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\footnote{\z{A coordination sample of the astrobots may be found in \url{http://y2u.be/MpXWvpz4h00.}}} are 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 a coordination before its execution. However, a formal verification method does not exist for this purpose. In this paper, we instead use machine learning to predict the convergence of astrobots swarm. \z{As the first solution to this problem}, we propose a weighted $k$-NN-based algorithm which \rr{requires the initial status of a swarm as well as 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.