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

Abstract

Formation maintenance with a 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. This paper proposes a number adaptive formation repositioning method for drone swarms. A hierarchical layering of the formation shape to mitigate downwash interference is incorporated, then the Lloyd algorithm for uniform $PA$ rtitioning and Hungarian algorithm for $AS$ signment (PAAS) are employed in DVS. Subsequently, a spatiotemporal trajectory involving DVS is planned using primitive-based path search and taking into account the dynamic constraints of the agents. Unlike virtual rigid structures, the DVS trajectory achieves adaptive transitions with respect to a varying number of drones while ensuring adaptability to narrow environments through affine transformation. Finally, a computationally light distributed trajectory optimization algorithm guided by desired spatiotemporal positions within the DVS is proposed. Compared to state-of-the-art formation planning method, we demonstrate the rapid formation recovery capacity and environmental adaptability. Our method is suitable for industrial environments featuring narrow passages such as doors and pipelines, where rigid virtual structures fail. Simulation and real-world experiments validate the effectiveness and resilience of our method. The source code is available at https://github.com/yzhou-zju/adaptive_formation Note to Practitioners—This work enables drone swarms to adapt formations in narrow industrial spaces (e.g., doors, pipelines) despite dynamic agent losses. Our Deformable Virtual Structure employs affine transformations for seamless shape adaptation. Combined with lightweight distributed optimization, it ensures rapid recovery and environmental adaptability under constraints, which is ideal for inspection and logistics tasks with low computation overhead.