Robust Low-Thrust Trajectory Design for the Power and Propulsion Element of the Lunar Gateway

Concepts de base

Robust low-thrust trajectory design framework to explore solutions for the Power and Propulsion Element (PPE) module to the Earth-Moon L2 Southern 9:2 Near Rectilinear Halo Orbit, incorporating algorithmic enhancements to improve the global search for robust solutions.

Résumé

The content discusses the importance of robust trajectory design for low-thrust missions in the cislunar domain, which are highly susceptible to operational disruptions such as unforeseen thruster outages or missed thrust events.
The authors present a robust trajectory design framework and apply it to explore solutions for the Power and Propulsion Element (PPE) module to the Earth-Moon L2 Southern 9:2 Near Rectilinear Halo Orbit (NRHO). They propose two algorithmic approaches to enhance the global search for robust solutions:

Nonconditional (random) global search: Randomly sampling the control solution from an a-priori chosen distribution to explore the solution space.
Conditional global search: Leveraging information from non-robust solutions to guide the optimizer toward robust solutions.

The authors provide a comprehensive statistical comparison between the non-robust and robust solutions obtained using both global search approaches. Key insights include:

Robust solutions generally exhibit higher fuel consumption and longer flight times compared to non-robust solutions.
Backward robust solutions (where the missed thrust event occurs during the backward shooting arc) have slightly lower average fuel consumption than forward robust solutions.
As the duration of the missed thrust event (Δτ) increases, the fuel consumption and flight time of robust solutions also increase monotonically.
The conditional global search approach is able to find more robust solutions compared to the nonconditional approach, but the optimality ratio is lower.
The authors highlight the importance of this work for the Artemis program and the broader goals of establishing a sustainable human presence in cislunar space and beyond.

Stats

The nominal non-robust feasible trajectory consumes approximately 2,038 kg of fuel and has a total time of flight of 225 days.
The reoptimized trajectory after a 2.5-day missed thrust event consumes ~8 kg more fuel than the nominal.

Citations

"Unless accounted for during preliminary mission design, [missed thrust events] can severely degrade the mission performance, and in some cases may even make the mission objective unachievable depending on available propellant mass, and remaining mission time."
"Doing so will allow us to not only build in the necessary margins, but also ensure that a robust alternative solution is readily available to deploy in the event that such outages disrupt the execution of a scheduled burn."

Idées clés tirées de

Algorithmic Considerations for Effective Global Search of Robust Low-Thrust Trajectories

by Amlan Sinha,... à arxiv.org 10-02-2024

https://arxiv.org/pdf/2410.00297.pdf

Questions plus approfondies

How can the proposed robust trajectory design framework be extended to handle multiple missed thrust events along the reference trajectory?

The proposed robust trajectory design framework can be extended to accommodate multiple missed thrust events (MTEs) by enhancing the stochastic modeling of the trajectory optimization problem. This can be achieved through the following strategies:

Multi-Event Stochastic Modeling: Instead of assuming a single MTE, the framework can incorporate a probabilistic model that accounts for multiple MTEs occurring at various points along the reference trajectory. This would involve defining a set of random variables that represent the initiation times and durations of each MTE, allowing for a more comprehensive analysis of the trajectory's robustness.

Adaptive Control Segmentation: The adaptive segmentation strategy can be modified to dynamically adjust the number of control segments based on the occurrence of MTEs. By allowing for variable segment lengths and control authority adjustments, the framework can better manage the impact of multiple MTEs on the trajectory.

Hierarchical Optimization: Implementing a hierarchical optimization approach can facilitate the simultaneous optimization of the reference trajectory and multiple realization trajectories. This would involve solving a series of nested optimization problems, where the outer loop optimizes the reference trajectory while the inner loop focuses on the realization trajectories for each potential MTE scenario.

Monte Carlo Simulations: Utilizing Monte Carlo methods can help in sampling various MTE scenarios, allowing the framework to evaluate the performance of the trajectory under different conditions. This would provide statistical insights into the likelihood of successful mission completion despite multiple MTEs.

Robustness Metrics: Developing new robustness metrics that quantify the trajectory's resilience to multiple MTEs can guide the optimization process. These metrics could include fuel consumption, time of flight, and the ability to reach the target orbit under various MTE scenarios.

By integrating these strategies, the robust trajectory design framework can effectively handle the complexities introduced by multiple MTEs, ensuring that the spacecraft remains capable of achieving its mission objectives even in the face of operational disruptions.

What are the potential drawbacks or limitations of the conditional global search approach, and how can they be addressed?

The conditional global search approach, while beneficial in leveraging non-robust solutions as initial guesses for robust solutions, has several potential drawbacks and limitations:

Dependence on Initial Guesses: The effectiveness of the conditional global search heavily relies on the quality of the initial guesses derived from non-robust solutions. If these initial guesses are suboptimal or far from the true robust solution, the local search may converge to a local minimum rather than the global optimum. To address this, a more diverse set of initial guesses can be generated by incorporating variations in the non-robust solutions, potentially through perturbation techniques or by sampling from a broader distribution.

Limited Exploration of Solution Space: The conditional approach may limit exploration of the solution space, as it primarily focuses on regions near the non-robust solutions. This could result in missing out on potentially better robust solutions located further away. To mitigate this, a hybrid approach that combines both conditional and nonconditional search strategies could be employed, allowing for broader exploration while still benefiting from the insights gained from non-robust solutions.

Computational Complexity: The conditional global search may introduce additional computational complexity, especially when dealing with a large number of non-robust solutions. This can lead to increased computational time and resource requirements. Implementing parallel processing techniques or optimizing the search algorithm to reduce the number of evaluations required can help alleviate this issue.

Sensitivity to MTE Parameters: The performance of the conditional global search can be sensitive to the parameters defining the MTE, such as the duration and timing of the events. If these parameters are not accurately modeled or if they vary significantly, the robustness of the solutions may be compromised. To address this, a more robust statistical framework can be developed to better characterize the uncertainties associated with MTEs, allowing for more resilient trajectory designs.

By recognizing and addressing these limitations, the conditional global search approach can be refined to enhance its effectiveness in finding robust solutions in the context of low-thrust trajectory design.

How can the insights from this study be leveraged to develop more efficient algorithms for robust trajectory design in other complex multibody dynamical environments, such as interplanetary missions?

The insights gained from this study on robust trajectory design for low-thrust missions in the cislunar domain can be effectively leveraged to enhance algorithms for robust trajectory design in other complex multibody dynamical environments, including interplanetary missions. Here are several ways to achieve this:

Robustness Framework Adaptation: The robust trajectory design framework developed in this study can be adapted to interplanetary missions by incorporating the unique dynamical characteristics of the interplanetary environment. This includes modeling the gravitational influences of multiple celestial bodies, such as planets and moons, and accounting for the varying thrust capabilities of spacecraft over long durations.

Advanced Stochastic Modeling: The stochastic modeling techniques used to account for missed thrust events can be extended to include other uncertainties typical in interplanetary missions, such as atmospheric drag during planetary flybys, solar radiation pressure, and navigation errors. By developing a comprehensive probabilistic model, the trajectory optimization process can better account for these uncertainties, leading to more robust mission designs.

Multi-Objective Optimization: Interplanetary missions often involve multiple objectives, such as minimizing fuel consumption, maximizing mission duration, and ensuring safety margins. The insights from this study can inform the development of multi-objective optimization algorithms that balance these competing objectives while ensuring robustness against operational disruptions.

Adaptive Control Strategies: The adaptive segmentation and control strategies employed in this study can be applied to interplanetary missions to dynamically adjust thrust profiles and control authority based on real-time conditions. This adaptability can enhance the spacecraft's ability to respond to unforeseen events, such as changes in trajectory due to gravitational assists or unexpected maneuvers.

Algorithmic Enhancements: The algorithmic techniques demonstrated in this study, such as the conditional and nonconditional global search approaches, can be refined and integrated into interplanetary trajectory optimization algorithms. By combining these techniques with advanced heuristics and machine learning methods, more efficient search algorithms can be developed that quickly converge to robust solutions.

Cross-Domain Knowledge Transfer: Finally, the findings from this study can facilitate knowledge transfer between different mission domains. By sharing best practices and lessons learned from low-thrust cislunar missions, researchers and engineers can apply these insights to improve the design and execution of interplanetary missions, ultimately enhancing mission success rates.

By leveraging these insights, the development of more efficient algorithms for robust trajectory design in interplanetary missions can be achieved, ensuring that spacecraft are better equipped to navigate the complexities of multibody dynamical environments while achieving their mission objectives.