Data-Driven Convergence Prediction of Astrobots Swarms

Astrobots are robotic artifacts whose swarms are used in astrophysical studies to generate the map of the observable universe. These swarms have to be coordinated with respect to various desired observations. Such coordination is so complicated that distributed swarm controllers cannot always coordinate enough astrobots to fulfill the minimum data desired to be obtained in the course of observations. Thus, a convergence verification is necessary to check the suitability of coordination before its execution. However, a formal verification method does not exist for this purpose. In this article, we instead use machine learning to predict the convergence of astrobots swarm. As the first solution to this problem, we propose a weighted
$k$
-NN-based algorithm that requires the initial status of a swarm and its observational targets to predict its convergence. Our algorithm learns to predict based on the coordination data obtained from previous coordination of the desired swarm. This method first generates a convergence probability for each astrobot based on a distance metric. Then, these probabilities are transformed to either a complete or an incomplete categorical result. The method is applied to two typical swarms, including 116 and 487 astrobots. It turns out that the correct prediction of successful coordination may be up to 80% of overall predictions. Thus, these results witness the efficient accuracy of our predictive convergence analysis strategy.
Note to Practitioners
—Observatories involved in the generation of spectroscopic surveys always encounter limited resources to check the throughputs of their planned observations before their executions. The information yielded by an observation directly depends on the convergence rate of the observatory’s astrobots in that particular observation. Namely, if the astrobots’ convergence rate is below a minimum, then the observation has to be revoked and replanned. Thus, one may define another observation that fulfills the minimum-information requirement. There has been yet no analytical tool developed to verify the convergence rate of the coordination computed by the state-of-the-art trajectory planners of astrobots swarms. Thus, we propose to use a machine learning scheme to predict the desired convergence rate instead of involving in the infeasible process of finding its exact value. This method is a supervised method that requires the target-to-astrobot assignments table of an observation. The algorithm also needs a data set including previous coordination results of various observations of a particular swarm. The simulated scenarios manifest magnificent accuracies in the convergence predictions of some astrobots swarms corresponding to modern spectroscopic surveys, such as SDSS-V (including ~500 astrobots). Our strategy is based on the smallest subset of the astrobots’ features that have a pivotal role in convergence rates, say, the projected positions of targets on a hosting telescope’s focal plane. We argue that more explorations have to be considered to find other important features, such as the motion direction of each astrobot, which may even further improve the obtained prediction accuracies.