Interplanetary Trajectory Optimization ISP - Lecture 2 Local and Global Optimization
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Significant payloads in Mercury orbit can be achieved through use of high-thrust, chemical propulsion systems on ballistic trajectories. Interplanetary trajectory characteristics are presented, for Venus swingbys to Mercury, were multiple revolutions about the sun are allowed on each leg to provide low energy mission in 1977, 1980, 1985 and 1988. Guidance and navigation results are shown for each opportunity. Additionally, the use of midcourse maneuvers and multiple Venus swingbys are explored as means of further reducing the energy requirements.
Low thrust interplanetary swingby trajectories optimization, considering thrusting and coasting within sphere of influence
Optimum low acceleration trajectories for interplanetary transfer orbits
Designing interplanetary missions is an iterative process, with a tight coupling between mission analysis and vehicle design. The ability to simultaneously process both analyses early on can provide significant benefits in both the concept formulation and in overall mission feasibility. To implement such a simultaneous analysis process, there is a need to model interplanetary trajectories rapidly while maintaining an acceptable level of fidelity. Many simple patched conics tools make too many assumptions to satisfactorily address all relevant constraints and objectives, while full-fidelity trajectory design tools often require more time and expertise than is available in early conceptual studies. Hence, some form of middle-ground modeling tool would provide value. This paper introduces the development of such a tool using Python. This tool, Keplerian Analysis for Versatile Evaluation of Arbitrary Trajectories (KAVEAT), implements a patched conics method that enforces continuity of state (time, mass, position, velocity) through all transitions between various spheres of influence on the trajectory. The trajectory is constructed in an object-oriented manner, dynamically assembling unique maneuvers such as departure burns, heliocentric transfers (ballistic or with electric propulsion), and planetary flybys (powered or unpowered). Each maneuver has its own specific set of basic inputs needed to define it. The tool then takes these defined maneuvers, strings them together creating all the interdependencies required, and solves for the ideal trajectory using a gradient-based optimizer.
Direct-ascent and parking-orbit trajectories for lunar and interplanetary space flight for both powered-flight and coasting phases
Computer program incorporates new isolation procedure to determine interplanetary trajectories which utilize a maximum of three flybys. Program also computes singe planet flybys and direct transfer trajectories. The three principle systems employed in MIST-1 use as their fundamental plane the mean plane of the earth's orbit around the sun.
The bounded-impulse approach to low-thrust interplanetary trajectory optimization is widely used. In an effort to efficiently implement this approach using NASA’s OpenMDAO optimization software, the authors have implemented implicit formulations of the forward shooting/backwards-shooting methods commonly used in bounded-impulse models. These implicit approaches allow for vectorization of the underlying calculations which can significantly reduce runtime in interpreted languages. An implicit approach may be either converged by using an underlying nonlinear solver to converge the state propagation, or as a constraint in an optimizer-driven multiple-shooting approach. Significant computational efficiency gains are realized through the utilization of the modular approach to unified derivatives. Further computational efficiency is achieved by capitalizing on the sparsity of the constraint Jacobian matrix. This work demonstrates that a vectorized multiple-shooting approach for propagating a state-time history is superior in terms of computational efficiency as the number of segments in the state-propagation is increased.
Iteration method using offset-aim technique to determine exact initial conditions for interplanetary ballistic trajectories
Heliocentric transfer orbit and launch hyperbolic excess velocity analyses are included in a study of interplanetary ballistic trajectories
A direct optimization method intended to be used primarily for preliminary design of low-thrust interplanetary trajectories, including those with multiple gravity assists, is presented.
Introduction: The current decadal survey published by the National Academies of Sciences has informed National Aeronautics and Space Administration (NASA) to prioritize the study of the Ice Giants, especially Uranus. To gather the required data that addresses the science questions raised in this survey, a mission to Uranus with an orbiter and atmospheric probe must be designed. The Uranus Orbiter and Probe (UOP) study, which the survey identified as the flagship mission of this decade, proposes a 2031 launch to take advantage of a Jupiter fly-by and utilizes a fully propulsive orbit insertion design with an Earth-to-Uranus transit times ranging from 13 to 15 years. This fully propulsive orbit insertion at Uranus will be very fuel expensive (wet mass percentages of around 60-70\%) thereby leaving less mass for the scientific payload and additional planetary probes. In addition, scientists are more interested in visiting Uranus before 2049, when the Spring Equinox will occur, as it allows studying Uranus seasons not seen during Voyager 2's flyby in 1987. A NASA Flagship-Class mission would require at least 10 years of lead time prior to launch thereby making the 2031 launch to take advantage of the Jupiter fly-by extremely challenging. The consequence of missing the Jupiter fly-by and launching in the late 2030s is the challenge of a fully-propulsive mission like UOP to have a feasible alternative interplanetary trajectory that reaches Uranus before 2050. As an alternative, to address the shortcomings of the fully propulsive mission, one can design a mission to Uranus using aerocapture. What is aerocapture: Aerocapture is an atmospheric maneuver that uses aerodynamic forces generated by flight within a planetary atmosphere to decelerate and achieve orbit insertion. Using aerocapture allows one to provide the change in velocity (Delta V) needed to slow down from the approach hyperbolic trajectory to achieve the desired captured orbit around the target planet using aerodynamic forces of the vehicle (lift and drag). Using aerodynamic forces instead of fully-propulsive maneuvers results in significant savings in the fuel. Furthermore, aerocapture can also allow one to consider interplanetary trajectories with higher approach hyperbolic velocities, thus reducing the mission transit times. Aerocapture as an enabling technology: To use aerocapture as an enabling technology for the Uranus exploration mission, one would require an integrated system-level design, including a Thermal Protection System (TPS), hardware needed for aerodynamic modulation, and autonomous Guidance, Navigation, and Control (GNC) systems. Aerocapture has yet to be demonstrated, despite considering it for several past missions. Recent advancements in TPS and GNC capabilities show the potential for using rigid, heritage entry vehicle configurations already flown at other planetary bodies for Uranus aerocapture. Aerocapture can be a robust technology that can deliver spacecraft to Uranus science orbits while substantially increasing on-orbit payload mass (more than 40\%) that can enable robust atmospheric entry probes. Additionally, the aerocapture maneuver would reduce the interplanetary transit time by 2–5 years (15-30\%) relative to fully-propulsive orbit insertion. Recent work has shown that one can conduct a flagship-class mission in a shorter period than fully-propulsive missions if using aerocapture. What does aerocapture bring in for a Uranus Mission: Using aerocapture for a Uranus orbiter and atmospheric probe mission can provide one with considerable propellant savings. Spacecraft in interplanetary trajectories to Uranus typically need an Delta V in orders of kilometers per second to insert into science orbit. One would require thousands of kilograms of fuel to achieve such a Delta V using a traditional fully propulsive maneuver, leaving less mass for payload during the mission launch. Aerocapture can reduce the propulsion needs by dissipating energy in the sizable atmosphere of Uranus without a significant mass increase due to the need for an aeroshell. One can use the mass savings achieved using the aerocapture to reduce the launch vehicle requirements. In addition, one can also have additional science instruments on the orbiter or create a robust instrumentation suite on an atmospheric probe that can significantly increase the science outcome of the Uranus exploration mission. Furthermore, since aerocapture performance is relatively insensitive to increases in hyperbolic excess velocity, one can design the interplanetary trajectory to arrive at Uranus faster, reducing the interplanetary transit time and operations cost. All these savings, achieved using aerocapture, could help fit a larger class mission, such as the Uranus mission within a smaller capital, e.g., a Flagship-class orbiter mission in a New Frontiers class capital. Summary: This talk will provide an overview of how aerocapture can enable the Uranus exploration mission. Specifically, this talk will discuss the latest advancements made in the Uranus aerocapture study, such as investigating interplanetary trajectories with higher hyperbolic approach velocities and their implications on the aero heating and the TPS design, incorporating FNPAG (an advanced numerical-predictor guidance) and comparison of multiple navigation approaches. In addition, this talk will focus on mechanical design that can house more than one atmospheric probe and the six degrees of freedom simulation of aerocapture at Uranus. Findings from a recent NASA Space Technology Mission Directorate (STMD)-funded activity studying the aerocapture as an enabling technology for a Uranus orbiter will be presented. Using the science payload recommended by the Decadal Survey for Uranus exploration, this work shows many improvements over the baseline fully-propulsive mission. These improvements include a shorter cruise phase, flexibility in launch opportunities late into the 2030s while reaching Uranus before the 2050 equinox for the desired science opportunities, and lower propellant mass needs. This talk will highlight how aerocapture can be utilized for Uranus science orbit insertion using a lower-risk, heritage entry vehicle configuration used extensively as a Mars entry, descent, and landing vehicle. Furthermore, this talk will explore how the demonstration of aerocapture at Earth can benefit the aerocapture-enabled Uranus mission.
Interplanetary missions were analyzed that utilize the gravity-assist orbital transfer technique to increase mission capabilities. This swingby maneuver provides a nonpropulsive change in the spacecraft's heliocentric energy which can reduce the amount of propellant needed to complete an interplanetary mission. For certain planetary orientations, incorporating a propulsive manuever at the periapsis of the swingby trajectory decreases the mission's propellant requirement. This decrease results in a reduced initial vehicle mass in low-earth orbit. This study analyzed the feasibility of using a three-dimensional powered swingby to reduce the initial vehicle size for an excursion class mission during the 2010-2025 time frame.
Segmented two-body low thrust interplanetary swingby trajectory and performance optimization program
Outline of specific solutions in the areas of attitude control, interplanetary trajectory parameters, and orbital configurations of major planetary spacecraft. It is shown that inertia wheel supplementation to a three-axis, stabilized attitude control system will substantially reduce propellant weight and attitude jet firings, especially when considering three-year orbital lifetimes as well as interplanetary trip times of several years. Eight interplanetary trajectory parameters including the earth injection energy and the declination of the launch asymptote are shown for a 1980 earth launch mission to Jupiter. The effects of the interplanetary trajectory parameters on the deboost velocities and resulting orbits about Jupiter are summarized. Orbital mode and science interfaces are defined, and a celestial mechanics experiment independent of earth tracking is briefly outlined.
Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical boundary value solution applicable to a broad class of trajectory problems. In addition, the earlier first-order solutions have been extended to second-order to determine if improved accuracy is possible. Comparisons between the asymptotic solution and numerical integration for several lunar and interplanetary trajectories show that the asymptotic solution is generally quite accurate. Also, since no iterations are required, a solution to the boundary value problem is obtained in a fraction of the time required for numerically integrated solutions.
The optimum-thrust equations for both variable and constant thrust are presented. These thrust programs are used to generate rendezvous trajectories from the Earth to Mars for various flight times and launch dates during the years 1968-71. The manner in which the propulsion requirements vary with flight time and launch date are considered, and a comparison of vehicle performance using the variable- and constant-thrust programs is presented. The optimization of the pro- pulsion system parameters is discussed, and the existence of optimum launch dates is interpreted in terms of certain transversality conditions derivable from the calculus of variations. A brief comparison of the advanced propulsion vehicle and the ballistic vehicle propulsion requirements is made for Earth-Mars rendezvous trajectories. An appendix considering the analytical basis for this work is included.