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Approximate analytic solution for variables describing three dimensional solar powered heliocentric low thrust trajectory in vicinity of ecliptic plane
Methodology employed in development of a computer program designed to analyze optimal low-thrust trajectories is described, and application of the program to a Solar Electric Propulsion Stage (SEPS) geosynchronous mission is discussed. To avoid the zero inclination and eccentricity singularities which plague many small-force perturbation techniques, a special set of state variables (equinoctial) is used. Adjoint equations are derived for the minimum time problem and are also free from the singularities. Solutions to the state and adjoint equations are obtained by both orbit averaging and precision numerical integration; an evaluation of these approaches is made.
Trajectory energy requirements for low-thrust flights throughout solar system using nuclear- electric propulsion
Low thrust satellite transfer between Earth and Moon orbits based on two-body trajectories and systematic synthesizing process
An application of the new optimization algorithm called Static/Dynamic Control (SDC) to the design of low-thrust interplanetary trajectories is presented.
Low thrust satellite transfer between Earth and Moon orbits based on two-body trajectories and systematic synthesizing process
Recent advances in thruster and solar array technology have resulted in the possibility of performing many high energy space missions previously considered infeasible. This capability was demonstrated by an extensive study last year of a comet Halley rendezvous mission. In order to perform this extremely high energy mission, several advanced concepts in electric propulsion technology were investigated; notably the use of very high power, lightweight solar arrays which directly powered the beam supply of the electric propulsion thrusters, and the use of solar concentrators on the arrays together with conventional thrusters and power processors. These technology advances have directly impacted the modeling of the solar arrays and thrusters in the programs used in generating low-thrust trajectories. The intent of this paper is to discuss the modeling of the solar arrays and thrusters as employed in the trajectory programs presently being used in low-thrust mission studies at JPL.
CISLUNAR is a stand-alone computer program designed to generate the trajectory of a low-thrust spacecraft travelling in Earth-Moon space. The program allows the creation of functional trajectories dependent on the supplied spacecraft characteristics. The trajectory generation is a user interactive process. The original intent was for the program user to modify the necessary control values until a staisfactory trajectory has been created.
Trajectory optimization methods using MBH have become well developed during the past decade. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing RVs from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by Englander significantly improves MBH performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness, where efficiency is finding better solutions in less time, and robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive RWs originally developed in the field of statistical physics.
Low thrust interplanetary swingby trajectories optimization, considering thrusting and coasting within sphere of influence
Trajectory optimization methods using monotonic basin hopping (MBH) have become well developed during the past decade [1, 2, 3, 4, 5, 6]. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing random variable (RV)s from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by J. Englander [3, 6]) significantly improves monotonic basin hopping (MBH) performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness. Efficiency is finding better solutions in less time. Robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive random walks (RWs) originally developed in the field of statistical physics.
The upcoming Lunar IceCube (LIC) mission will deliver a 6U CubeSat to a low lunar orbit via a ride-share opportunity during NASAs Artemis 1 mission. This presents a challenging trajectory design scenario, as the vast change in energy required to transfer from the initial deployment state to the destination orbit is compounded by the limitations of the LICs low-thrust engine. This investigation addresses these challenges by developing a trajectory design framework that utilizes dynamical structures available in the Bicircular Restricted Four-Body Problem (BCR4BP) along with a robust direct collocation algorithm. Maps are created that expedite the selection of invariant manifold paths from a periodic staging orbit in the BCR4BP that offer favorable connections between the LIC transfer phases. Initial guesses assembled from these maps are passed to a direct collocation algorithm that corrects them in the BCR4BP while including the variable low-thrust acceleration of the spacecraft engine. Results indicate that the ordered motion provided by the BCR4BP and the robustness of direct collocation combine to offer an efficient and adaptable framework for designing a baseline trajectory for the LIC mission.
The upcoming Lunar IceCube (LIC) mission will deliver a 6U CubeSat to a low lunar orbit via a ride-share opportunity during NASAs Artemis 1 mission. This presents a challenging trajectory design scenario, as the vast change in energy required to transfer from the initial deployment state to the destination orbit is compounded by the limitations of the LICs low-thrust engine. This investigation addresses these challenges by developing a trajectory design framework that utilizes dynamical structures available in the Bicircular Restricted Four-Body Problem (BCR4BP) along with a robust direct collocation algorithm. Maps are created that expedite the selection of invariant manifold paths from a periodic staging orbit in the BCR4BP that offer favorable connections between the LIC transfer phases. Initial guesses assembled from these maps are passed to a direct collocation algorithm that corrects them in the BCR4BP while including the variable low-thrust acceleration of the spacecraft engine. Results indicate that the ordered motion provided by the BCR4BP and the robustness of direct collocation combine to offer an efficient and adaptable framework for designing a baseline trajectory for the LIC mission.
The best way to understand a mission design trade space is by creating a good map of all the possibilities, and by knowing how to read it. Bacon plots, which are low-thrust analogs to porkchop plots, give insight into key parameters and sensitivities of possible transfers to Mars (or other destinations). They are mission and parameter specific, and can be created to represent single or multiple legs. This paper outlines the creation process and lessons learned in interpreting the results. An example is given on how bacon plots have been employed for complex mission-level optimization.
Planning the logistics of multiple launches to support a Mars surface expedition requires good trajectory design tools. Traditional ballistic transfers are well characterized by performance maps known as pork-chop plots. However, the transportation of cargo can benefit from the use of low-thrust solar electric propulsion, both in terms of mass delivered and the flexibility of flight durations and dates. This paper describes the design and use of bacon plots (the low-thrust analog to pork-chop plots) and their application to the architectural design of a human Mars surface expedition.
Low thrust propulsion interplanetary trajectory flight optimization - guidance systems
The modifications and improvements made to the HILTOP electric propulsion trajectory optimization computer program up through the end of 1974 is described. New program features include the simulation of power degradation, housekeeping power, launch asymptote declination optimization, and powered and unpowered ballistic multiple swingby missions with an optional deep space burn. The report contains the new analysis describing these features, a complete description of program input quantities, and sample cases of computer output illustrating the new program capabilities.
Modifications and improvements are described that were made to the HILTOP electric propulsion trajectory optimization computer program during calendar years 1973 and 1974. New program features include the simulation of power degradation, housekeeping power, launch asymptote declination optimization, and powered and unpowered ballistic multiple swingby missions with an optional deep space burn.