Origins, Worlds, and Life: Planetary Science and Astrobiology in the Next Decade identified a Uranus Orbiter and Probe as the highest-priority strategic mission for the decade 2023-2032, as it enables broad cross-disciplinary science in the largely unexplored Uranian system. The mission architecture evaluated by the Decadal Survey was a singular proof of concept demonstrating that a moderately instrumented mission could deliver Decadal-priority science with a reduced cost and risk posture by leveraging existing technologies to the maximum extent possible. With revised assumptions since the Decadal, we have explored a large trade space including launch vehicles, propulsion options, cruise trajectories, available power sources, viable concept of operations, and science data return for later launch dates without a Jupiter gravity assist. The most repeatable trajectory solutions employ either a commercially derived solar electric propulsion (SEP) transfer stage or the availability of a more capable launch vehicle under development, such as the SpaceX Starship. Orbit insertion has been moved farther from Uranus to acknowledge the remaining uncertainty in Uranian ring structure. A streamlined, SEP-adaptable, orbiter design was developed using two Next Gen Radioisotope Thermoelectric Generators, and the probe design was matured, reducing the entry gravitational acceleration, and assuming the largest Decadal-recommended payload to provide margin for future instrument selections. With this updated design, we also constructed a detailed concept of operations for three representative science cases, returning 13-15 Gbit of science data and spacecraft telemetry per similar to 34 day orbit.

The Lucy mission is NASA’s 13th Discovery-class mission and the first mission to the Trojan asteroids. The spacecraft conducts flybys of 8 Trojan asteroids over the course of 12 years. A series of 3 Earth Gravity Assists are used to increase the aphelion of the spacecraft’s orbit and to target the final Trojan asteroid flyby. Over the course of 2 years the spacecraft conducts 4 flybys in the L4 swarm to explore 6 Trojan asteroids, which includes two small satellites. Near the end of the mission, Lucy flies past the near-equal size binary, Patroclus-Menoetius, in the L5 swarm. The concept of operations for the Trojan flybys invokes a standard timeline for spacecraft operations to allow a science sequence that is tailored to each Trojan asteroid. The concept of operations enables efficiency of observations and resiliency in the observing sequence to robustly meet the Lucy science requirements.

The global optimization of the moon tour design problem is addressed in this paper. These missions are usually designed using graphical methods or grid search, which require simplifying assumptions, and a skillful mission designer. The grid search methods are computationally intense. Trajectories with a high number of flybys and multiple resonance flybys are usually hard to optimize, especially with small-size/short-period flyby moons. This work proposes a new mutation operator that is incorporated with the Monotonic Basin Hopping in the Evolutionary Mission Trajectory Generator tool; this mutation operator increases the exploration of resonance flybys to improve convergence in moon tour design optimization problems. In this work, the Hidden Genes Genetic Algorithm is used to optimize the undetermined number of moon flybys. A Europa Clipper-like mission is optimized assuming two-body dynamics, and a validation study for the proposed resonance mutation operator is presented. The results include an optimized baseline solution and a new solution with a different sequence of flybys with a different sequence of flybys for the Europa Clipper-like mission, in addition to an optimized moon tour in the Saturnian system.

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In multigravity-assist trajectory optimization, the size of the design space is a variable itself. The objective functions are usually replete with local minima. This paper presents a multi-objective hidden genes genetic algorithm (MOHGGA) for trajectory optimization. The length of the chromosome is selected large enough to enable modeling a given maximum number of swing-bys and maximum number of deep space maneuvers (DSMs). Binary tags are appended to those genes that control the swing-bys and DSMs. These binary tags are used to remove/add swing-bys and DSMs to a trajectory solution, and hence enable optimization among solutions of different sizes (different topologies). The MOHGGA generates Pareto fronts that have solutions of, in general, different number of swing-bys, swing-by planets, launch and arrival dates, and number of DSMs. Two objectives are considered in this paper: the total mission cost and total time of flight. An elitist nondominated sorting genetic algorithm is used. Local optimization is conducted on one objective function, holding the other objective function constant, to further improve the resulting Pareto front. Numerical results of four benchmark test cases for missions to Mars, Jupiter, Saturn, and Mercury are presented. The results demonstrate the capability of MOHGGA in searching for optimal trajectory topologies while optimizing two objectives.

Small spacecraft are likely to be launched as part of a rideshare mission rather than on a dedicated launch. These spacecraft typically use low-thrust propulsion systems as they have lower fuel mass requirements. However, without a dedicated launch, the lower thrust can make it difficult to reach interplanetary targets. Further mission design difficulties arise as the optimizers used to search for such trajectories often require a good initial guess, which can be difficult to find. This work patches together a perturbed Sims-Flanagan transcription in three different regimes, each with a different central body, to performa preliminary search for trajectories from a lunar rideshare to a weak capture around Venuswith little input required fromthemission designer. Example trajectories of such amission are presented. The ability of this mission architecture to arrive as close to Venus's upper atmosphere as possible is explored.

View Video Presentation: https://doi.org/10.2514/6.2022-2469.vid After jettisoning its Sample Return Capsule (SRC) containing regolith samples from the near-Earth asteroid (101955) Bennu to Earth in September 2023, the Origins, Spectral Interpretation, Resource Identification, and Security–Regolith Explorer (OSIRIS-REx) spacecraft will perform a divert maneuver and safely fly by Earth at an altitude of 250 km. SRC return and the divert maneuver officially mark the completion of the spacecraft's primary mission; however, it will continue on in heliocentric orbit with a nearly fully-functional instrument suite and enough propellant for nearly 600 m/s Delta-V. The post-Earth flyby trajectory fortuitously enables an exciting extended mission opportunity: rendezvous with the near-Earth asteroid (99942) Apophis immediately following its historic Earth close approach in April 2029. In this paper, we detail the discovery, optimization, and analysis of the Apophis rendezvous trajectory for an extended OSIRIS-REx mission. We also present the technical approach for an alternate target search and corresponding results, assessing the alternate trajectories compared to the baseline Apophis rendezvous from a trajectory design standpoint.

This paper introduces a new technique for directly controlling the missed thrust recovery margin (MTRM) of a low-thrust spacecraft trajectory. MTRM is defined here as the longest amount of time a spacecraft may coast away from a nominal trajectory while still being able to reach a terminal manifold once thruster operations are resumed. The "virtual swarm" optimization technique developed here simultaneously optimizes the nominal spacecraft trajectory along with many recovery trajectories. The objective can be to maximize the MTRM of the nominal trajectory at its weakest point or to constrain the worst-case MTRM to be at or above a desired level while optimizing a different value (e.g., mass, time of flight). The technique is demonstrated for a direct Earth-Mars transfer and for a gravity assist trajectory to the asteroid Psyche. Further, a method for finding the Pareto front of MTRM, arrival mass, and arrival date is presented to address the related multi-objective optimization problem.

Deep-space-distributed spacecraft missions continue to gain relevance as real-world missions such as the Laser Interferometer Space Antenna, Mars Sample Return, and others are conceived, designed, and flown. These classes of mission designs continue to challenge state-of-the-art trajectory optimization tools, often requiring significant changes to software and even new problem transcriptions entirely, in order to solve for optimal solutions. Trajectory optimization for multiple-vehicle missions poses all the challenges of the optimization of single-vehicle missions, but with added complexity of increased combinatorial scope due to multiple spacecraft, interspacecraft coordination constraints, and coordinated science objectives, motivating the need for new technical capabilities. The goal of this paper is to apply a multi-objective, multi-agent hybrid optimal control problem transcription, utilizing several new techniques, to optimize a very-long-baseline interferometry mission design. We develop and apply several new techniques in this capability, including a HashMap archive utility to prevent resolving missions, and a null gene transcription to vary both fleet size, and observation multiplicity. Applying these techniques enables efficient exploration the multi-objective nondominated front of a multivehicle design space where the number of spacecraft varies. The HashMap archive utility proves an essential component of this capability as duplicate candidate missions are discovered on average 17% of the time, and it yields an order of magnitude quicker lookup time compared with a text file analog. Within the resulting nondominated front of solution missions, many interesting solutions appear, including one mission with a fleet of 7 spacecraft that images 16 radio sources.

Several formulations are possible for the optimization of N-impulse two-body orbit transfers. One formulation that assumes the first N − 1 impulses are design variables, and implements Lambert’s algorithm in the final leg is considered here. This paper presents a derivation for the analytic expressions of the gradients needed to optimize a transfer using this formulation. The derivations of the analytic gradients, verification tests using complex-step differentiation, as well as numerical case studies for three-impulse orbit transfers are presented. The numerical case studies highlight a significant reduction in the computational cost, measured in terms of the number of objective function evaluations.

Accessing interplanetary space is challenging when using low thrust systems. Injecting spacecraft onto interplanetary trajectories is difficult with small launch vehicles, but it is possible to instead transfer to an interplanetary trajectory from a lunar flyby. Such cases are useful, for example, in rideshares between lunar and interplanetary missions. This work examines the problem of rideshare for small satellites onto lunar flyby trajectories, with transfers to an interplanetary trajectory. Low thrust interplanetary trajectories are examined starting from a rideshare mission on a lunar trajectory using delivery systems based on a modified Rocket Lab USA Electron vehicle and Photon stage.

Distributed Spacecraft Missions present challenges for current trajectory optimization capabilities. When tasked with the global optimization of interplanetary Multi-Vehicle Mission (MVM) trajectories specifically, state-of-the-art techniques are hindered by their need to treat the MVM as multiple decoupled trajectory optimization subproblems. This shortfall blunts their ability to utilize inter-spacecraft coordination constraints and may lead to suboptimal solutions to the coupled MVM problem. Only a handful of platforms capable of fully-automated multi-objective interplanetary global trajectory optimization exist for single -vehicle missions (SVMs), but none can perform this task for interplanetary MVMs. We present a fully-automated technique that frames interplanetary MVMs as Multi-Objective, Multi-Agent, Hybrid Optimal Control Problems (MOMA HOCP). This framework is introduced with three novel coordination constraints to explore different coupled decision spaces. The technique is applied to explore the preliminary design of a dual-manifest mission to the Ice Giants: Uranus, and Neptune, which has been shown to be infeasible using only a single spacecraft anytime between 2020 and 2070.

This presentation describes active research and development in interplanetary and cislunar trajectory optimization and global search at NASA Goddard Space Flight Center. Two point and parallel direct shooting transcriptions are described, along with monotonic basin hopping and batch seed sharing. Applications to the Lucy mission are presented, as well as a variety of other interplanetary and cislunar examples.

Rendering a complex spacecraft trajectory in high fidelity can be an expensive endeavor, both computationally and from a human time/cost standpoint. However, in many cases, a low-fidelity trajectory that reasonably approximates a high-fidelity counterpart is much easier to obtain. Thus, it is important to have an efficient process for converting a trajectory from lower-fidelity model to high fidelity. We present a method for converting low-fidelity trajectories into high fidelity that relies on multiple shooting, nonlinear programming, and numerical integration. The procedure converts any zero-radius sphere-of-influence gravity-assist events to fully integrated flyby events. Several numerical examples are presented that showcase the flexibility of the high-fidelity rendering process across multiple mission types and flight regimes.

Lucy is NASA’s next Discovery-class mission and will explore the Trojan asteroids in the Sun-Jupiter L4 and L5 regions. This paper details the design of Lucy’s interplanetary trajectory using a two-point direct shooting transcription, nonlinear programming, and monotonic basin hopping. These techniques are implemented in the Evolutionary Mission Trajectory Generator (EMTG), a trajectory optimization tool developed at NASA Goddard Space Flight Center. We present applications to the baseline trajectory design, Monte Carlo analysis, and operations.

Rendering a complex spacecraft trajectory in high fidelity can be an expensive endeavor, both computationally and from a human time/cost standpoint. However, in many cases, a low-fidelity trajectory that reasonably approximates a high-fidelity counterpart is much easier to obtain. Thus, it is important to have an efficient process for converting a trajectory from lower-fidelity model to high fidelity. We present a method for converting low-fidelity trajectories into high fidelity that relies on multiple shooting, nonlinear programming, and numerical integration. The procedure converts any zero-radius sphere-of-influence gravity-assist events to fully integrated flyby events. Several numerical examples are presented that showcase the flexibility of the high-fidelity rendering process across multiple mission types and flight regimes.

Recent advances linking medium-fidelity trajectory optimization and high-fidelity trajectory propagation/maneuver design software with Monte Carlo maneuver analysis and parallel processing enabled realistic statistical delta-V estimation well before launch. Completing this high-confidence, refined statistical maneuver analysis early enabled release of excess delta-V margin for increased dry mass margin for the Lucy Jupiter Trojan flyby mission. By 3.3 years before launch, 16 of 34 TCMs had 1000 re-optimized trajectory design samples, yielding tens of m/s lower 99%-probability delta-V versus targeting maneuvers to one optimal trajectory. One year later, 1000 re-optimized samples of all deterministic maneuvers and subsequent flybys further lowered estimated delta-V.

Lucy, NASA’s next Discovery-class mission, will explore the diversity of the Jupiter Trojan asteroids. The Jupiter Trojans are thought to be remnants of the early solar system that were scattered inward when the gas giants migrated to their current positions as described in the Nice model. There are two stable subpopulations, or “swarms,” captured at the Sun-Jupiter L4 and L5 regions. These objects are the most accessible samples of what the outer solar system may have originally looked like. Lucy will launch in 2021 and will visit five Trojans, including one binary system. This paper discusses the target selection process, including a description of “alternate Lucys” that were ultimately passed over in favor of the final design. The mathematics of the trajectory optimization are also discussed.

Solar electric propulsion (SEP) is the dominant design option for employing low-thrust propulsion on a space mission. Spacecraft solar arrays power the SEP system but are subject to blackout periods during solar eclipse conditions. Discontinuity in power available to the spacecraft must be accounted for in trajectory optimization, but gradient-based methods require a differentiable power model. This work presents a power model that smooths the eclipse transition from total eclipse to total sunlight with a logistic function. Example trajectories are computed with differential dynamic programming, a second-order gradient-based method.