Brian McCarthy, a.i. solutions, Inc; Fabio Chiappina, a.i. solutions, Inc
Keywords: cislunar, trajectory design, machine learning, path planning, multi-body dynamics
Abstract:
With the proliferation of civil and defense infrastructure in cislunar space, effective methods to rapidly plan trajectories throughout the regime are becoming increasingly necessary. However, given that cislunar dynamics are inherently chaotic and highly sensitive, finding a viable path through space that connects any two points is critical, albeit challenging. Additionally, the potential types of trajectory geometries that exist in cislunar space are widely varied. Conic sections, which characterize nearly all near-Earth orbits, no longer approximate the types of paths that a vehicle can take through cislunar space. Consequently, as in any engineering design process, an approach of increasing levels of fidelity to reach a final solution must be taken to properly assess potential paths. By starting in an appropriate simplified model, fundamental motion through cislunar space is captured and is used to inform a higher-fidelity design. In this investigation, an approach is discussed using various machine learning techniques to find viable paths through the simplified model to provide initial guesses to a higher-fidelity model. The initial guess results are validated in a higher-fidelity model to demonstrate an end-to-end trajectory design process. Ultimately, an effective, streamlined end-to-end trajectory construction process enables rapid delivery of viable options to decision makers, improving threat assessment and allowing quicker deployment of assets to respond to possible threats.
Obtaining an initial guess trajectory through cislunar space by traditional methods is a time-intensive process, requiring a high level of astrodynamics expertise, specifically in multi-body dynamical structures. An initial guess must then be provided to a targeting or optimization tool to produce an end-to-end design, and that initial guess typically drives which basin of convergence the optimized solution tends toward. The initial guess therefore often drives the overall time of flight and maneuver cost of a cislunar mission. To reduce dependency on constant, high-level astrodynamics expertise, an automated trajectory planning process is developed to rapidly construct initial guess cislunar trajectories, leveraging various known dynamical structures in the Earth-Moon Circular Restricted Three-Body Problem (CR3BP). The Earth-Moon CR3BP serves as the simplified cislunar dynamics model.
The autonomous trajectory planning process leverages several steps to produce end-to-end solutions. First, using a database of known cislunar orbit and trajectory classifications, a previously developed unsupervised machine learning technique is used to cluster sets of these trajectories into motion primitives, each containing the representative path from its respective cluster. From these motion primitives, a weighted, directed graph is constructed using information from the representative trajectory of the motion primitive, where edge weights encode the state differences between trajectory arcs. Using clustered motion primitive information, instead of the entire database of trajectories, reduces the amount of time to search through the graph to construct paths between different locations, while simultaneously ensuring that each path through the graph corresponds to a relatively distinct trajectory geometry. Departure and destination orbits are selected, and then a graph search algorithm is used to construct multiple possible paths from the departure orbit to the destination orbit. Depending on how the edge weights of the graph are defined, solutions with lower maneuver costs or lower time-of-flight are prioritized in the search. Once paths are constructed using the motion primitives sets, a refinement step reduces discontinuities between the trajectory segments by selecting the ideal member of each cluster.
Of the trajectories produced after the refinement process, some of the trajectories can possess very similar paths and would ultimately fall into the same convergence basin if passed to higher fidelity targeting/optimization process. To eliminate these redundant trajectory solutions, a clustering procedure organizes the solutions into groups, each containing trajectories with similar properties. Similarity of trajectories is autonomously evaluated based on the visual properties of the trajectories. Images of each trajectory are provided to a pre-trained convolutional neural network image classifier. The output of one of the internal fully connected network layers served an abstract feature vector, encoding the visual properties of that trajectory. This machine vision clustering approach is evaluated, in addition to alternative feature spaces that can be used to cluster similar trajectories. Following the refinement step and reduction of redundant trajectories, a collocation process is used to produce an end-to-end trajectory, using maneuvers to connect the segments. The result is production of multiple, distinct options so decision makers have options to select if other mission constraints also drive the final trajectory chosen for a particular scenario.
The algorithm developed in this investigation seeks to reduce the amount of effort required to construct paths through cislunar space, ideally allowing even a novice trajectory designer to quickly generate high-quality solutions. By leveraging motion primitives and transforming the problem into a directed graph search, the solution space is reduced to a more manageable set while still capturing the fundamental motion through cislunar space. Ultimately, a robust method to generate initial guess trajectories streamlines the design process and reduces the expertise required to construct paths in this sensitive regime. Given that cislunar space will be populated rapidly in the coming decades, tools to effectively plan ways to traverse the region will be increasingly necessary. Not only are these methods useful for planning paths for controllable assets, but these same concepts and tools are also important in understanding adversarial assets’ movements. Tools that assess where and how quickly vehicles could move in cislunar space will be critical to protecting against threats.
Date of Conference: September 17-20, 2024
Track: Cislunar SDA