Explainable machine learning model of disorganisation in swarms of drones

www.nature.com/scientificreports OPEN Explainable machine learning model of disorganisation in swarms of drones Marta Gackowska-Kątek & Piotr Cofta The main challenges when managing a fleet of unmanned aerial vehicles are to ensure the relative stability of its formation and to minimise disorganisation, specifically when undergoing an intrusion. When planning the mission it is beneficial for the operator to set the parameters of the formation to balance the needs of the mission with the disorganisation that an intruder may cause. The model developed in this research predicts the anticipated disturbance as a function of the parameters of the formation. The effectiveness of six machine learning methods are compared with a previously established baseline, using data obtained from simulations. CatBoost (categorical boosting) delivered the best results, with an R2 (coefficient of determination) value of 83.3%, representing an improvement of 80% over the baseline. The SHAP (Shapley Additive Explanations) method was used to extend the model beyond predictability for particular combinations of values of parameters, towards generalised recommendations for the operator of the formation. Maintaining a static formation of a swarm of drones and avoiding collisions are two of the main challenges in the field of unmanned aerial vehicles, particularly if they are engaged in observation or sensing missions or are covering a fixed area. The correct execution of the mission is contingent upon satisfying both the mission objectives of maintaining the formation in position, while avoiding intruders and preventing collisions within the formation. Of these, the primary challenge is the need to deal with intruders and unexpected random events, as described by Kallinikos1. For unmanned aerial vehicles, this issue routinely resolved by fitting drones with a collision avoidance algorithm, as noted by Wei et al.2. The appearance of an intruder introduces an undesired disturbance to the formation. Guided by their collision-avoidance algorithms, drones move from their positions to let the intruder pass, and then need to return to their positions while avoiding collisions with other drones in the swarm. As this disturbance can result in additional energy expenses, delays or reductions in mission readiness, it is essential to plan for it. As highlighted by Atyabi et al.3 as long as the operator of the formation knows the extent of the disorganisation that will be caused by an anticipated intruder, the parameters of the formation can be altered to balance this with the mission of the formation. Jiang4 observed that the ability to predict the level of disturbance to a given formation is therefore essential. As an outcome of our research, this paper presents a set of two tools that can aid an operator undertaking this type of planning. The first is a predictive model that was developed using selected machine learning methods. The model predicts the level of disturbance that the average intruder will impose, expressed as the level of crossentropy, on the basis of selected parameters of the formation, including the parameters of the collision avoidance algorithm. Our research indicated that the most productive method was based on CatBoost, delivering an R2 of 83.3%. Catboost was developed by Dorogush et al.5 and employs gradient boosting, a powerful ensemble learning technique that builds models in a sequential manner. By combining multiple weak learners, typically decision trees, it can create a strong predictive model. This algorithm minimizes overfitting through the use of techniques such as ordered boosting and oblivious trees, which ensure robust and accurate performance even on smaller datasets. The coefficient of determination, denoted as R2, is a key metric in regression analysis, as it represents the proportion of the variance in the dependent variable that is predictable from the independent variables. Moreover in predictive modelling, a higher R2 suggests that the model has better predictive accuracy, meaning it can more reliably predict future outcomes based on the input variables. However, the use of machine learning tools can make the model opaque, preventing its interpretation by the operator. That is, although the operator may obtain a prediction for the disturbance arising from a given set of parameters, there is no indication of the effects of increasing or decreasing some of the parameters on Faculty of Telecommunications, Computer Science and Electrical Engineering, Bydgoszcz University of Science and Technology, Al. prof. S. Kaliskiego 7, 85-796 Bydgoszcz, Poland. email: Scientific Reports | (2024) 14:22519 | https://doi.org/10.1038/s41598-024-73220-2 1 www.nature.com/scientificreports/ the disturbance. The SHAP method can be applied to the best model to provide concrete guidelines regarding alterations in the parameters. The novelty of this work lies in the following aspects: • A new model to predict the disturbance caused by an intruder was developed by exploring several methods from the machine learning domain.Our model employs the CatBoost method and delivers R2 equal to 83.3%, an improvement of 80% over the baseline drawn from work reported by Gackowska et al.6 for the same dataset, obtained through simulations. • The SHAP method is applied to the model, and the outcome is used to formulate guidelines for the operator regarding the alteration to parameters. This approach can overcome the limitations of the machine learning models, i.e. the lack of anexplainable relationship between the values of the parameters and the outcome of the model.This paper is organised as follows: Section 2 presents a literature review in the areas of disorganisation, machine learning models, and explainability. Section 3 describes the proposed methodology. Section 4 presents some results and a discussion. Section 5 summarises our work and draws some conclusions from this research. Literature review As observed by Wu et al.7 disorganisation is related to the state of the system structure. It concerns the occurrence of anomalies, i.e. certain events or patterns that deviate from the well-defined concept of normal and expected behaviour, as noted by Chandola et al.8. Kelso9 points out that disorganisation also involves to the occurrence of disturbances in coordination, i.e. the spatial, temporal and functional order. As defined by Chaudhury et al.10 coordination can be considered as a cycle consisting of four phases: definition phase, conflict resolution, action and adaptation. The effects of interactions such as chaos effects, interference effects or one-time anomalies, as identified on the basis of Luhmann’s theory11, can negatively affect the organisation and hence, the performance and the security of the system. Initially, the concept of cross-entropy was closely related to thermodynamics, and was considered as a measure of the disorder or randomness in a thermodynamic system, as noted b (...truncated)