A document discusses a multi-objective, genetic algorithm designed to optimize Lyapunov feedback control law (Q-law) parameters in order to efficiently find Pareto- optimal solutions for low-thrust trajectories for electronic propulsion systems. These would be propellant-optimal solutions for a given flight time, or flight time optimal solutions for a given propellant requirement. The approximate solutions are used as good initial solutions for high-fidelity optimization tools. When the good initial solutions are used, the high-fidelity optimization tools quickly converge to a locally optimal solution near the initial solution.
Q-law control parameters are represented as real-valued genes in the genetic algorithm. The performances of the Q-law control parameters are evaluated in the multi-objective space (flight time vs. propellant mass) and sorted by the non-dominated sorting method that assigns a better fitness value to the solutions that are dominated by a fewer number of other solutions. With the ranking result, the genetic algorithm encourages the solutions with higher fitness values to participate in the reproduction process, improving the solutions in the evolution process. The population of solutions converges to the Pareto front that is permitted within the Q-law control parameter space.
This work was done by Seungwon Lee, Paul von Allmen, Anastassios Petropoulos, and Richard Terrile of Caltech for NASA's Jet Propulsion Laboratory.
The software used in this innovation is available for commercial licensing. Please contact Karina Edmonds of the California Institute of Technology at (626) 395-2322. Refer to NPO-44489.
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Genetic Algorithm Optimizes Q-LAW Control Parameters
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Overview
The document discusses the optimization of the Q-law control parameters for low-thrust spacecraft orbit transfer problems, developed by Anastassios E. Petropoulos at NASA's Jet Propulsion Laboratory (JPL). The Q-law is a heuristic control law that utilizes a set of internal parameters with nominal values. While the Q-law performs adequately with these nominal values, there is a need for optimization to achieve Pareto-optimal solutions that minimize both flight time and fuel consumption.
To address this, the authors apply a multi-objective genetic algorithm (MOGA) to optimize the Q-law parameters. In this approach, the Q-law control parameters are represented as real-valued genes within the genetic algorithm framework. The performance of these parameters is evaluated in a multi-objective space, specifically focusing on the trade-off between flight time and propellant mass. The optimization process employs a nondominated sorting method, which ranks solutions based on their dominance over one another without artificially weighting the competing objectives. A solution is considered nondominated if it is not outperformed by any other solution in both objectives.
The document highlights that the optimization of the Q-law parameters can yield significant propellant savings, ranging from 10% to 30%, compared to using the nominal values. Furthermore, the Pareto-optimal solutions derived from the optimized parameters are found to be comparable to those obtained through other optimization methods. The optimization process also enhances the robustness of the Q-law performance across various orbit transfer scenarios, mitigating sensitivity to specific parameter choices.
The optimization is conducted in a single synergetic run on multiprocessors, allowing for parallel processing. The typical computation time for generating an extensive Pareto front, which includes hundreds of Pareto-optimal solutions, is a few hours on approximately ten processors. Notably, when these Pareto-optimal solutions are used as initial guesses for a high-fidelity trajectory optimization tool (referred to as Mystic), convergence is achieved approximately ten times faster than with standard initial guesses.
In summary, this document presents a novel approach to optimizing the Q-law control parameters using a multi-objective genetic algorithm, resulting in improved efficiency and performance for low-thrust spacecraft orbit transfers, with significant implications for future aerospace missions.
