The interaction between the swarm individuals affects the dynamic behavior of the swarm, but it is difficult to obtain directly from outside observation. Therefore, the problem we focus on is inferring the structure of the interactions in the swarm from the individual behavior trajectories. Similar inference problems that existed in network science are named network reconstruction or network inference. It is a fundamental problem pervading research on complex systems. In this paper, a new method, called Motion Trajectory Similarity, is developed for inferring direct interactions from the motion state of individuals in the swarm. It constructs correlations by combining the similarity of the motion trajectories of each cross section of the time series, in which individuals with highly similar motion states are more likely to interact with each other. Experiments on the flocking systems demonstrate that our method can produce a reliable interaction inference and outperform traditional network inference methods. It can withstand a high level of noise and time delay introduced into flocking models, as well as parameter variation in the flocking system, to achieve robust reconstruction. The proposed method provides a new perspective for inferring the interaction structure of a swarm, which helps us to explore the mechanisms of collective movement in swarms and paves the way for developing the flocking models that can be quantified and predicted.

Unmanned Aerial Vehicles(UAV) swarm is a rapidly developing field, and with it comes the need to identify the swarm based on observations. The problem of trajectory clustering is put forward in the identification of UAV swarms, especially modularized UAV swarms. We propose a new method of Network Integrated trajectory clustering(NIT) to solve the trajectory clustering problem in a fast-changing and chaotic environment which requires a quick response, fault tolerance, and accuracy. The experiment results prove the flexibility and adaptability of the NIT method towards various demands and multi-dimensional data. Moreover, the algorithm proposed based on the method shows priority over the other three trajectory clustering methods(DTW, Fréchet distance, GMM) on the accuracy, and fault tolerance in clustering swarm trajectories. The method raised in this paper is an innovation to both multi-agent systems identification and trajectory clustering methods.

Interactions and dynamics are critical mechanisms for multi-agent systems to achieve complex intelligence through the cooperation of simple agents. Yet, inferring interactions of the multi-agent system is still a common and open problem. A new method named K-similarity is designed to measure the global relative similarities for inferring the interactions among multiple agents in this paper. K-similarity is defined to be a synthetic measure of relative similarity on each observation snapshot where regular distances are nonlinearly mapped into a network. Therefore, K-similarity contains the global relative similarity information, and the interaction topology can be inferred from the similarity matrix. It has the potential to transform into distance strictly and detect multi-scale information with various K strategies. Therefore, K-similarity can be flexibly applied to various synchronized dynamical systems with fixed, switching, and time-varying topologies. In the experiments, K-similarity outperforms four benchmark methods in accuracy in most scenarios on both simulated and real datasets, and shows strong stability towards outliers. Furthermore, according to the property of K-similarity we develop a Gaussian Mixture Model (GMM)-based threshold to select probable interactions. Our method contributes to not only similarity measurement in multi-agent systems, but also other global similarity measurement problems.

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Change point detection (CPD) for multi-agent systems helps one to evaluate the state and better control the system. Multivariate CPD methods solve the [Formula: see text] time series well; however, the multi-agent systems often produce the [Formula: see text] dimensional data, where [Formula: see text] is the dimension of multivariate observations, [Formula: see text] is the total observation time, and [Formula: see text] is the number of agents. In this paper, we propose two valid approaches based on higher-order features, namely, the Betti number feature extraction and the Persistence feature extraction, to compress the [Formula: see text]-dimensional features into one dimension so that general CPD methods can be applied to higher-dimensional data. First, a topological structure based on the Vietoris–Rips complex is constructed on each time-slice snapshot. Then, the Betti number and persistence of the topological structures are obtained to separately constitute two feature matrices for change point estimates. Higher-order features primarily describe the data distribution on each snapshot and are, therefore, independent of the node correspondence cross snapshots, which gives our methods unique advantages in processing missing data. Experiments in multi-agent systems demonstrate the significant performance of our methods. We believe that our methods not only provide a new tool for dimensionality reduction and missing data in multi-agent systems but also have the potential to be applied to a wider range of fields, such as complex networks.