Autonomous Laser-Link Reacquisition for Gravitational Wave Detection Using Multistage Convex Optimization

The autonomous reacquisition of laser links between distributed spacecraft is the fundamental technique in missions to detect gravitational waves in space. It involves rapidly maneuvering three spacecraft’s attitudes to adjust their laser beams so that they can cover one another within regions of uncertainty that arise owing to various spatial disturbances and system errors. This paper develops a methodology within the framework of convex optimization to optimize the reacquisition procedure on board and to reduce the duration of reacquisition, and therefore the region of uncertainty changing over the temporal history. A sampling-based method of modeling is first developed to remodel the problem of reacquisition as an equivalent problem of convex optimization with additional minimum-function constraints. An approach to penalization relaxation is then presented to convexify the minimum-function constraint and significantly improve the convergence of the algorithm by overcoming the drawbacks of potential artificial infeasibility, zero-gradient singularity, and solution-chattering situations. Finally, a detailed characterization of task uncertainty is considered to improve the applicability of the proposed method. Numerical comparisons between the proposed method and the most relevant techniques researched in recent studies are provided under multiple, randomly generated simulation environments to demonstrate its efficiency, universality, and robustness.