Determination of multi-UAVs formation shape: Using a requirement satisfaction and spherical fuzzy ANP based TOPSIS approach

Multiple unmanned aerial vehicles (multi-UAVs) formation shape refers to the geometric shape when multi-UAVs fly in formation and describes their relative positions. It plays a necessary role in multi-UAVs collaboration to improve performance, avoid collision, and provide reference for control. This study aims to determine the most appropriate multi-UAVs formation shape in a specific mission to meet different and even conflicting requirements. The proposed approach introduces requirement satisfaction and spherical fuzzy analytic network process (SFANP) to improve the technique for order preference by similarity to ideal solution (TOPSIS). First, multi-UAVs capability criteria and their evaluation models are constructed. Next, performance data are transformed into requirement satisfaction of capability and unified into a same scale. Qualitative judgments are made and quantified based on spherical fuzzy sets and nonlinear transformation functions are developed for benefit, cost, and interval metrics. Then, SFANP is used to handle interrelationships among criteria and determine their global weights, which takes decision vagueness and hesitancy into account and extends decision-makers' preference domain onto a spherical surface. Finally, alternative formation shapes are ranked by their distances to the positive and negative ideal solution according to the TOPSIS. Furthermore, a case study of 9 UAVs performing a search-attack mission is set up to illustrate the proposed approach, and a comparative analysis is conducted to verify the applicability and credibility.