this mission design method to be of use. The proposed mission design method will first identify low-thrust periodic orbits whose manifolds provide access to the desired regions of space. Next, the method will calculate the manifolds which provide the preferred trajectory characteristics at the lowest cost. The result of this determination will be used as an initial guess in an optimization technique. Finally, the resulting solution will be tested in a higher fidelity model. This entire process will be made as autonomous as possible to allow for ease of use by mission designers. The improved initial guesses generated by this method will produce superior locally optimal trajectories, which could entail fuel or time savings for spacecraft. Therefore, mission design strategies produced by this study could yield innovative trajectories that would reduce mission cost and increase scientific return. Furthermore, this research will yield methods for understanding the stability of low-thrust enabled periodic orbits. The potential of low-thrust spacecraft has only begun to be realized. Investment in astrodynamics research will expand the space attainable by these spacecraft, opening up new regions of space for science and exploration by NASA and its partners.","startYear":2016,"startMonth":8,"endYear":2020,"endMonth":8,"statusDescription":"Completed","principalInvestigators":[{"contactId":262536,"canUserEdit":false,"firstName":"Kathleen","lastName":"Howell","fullName":"Kathleen C Howell","fullNameInverted":"Howell, Kathleen C","middleInitial":"C","primaryEmail":"howell@purdue.edu","publicEmail":false,"nacontact":false}],"programDirectors":[{"contactId":84634,"canUserEdit":false,"firstName":"Claudia","lastName":"Meyer","fullName":"Claudia M Meyer","fullNameInverted":"Meyer, Claudia M","middleInitial":"M","primaryEmail":"claudia.m.meyer@nasa.gov","publicEmail":true,"nacontact":false}],"programExecutives":[{"contactId":84634,"canUserEdit":false,"firstName":"Claudia","lastName":"Meyer","fullName":"Claudia M Meyer","fullNameInverted":"Meyer, Claudia M","middleInitial":"M","primaryEmail":"claudia.m.meyer@nasa.gov","publicEmail":true,"nacontact":false}],"programManagers":[{"contactId":183514,"canUserEdit":false,"firstName":"Hung","lastName":"Nguyen","fullName":"Hung D Nguyen","fullNameInverted":"Nguyen, Hung D","middleInitial":"D","primaryEmail":"hung.d.nguyen@nasa.gov","publicEmail":true,"nacontact":false}],"coInvestigators":[{"contactId":403592,"canUserEdit":false,"firstName":"Robert","lastName":"Pritchett","fullName":"Robert E Pritchett","fullNameInverted":"Pritchett, Robert E","middleInitial":"E","primaryEmail":"robert.e.pritchett@nasa.gov","publicEmail":true,"nacontact":false}],"website":"https://www.nasa.gov/strg#.VQb6T0jJzyE","libraryItems":[],"transitions":[{"transitionId":75910,"projectId":88588,"transitionDate":"2020-08-01","path":"Closed Out","details":"In recent decades the revolutionary possibilities of low-thrust electric propulsion have been demonstrated by the success of missions such as Dawn and Hayabusa 1 and 2. The efficiency of low-thrust engines reduces the propellant mass required to achieve mission objectives and this benefit is frequently worth the additional time of flight incurred, particularly for robotic spacecraft. However, low-thrust trajectory design poses a challenging optimal control problem. At each instant in time, spacecraft control parameters that minimize an objective, typically propellant consumption or time of flight, must be determined. The characteristics of low-thrust optimal solutions are often unintuitive, making it difficult to develop an a priori estimate for the state and control history of a spacecraft that can be used to initialize an optimization algorithm. This investigation seeks to develop a low-thrust trajectory design framework to address this challenge by combining the existing techniques of orbit chaining and direct collocation. Together, these two methods offer a novel approach for low-thrust trajectory design that is intuitive, flexible, and robust. This investigation presents a framework for the construction of orbit chains and the convergence of these initial guesses to optimal low-thrust solutions via direct collocation. The general procedure is first demonstrated with simple trajectory design problems which show how dynamical structures, such as periodic orbits and invariant manifolds, are employed to assemble orbits chains. Following this, two practical mission design problems demonstrate the applicability of this framework to real world scenarios. An orbit chain and direct collocation approach is utilized to develop low-thrust transfers for the planned Gateway spacecraft between a variety of lunar and libration point orbits (LPOs). Additionally, the proposed framework is applied to create a systematic method for the construction of transfers for the Lunar IceCube spacecraft from deployment to insertion upon its destination orbit near the Moon. Three and four-body dynamical models are leveraged for preliminary trajectory design in the first and second mission design applications, respectively, before transfers are transitioned to an ephemeris model for validation. Together, these realistic sample applications, along with the early examples, demonstrate that orbit chaining and direct collocation constitute an intuitive, flexible, and robust framework for low-thrust trajectory design. ","infoText":"Closed out","infoTextExtra":"","dateText":"August 2020"}],"responsibleMd":{"acronym":"STMD","canUserEdit":false,"city":"","external":false,"linkCount":0,"organizationId":4875,"organizationName":"Space Technology Mission Directorate","organizationType":"NASA_Mission_Directorate","naorganization":false,"organizationTypePretty":"NASA Mission Directorate"},"program":{"acronym":"STRG","active":true,"description":"
\tThe Space Technology Research Grants Program will accelerate the development of "push" technologies to support the future space science and exploration needs of NASA, other government agencies and the commercial space sector. Innovative efforts with high risk and high payoff will be encouraged. The program is composed of two competitively awarded components.
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