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. To address this challenge, this paper proposes a formation planning method guided by Deformable 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 $\underline{PA}$rtitioning and Hungarian algorithm for $\underline{AS}$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. Real-world experiments validate the effectiveness and resilience of our formation planning method.