Number Adaptive Formation Flight Planning via Affine Deformable Guidance in Narrow Environments

Abstract--Formation maintenance with varying number of drones in narrow environments hinders the convergence of planning to the desired configurations. T o address this challenge, this paper proposes a formation planning method guided by De-formable Virtual Structures (DVS) with continuous spatiotemporal transformation. Firstly, to satisfy swarm safety distance and preserve formation shape filling integrity for irregular formation geometries, we employ Lloyd algorithm for uniform PA rtitioning and Hungarian algorithm for AS signment (PAAS) in DVS. Subsequently, a spatiotemporal trajectory involving DVS is planned using primitive-based path search and nonlinear trajectory optimization. The DVS trajectory achieves adaptive transitions with respect to a varying number of drones while ensuring adaptability to narrow environments through affine transformation. Finally, each agent conducts distributed trajectory planning guided by desired spatiotemporal positions within the DVS, while incorporating collision avoidance and dynamic feasibility requirements. Our method enables up to 15% of swarm numbers to join or leave in cluttered environments while rapidly restoring the desired formation shape in simulation. Compared to cutting-edge formation planning method, we demonstrate rapid formation recovery capacity and environmental adaptability. In recent years, formation flight becomes the foundation requirement for aerial swarms in practical applications, such as collaborative exploration [1], light show [2], search and rescue [3]. For large-scale swarms [4], [5], formation inevitably encounters agent loss in narrow environments [6]- [8].