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Previously funded by NASAÌýSpace Technology Research FellowshipÌý(NSTRF) awarded to Dr. Thomas Smith

Robotic and crewedÌýspacecraft are more frequently operating in chaotic regimes where human analysts can struggle to solve constrained and combinatorial path-planning problems to design feasible spacecraft trajectories. This research focuses on extractingÌýmotion primitives in a multi-body system to support rapid trajectoryÌýdesign and design space exploration. Motion primitives areÌýa concept from robotics thatÌýsummarize a set ofÌýfundamental building blocks of motion or actionsÌýin a dynamical system; complex trajectories or actions can then be rapidly constructed using sequences of motion primitives. This concept has previously been successfully used in robotics, pedestrian motion analysis and prediction, and human and animal motion prediction. To apply this general idea to spacecraft trajectories, we use clustering for data-driven extraction of motion primitives that summarize the fundamental geometries of selected arcs. A library of these motion primitives is then used to construct a motion primitive graph, discretely summarizing segments of a continuous solution space. We then use graph search algorithms to generate a sequences of motion primitive that is refined and corrected to produce aÌýcomplex spacecraft trajectory. Due to the definition of motion primitives as geometrically distinct arcs, a set of distinct motion primitive sequences can rapidly produce an array of geometrically distinct trajectories across the design space. Our research in this project focused on developing a motion primitive approach to spacecraft trajectory design. As a proof of concept, weÌýdemonstrated this approach by designing spacecraft trajectoriesÌýbetween libration point and Moon-centered orbits in the Earth-Moon circular restricted three-body problem with impulsive maneuvers.

Relevant journal papers:

• Smith, T.R.; Bosanac, N,Ìý‘Motion Primitive Approach to Spacecraft Trajectory Design in a Multi-Body System,’ September 2023, Vol. 70, No. 34, The Journal of Astronautical Sciences, DOI:ÌýÌý[Open Access manuscript at link]
• Smith, T.R; Bosanac, N, 'Constructing Motion Primitive Sets to Summarize Periodic Orbit Families and Hyperbolic Invariant Manifolds in a Multi-Body Systems,' February 2022, Vol. 134, No. 7,ÌýCelestial Mechanics and Dynamical Astronomy, DOI:ÌýÌý[Accepted manuscript]

Dissertation:

• Smith, T.R., 'Using Motion Primitives to Rapidly Design Trajectories in Multi-Body Systems', Ph.D. Dissertation, University of Colorado Boulder, May 2023. [pdf]

Earlier conference papers:

• Smith, TR; Bosanac, N, ‘A Motion Primitive Approach to Trajectory Design in a Multi-Body System,’ AAS/AIAA Astrodynamics Specialist Conference, August 2022, Charlotte, NC. [pdf]
• Smith, T.R; Bosanac, N, ‘Using Motion Primitives to Design Libration Point Orbit Transfers in the Earth-Moon System,’ AAS/AIAA Astrodynamics Specialist Virtual Conference, August 2021.Ìý[pdf]
• Smith, T.; Bosanac, N, 'Motion Primitives Summarizing Periodic Orbits and Natural Transport Mechanisms in the Earth-Moon System,'Ìý 2020 AAS/AIAA Astrodynamics Specialist Virtual Conference, August 2020. [pdf]

Funded by NASA/Caltech Jet Propulsion Laboratory, work performed by Giuliana Miceli

The goal of this research is to design maneuver-enabled trajectories for primary and secondary spacecraft to explore the Uranian and Neptunian systems. These ice giant systems are high priority science targets that have not been visited by spacecraft since the Voyager flybys. However, trajectory design for spacecraft in these scenarios is challenging due to the high-energy of interplanetary arrival conditions, limited maneuverability, and complexity of the solution space. To address this challenge, we are applying and extending our motion primitive approach (see above description)Ìýto examine the trade space ofÌýconstrained trajectories that could enable scientific measurements in theseÌýice giant systems.

Relevant conference papers:

• Miceli, G.E.; Bosanac, N.; Stuart, J.R.; Alibay, F., ‘Motion Primitive Approach to Spacecraft Trajectory Design in the Neptune-Triton System,’ AIAA SciTech Forum and AAS/AIAA Space Flight Mechanics Meeting, January 2024.

National Defense Science and Engineering Graduate (NDSEG) fellowship awarded to Renee Spear

This research focuses on developing a new approach to collision-free, optimal spacecraft trajectory design within a multi-body system. While heritage methods exist for this task in geocentric operations, they are insufficient for operations in cislunar space due to increased environment complexity and sensitivity. New approaches to safe trajectory design will enable the construction of feasible and optimal paths in complex dynamical regimes while also avoiding dynamic obstacles defined by the paths of potential future hazards. This research will use multidisciplinary approaches from the fields of robotics and data mining to enable safe travel amidst cislunar space traffic, supporting robust and agile space operations.

Relevant conference papers:

• Spear, R.L., Bosanac, N, ‘Data-Driven Categorization of Spacecraft Motion with Uncertainty in the Earth-Moon System’ 2023 AAS/AIAA Astrodynamics Specialist Conference, August 2023, Big Sky, MT. [pdf]

Previously Funded by: NASA Goddard Space Flight Center

Existing techniques like Poincaré mapping, from dynamical systems theory, have been quite helpful in studying and visualizing chaotic environments governing the motion of spacecraft and separating chaos from order. However, these techniques can be challenging for studying spatial motion, high-energy motion, and trajectories in nonautonomous dynamical models that depend on system parameters. Furthermore, they require extensive low-level analytical work from a human and do not convey variations in geometry across the solution space. To address these challenges, we have developed a new approach to trajectory analysis by usingÌýtechniques from data mining to automatically extract a summary of the distinct geometries exhibited by a specified set of spacecraft trajectories. As a proof of concept, we have applied this approach to generate a data-driven summary of trajectories in the Sun-Earth CR3BP and demonstrated the association of known dynamical structures to the characteristics of the summary. We have since been building on this initial proof of concept in follow-up research projects described below.

Relevant journal papers:

• Bonasera, S; Bosanac, N, 'Applying Data Mining Techniques to Higher-Dimensional Poincaré Maps in the Circular Restricted Three-Body Problem,' November 2021, Vol. 133, No. 51,ÌýCelestial Mechanics and Dynamical Astronomy, DOI:Ìý. [Accepted manuscript]
• Bosanac, N, 'Data Mining Approach to Poincaré Maps in Multi-Body Trajectory Design,' June 2020, Vol. 43, No. 6, pp. 1190-1200, Journal of Guidance, Control and Dynamics, DOI:ÌýÌý[Accepted manuscript]

Relevant dissertation:

• Bonasera, S, 'Incorporating Machine Learning into Trajectory Design Strategies in Multi-Body Systems,'ÌýPh.D. Dissertation, University of Colorado Boulder, May 2022. [pdf]

Relevant conference papers:

• Bonasera, S.; Bosanac, N, 'Unsupervised Learning to Aid Visualization of Higher-Dimensional Poincarè Maps in Multi-Body Trajectory Design,'Ìý2020 AAS/AIAA Astrodynamics Specialist Virtual Conference, August 2020. [pdf]
• Bonasera, S.; Bosanac, N, 'Applications of Clustering to Higher-Dimensional PoincaréÌýMaps in Multi-Body Systems,' 30th AIAA/AAS Space Flight Mechanics Meeting, January 2020, Orlando, FL. [pdf]
• Bosanac, N, 'A Data Mining Approach to Using Poincaré Maps in Multi-Body Trajectory Design Strategies,'Ìý29th AAS/AIAA Spaceflight Mechanics Meeting, January 2019, Ka'anapali,ÌýHI. [pdf]

In collaboration with: Prof. Holzinger (PI), Prof. Scheeres, Prof. Schaub, Prof. Lahijanian, Prof. Minton

Funded by: Air Force Research Laboratory

In the near future, an increasing number of spacecraft are expected to operate in cislunar space. Accordingly, trajectory designers will need to design mission orbits and transfers to achieve a wide variety of objectives. Simultaneously, analysts will need to regularly predict the possible future motions of space objects for space domain awareness and collision avoidance. Both of these astrodynamics tasks require an initial understanding of the wide array of spacecraft motions that are possible within the complex and chaotic dynamical environment of cislunar space. Existing techniques like Poincaré mapping, from dynamical systems theory, have been quite helpful in studying and visualizing chaotic environments and separating chaos from order. However, these techniques can be challenging for studying spatial motion, high-energy motion, and trajectories in nonautonomous dynamical models that depend on system parameters. Furthermore, they require extensive low-level analytical work from a human and do not convey variations in geometry across the solution space. We have previously developed a new approach to trajectory analysis that uses techniques from data mining to automatically extract a data-driven summary of the distinct geometries exhibited by a specified set of spacecraft trajectories. In this project, we have substantially built upon and improved this approach to produce a higher quality summary of the solution space. In addition, we have been generating summaries of natural and thrust-enabled spacecraft trajectories in the Earth-Moon circular restricted three-body problem and a point mass ephemeris model of cislunar space.

Relevant conference papers:

• Bosanac, N, ‘Data-Driven Summary of Natural Spacecraft Trajectories in the Earth-Moon System,’ 2023 AAS/AIAA Astrodynamics Specialist Conference, August 2023, Big Sky, MT. [pdf]

Previously funded by: NASA Goddard Space Flight Center

Since the early 1960s, astrodynamicists have studied frozen orbits: trajectories that exhibit small variations in the orbital elements relative to a selected celestial body over long time intervals. Low lunar frozen orbits have been of significant interest for designing mission orbits near the Moon that require little maintenance over long time intervals. These trajectories can support scientific missions, placement of critical infrastructure, and extended imaging of the lunar surface.ÌýPrior approaches toÌýidentifying and characterizing lunar frozen orbits tend to either use analytical approximations in truncated dynamical models or numerical integration and differential corrections in higher-fidelity models. In our work, we have developed and applied a data-driven approach to automatically extract an array of geometrically distinct low lunar frozen orbits as well as a summary of the solution space in a high-fidelity gravity model of the Moon. Specifically, we useÌýclustering to extract a summary of trajectories that are numerically generated in the high-fidelity model for 180 days: within each cluster, trajectories possess a geometrically similar evolution of perilune but varying drift and lifetimes. Within some clusters, trajectories with a bounded perilune evolution produce candidates for lunar frozen orbits of distinct geometries.

Relevant conference papers:

• Miceli, G; Bosanac, N; Mesarch, M.A.; Folta, D.C.; Mesarch, R.L., ‘Clustering Approach To Identifying Low Lunar Frozen Orbits In A High-Fidelity Model,’ 2023 AAS/AIAA Astrodynamics Specialist Conference, August 2023, Big Sky, MT.Ìý[pdf]

Funded by the Air Force Office of Scientific Research

With the increasing utilization of cislunar space, a variety of spacecraft will need to be characterized and their motions predicted. However, when observing an unknown spacecraft in cislunar space, there may be limited or no information about it properties and maneuvering behavior (i.e., its intent and objectives) as well as brief, uncertain sequences of state estimates. With these limitations, predicting the trajectory, behavior, and parameters of a spacecraft in the chaotic dynamics of cislunar space is challenging. In fact, traditional orbit determination strategies either fail or require generating a wide variety of possible predictions that a decision-maker must analyze. The goal of our work is toÌýdevelop a new data-driven framework for rapid, early, and informative prediction of possible trajectories and behaviors of maneuvering spacecraft in cislunar space given limited information about their model parameters, maneuvers, and state estimates. This framework relies on substantially building upon our motion primitive approach to spacecraft trajectory design to solve the more complexÌýinverse problem of trajectory and behavioral prediction for maneuvering spacecraft.

In collaboration with: Prof. Jay McMahon, Prof. Nisar Ahmed

Previously funded by: NASA 2018 Early Stage Innovations

Orbital maneuvers represent a significant operational activity post-launch that continues throughout the entire lifetime of a spacecraft and must be performed safely with minimal risk to mission success. Typically, this activity relies heavily on human planners, who possess the ability to reason, learn and adapt. However, enabling robust and resilient space-based assets that are able to operate autonomously in chaotic gravitational environments (e.g., cislunar space) will require the development of new algorithms to plan and schedule orbital maneuvers, with a reduced dependency on a human-in-the-loop. These algorithms must be able to efficiently design maneuvers to be feasible, safe and robust to uncertainties while achieving a variety of short-term and long-term goals. This research will focus on leveraging autonomous learning and adaptation capabilities via machine learning to address these requirements. Specifically, we will develop offline learning algorithms for feasible and efficient maneuver planning, adapt these algorithms to support robust and resilient online learning, and develop new techniques for autonomous introspection and machine self-confidence. Onboard maneuver planning, enabled by machine learning methods that can be verified and validated for operational conditions, can enhance missions comprised of a large number of components by reducing the operational cost and complexity, and enable space-based assets to exhibit resilience in the presence of unexpected challenges or changes in their environment – particularly those that require rapid responses.

Relevant journal papers:

• Bonasera, S; Bosanac, N; Sullivan, C; Elliott, I; Ahmed, N; McMahon, J, 'Designing Sun-Earth L2 Halo Orbit Stationkeeping Maneuvers via Reinforcement Learning,' February 2023, Vol. 46, No. 2, Journal of Guidance, Control, and Dynamics, DOI:ÌýÌý[Accepted manuscript]

Relevant dissertation:

• Bonasera, S, 'Incorporating Machine Learning into Trajectory Design Strategies in Multi-Body Systems,'ÌýPh.D. Dissertation, University of Colorado Boulder, May 2022. [pdf]

Relevant conference papers:

• Bosanac, N; Bonasera, S; Sullivan, C; McMahon, J; Ahmed, N, ‘Reinforcement Learning for Reconfiguration Maneuver Design in Multi-Body Systems,’ AAS/AIAA Astrodynamics Specialist Virtual Conference, August 2021.Ìý
• Bonasera, S; Elliott, I; Sullivan, C;ÌýBosanac N; Ahmed, N; McMahon, J; ‘Designing Impulsive Station-Keeping Maneuvers Near a Sun-Earth L2 Halo Orbit via Reinforcement Learning’ AAS/AIAA Space Flight Mechanics Meeting,ÌýFebruary 2021. [pdf]
• Elliott, I; Bosanac, N; Ahmed, N; McMahon, J.W., 'ApprenticeshipÌýLearning for Maneuver Design in Multi-Body Systems,' Ìý30th AIAA/AAS Space Flight Mechanics Meeting, January 2020, Orlando, FL. [pdf]

Previously funded by NASAÌýSpace Technology Research Fellowships (NSTRF) awarded to Dr. Christopher "Jack" Sullivan

Missions operating in chaotic, multi-body environments, such as the Earth-Moon and Sun-Earth systems, have long been at the forefront of NASA’s goal to better humanity’s understanding of the solar system. However, trajectory design for these missions are inhibited by the high dimensionality that is inherent to the trajectory design process.ÌýThis high dimensionality prohibits a thorough exploration of the design space, and necessarily constrains the design process to only examining a limited number of mission architectures.ÌýTo enhance the design space exploration and uncover solutions that would further enable missions in multi-body gravitational environments, advancements in machine learning can be utilized to explore the global trajectory design space.ÌýThis research focuses on applying dynamical systems theory and machine learning techniques to multi-body systems to design complex and innovative trajectories within these systems to enhance current mission capabilities and advance our understanding of the solar system.Ìý

Relevant journal papers:

• Sullivan, C.J.; Bosanac, N; Anderson, R.L.,Ìý'Designing Low-Thrust Transfers near Earth-Moon L2 via Multi-Objective Reinforcement Learning,' March 2023, Vol. 60, No. 2, Journal of Spacecraft and Rockets. DOI:ÌýÌý[Accepted manuscript]

Relevant dissertation:

• Sullivan, C, 'Low-Thrust Trajectory Design in Multi-Body Systems via Multi-Objective Reinforcement Learning,'ÌýPh.D. Dissertation, University of Colorado Boulder, May 2022. [pdf]

Relevant conference papers:

• Sullivan, C.J.; Bosanac, N; Anderson, R.L.; Mashiku, A.K., 'Exploring the Low-Thrust Transfer Design Space in an Ephemeris Model via Multi-Objective Reinforcement Learning,'Ìý32nd AIAA/AAS Space Flight Mechanics Meeting at the AIAA Scitech Forum, San Diego, CA, January, 2022 []
• Sullivan, C; Bosanac, N; Mashiku, A.; Anderson, R.L., ‘Multi-Objective Reinforcement Learning for Low-Thrust Transfer Design between Libration Point Orbits,’ AAS/AIAA Astrodynamics Specialist Virtual Conference, August 2021. [pdf]
• Sullivan, C;ÌýBosanac, N; Anderson, R; Mashiku, A; Stuart, J.R., ‘Exploring Transfers between Earth-Moon Halo Orbits via Multi-Objective Reinforcement Learning,’ÌýIEEE Aerospace Conference, March 2021, Virtual.
• Sullivan, C.; Bosanac, N, 'Using Multi-Objective Deep Reinforcement Learning to Uncover a Pareto Front in Multi-Body Trajectory Design,'Ìý 2020 AAS/AIAA Astrodynamics Specialist Virtual Conference, August 2020. [pdf]
• Sullivan, C; Bosanac, N, 'Using Reinforcement Learning to Design Low-Thrust Approaches into Periodic Orbits in a Multi-Body System,' 30th AIAA/AAS Space Flight Mechanics Meeting, January 2020, Orlando, FL. [pdf]

National Defense Science and Engineering Graduate (NDSEG) fellowship awarded to Sai Chikine

Description Coming Soon

Funded by NASAÌýSpace Technology Graduate Research Opportunities (NSTGRO)Ìýfellowship awarded to Kristen Bruchko

Designing a feasible and efficient trajectory in a chaotic environment is a complex process that is time-consuming for a human, requires an adequate initial guess, and expert knowledge of the environment. This research focuses on incorporating roadmap generation techniques to solve the path-planning problem to autonomously choose the trajectory path and use dynamical systems theory to summarize the total solution space. By combining these approaches, an efficient method for trajectory construction will be developedÌýthat requires less human intervention and will address common challenges in mission planning. This approach to autonomous trajectory designÌýwill support mission planning in cislunar and deep space.

Relevant conference papers:

• Bruchko, K; Bosanac, N, ‘Rapid Trajectory Design In Multi-Body Systems Using Sampling-Based Kinodynamic Planning,’ 2023 AAS/AIAA Astrodynamics Specialist Conference, August 2023, Big Sky, MT. [pdf]
• Bruchko, K; Bosanac, N, 'Adaptive Roadmap Generation for Trajectory Design in the Earth-Moon System', 33rd AIAA/AAS Space Flight Mechanics Meeting, Austin, TX, January 2023.Ìý
• Bruchko, K; Bosanac, N, ‘A Preliminary Exploration of Path Planning for Initial Guess Construction in Multi-Body Systems,’ AAS/AIAA Astrodynamics Specialist Virtual Conference, August 2021.Ìý[pdf]

Funded by NASA/Caltech Jet Propulsion Laboratory, work performed by Giuliana Miceli

The goal of this research is to design maneuver-enabled trajectories for primary and secondary spacecraft to explore the Uranian and Neptunian systems. These ice giant systems are high priority science targets that have not been visited by spacecraft since the Voyager flybys. However, trajectory design for spacecraft in these scenarios is challenging due to the high-energy of interplanetary arrival conditions, limited maneuverability, and complexity of the solution space. To address this challenge, we are applying and extending our motion primitive approach (see above description)Ìýto examine the trade space ofÌýconstrained trajectories that could enable scientific measurements in theseÌýice giant systems.

Relevant conference papers:

• Miceli, G.E.; Bosanac, N.; Stuart, J.R.; Alibay, F., ‘Motion Primitive Approach to Spacecraft Trajectory Design in the Neptune-Triton System,’ AIAA SciTech Forum and AAS/AIAA Space Flight Mechanics Meeting, January 2024.

Previously funded by: Jet Propulsion Laboratory Strategic University Research Partnerships

We have developed an approach to enable SmallSat mission concepts to the Sun-Earth (SE) L4 and L5ÌýLagrange points in support of advancing our understanding of solar processes and weather monitoring capabilities by addressing one of the primary challenges of such a mission: traveling to this distant region with limited propulsive capability. Heliophysicists have long been interested in missions to SE L4 and L5, due to the capability for viewing solar and interplanetary phenomena. We leverage dynamical systems techniques to construct an efficient and guided approach to trajectory design that captures low-thrust propulsive capabilities, the fixed deployment conditions associated with secondary payloads and a variety of operational and mission constraints. We use this technique to explore the design space for low-thrust-enabled trajectories to the L4 and L5 equilibrium points and for variousÌýform factors from CubeSat to SmallSat.

Relevant journal papers:

• Elliott, I; Sullivan, C; Bosanac, N; Stuart, J; Alibay, F, 'Designing Low-Thrust Trajectories for a SmallSat Mission to Sun-Earth L5,' October 2020, Vol. 43, No. 10, pp. 1854-1864, Journal of Guidance, Control and Dynamics, DOI:ÌýÌý[Accepted manuscript]

Relevant conference papers:

• Elliott, I;ÌýSullivan, C; Bosanac, N; Alibay, F; Stuart, J, 'Designing Low-Thrust Enabled Trajectories for A Heliophysics SmallSat Mission to Sun-Earth L5,'Ìý29th AAS/AIAA Spaceflight Mechanics Meeting, January 2019, Ka'anapali,ÌýHI. [pdf]
• Sullivan, C; Elliott, I;ÌýBosanac, N; Alibay, F; Stuart, J, 'Exploring the Low-Thrust Trajectory Design Space for SmallSat Missions to the Sun-Earth Triangular Equilibrium Points,'Ìý29th AAS/AIAA Spaceflight Mechanics Meeting, January 2019, Ka'anapali,ÌýHI. [pdf]
• Bosanac, N; Alibay, F; Stuart, J.R., 'A Low-Thrust-Enabled SmallSat Heliophysics MissionÌýto Sun-Earth L5,'ÌýIEEE Aerospace Conference, March 2018, Big Sky, MT. [pdf]

In collaboration with: Prof. Holzinger (PI), Prof. Scheeres, Prof. Schaub, Prof. Lahijanian, Prof. Minton

Funded by: Air Force Research Laboratory

In the near future, an increasing number of spacecraft are expected to operate in cislunar space. Accordingly, trajectory designers will need to design mission orbits and transfers to achieve a wide variety of objectives. Simultaneously, analysts will need to regularly predict the possible future motions of space objects for space domain awareness and collision avoidance. Both of these astrodynamics tasks require an initial understanding of the wide array of spacecraft motions that are possible within the complex and chaotic dynamical environment of cislunar space. Existing techniques like Poincaré mapping, from dynamical systems theory, have been quite helpful in studying and visualizing chaotic environments and separating chaos from order. However, these techniques can be challenging for studying spatial motion, high-energy motion, and trajectories in nonautonomous dynamical models that depend on system parameters. Furthermore, they require extensive low-level analytical work from a human and do not convey variations in geometry across the solution space. We have previously developed a new approach to trajectory analysis that uses techniques from data mining to automatically extract a data-driven summary of the distinct geometries exhibited by a specified set of spacecraft trajectories. In this project, we have substantially built upon and improved this approach to produce a higher quality summary of the solution space. In addition, we have been generating summaries of natural and thrust-enabled spacecraft trajectories in the Earth-Moon circular restricted three-body problem and a point mass ephemeris model of cislunar space.

Relevant conference papers:

• Bosanac, N, ‘Data-Driven Summary of Natural Spacecraft Trajectories in the Earth-Moon System,’ 2023 AAS/AIAA Astrodynamics Specialist Conference, August 2023, Big Sky, MT. [pdf]

Previously funded by and in collaboration with: NASA Goddard Space Flight Center

With our collaborators, we have developed a preliminary reference document of relevant astrodynamics concepts for spacecraft moving within cislunar space:Ìý

Folta, D.; Bosanac, N.; Elliott, I.L.; Mann, L.; Mesarch, R.; Rosales, J., 2022, "Astrodynamics Convention and Modeling Reference for Lunar, Cislunar, and Libration Point Orbits (Version 1.1)",ÌýNASA/TP–20220014814 [pdf][]