This paper presents an autonomous guidance and control strategy for a satellite swarm that enables scalable distributed space structures for innovative science and business opportunities. The averaged $J_2$ orbital parameters that describe the drift and periodic orbital motion were derived along with their target values to achieve a distributed space structure in a decentralized manner. This enabled the design of a distance-based orbital stabilizer to ensure autonomous deployment into a monolithic formation of a coplanar equidistant configuration on a user-defined orbital plane. Continuous formation control was assumed to be achieved through fuel-free actuation, such as satellite magnetic field interaction and differential aerodynamic forces, thereby maintaining long-term formation stability without thruster usage. A major challenge for such actuation systems is the potential loss of control capability due to increasing inter-satellite distances resulting from unstable orbital dynamics, particularly for autonomous satellite swarms. To mitigate this risk, our decentralized deployment controller minimized drift distance during unexpected communication outages. As a case study, we consider the deployment of palm-sized satellites into a coplanar equidistant formation in a $J_2$-perturbed orbit. Moreover, centralized grouping strategies are presented.

In the last post on high-dimensional learning, we saw that learning in high dimensions is impossible without assumptions due to the curse of dimensionality, i.e., the number of samples required in our learning problem grows exponentially with dimensions. We also introduced the main geometric function spaces, in which our points in high-dimensional space can be considered as signals over the low-dimensional geometric domain. From this assumption, and to make learning tractable, I will present symmetry (in this post) and scale separation (in the next one). In addition, we also discussed the three kinds of errors we need to be aware of, namely, approximation error, statistical error, and optimization error. The approximation error increases if our function class decreases (the true function that we are trying to estimate is far outside of this class), which suggests having a large function class. In contrast, the statistical error implies we are unlikely to find the true function based on a finite number of data points. This error increases as the function class grows.

Large space structures, such as telescopes and spacecraft, should ideally be assembled directly in space, as they are difficult or impossible to launch from Earth as a single piece. In several cases, however, assembling these technologies manually in space is either highly expensive or unfeasible. In recent years, roboticists have thus been trying to develop systems that could be used to automatically assemble structures in space. To simplify this assembly process, space structures could have a modular design, which essentially means that they are comprised of different building blocks or modules that can be shifted to create different shapes or forms. Researchers at the German Aerospace Center (DLR) and Technische Universität München (TUM) have recently developed an autonomous planner that could be used to assemble reconfigurable structures directly in space.

But manufacturing a reliable structure in an innovative manner is not enough--first-time certification needs to be realised as well.

Hypergraph data appear and are hidden in many places in the modern age. They are data structure that can be used to model many real data examples since their structures contain information about higher order relations among data points. One of the main contributions of our paper is to introduce a new topological structure to hypergraph data which bears a resemblance to a usual metric space structure. Using this new topological space structure of hypergraph data, we propose several approaches to study community detection problem, detecting persistent features arising from homological structure of hypergraph data. Also based on the topological space structure of hypergraph data introduced in our paper, we introduce a modified nearest neighbors methods which is a generalization of the classical nearest neighbors methods from machine learning. Our modified nearest neighbors methods have an advantage of being very flexible and applicable even for discrete structures as in hypergraphs. We then apply our modified nearest neighbors methods to study sign prediction problem in hypegraph data constructed using our method.

Multi-modal data is becoming more common than before because of big data issues. Finding the semantically equal or similar objects from different data sources(called entity resolution) is one of the heart problem of multi-modal task. Current models for solving this problem usually needs much paired data to find the latent correlation between multi-modal data, which is of high cost. A new kind latent correlation is proposed in this article. With the correlation, multi-modal objects can be uniformly represented in a commonly shard space. A classifying based model is designed for multi-modal entity resolution task. With the proposed method, the demand of training data can be decreased much.