  Formation flight has a vast potential for aerial robot swarms in various
applications. However, existing methods lack the capability to achieve fully
autonomous large-scale formation flight in dense environments. To bridge the
gap, we present a complete formation flight system that effectively integrates
real-world constraints into aerial formation navigation. This paper proposes a
differentiable graph-based metric to quantify the overall similarity error
between formations. This metric is invariant to rotation, translation, and
scaling, providing more freedom for formation coordination. We design a
distributed trajectory optimization framework that considers formation
similarity, obstacle avoidance, and dynamic feasibility. The optimization is
decoupled to make large-scale formation flights computationally feasible. To
improve the elasticity of formation navigation in highly constrained scenes, we
present a swarm reorganization method that adaptively adjusts the formation
parameters and task assignments by generating local navigation goals. A novel
swarm agreement strategy called global-remap-local-replan and a formation-level
path planner is proposed in this work to coordinate the global planning and
local trajectory optimizations. To validate the proposed method, we design
comprehensive benchmarks and simulations with other cutting-edge works in terms
of adaptability, predictability, elasticity, resilience, and efficiency.
Finally, integrated with palm-sized swarm platforms with onboard computers and
sensors, the proposed method demonstrates its efficiency and robustness by
achieving the largest scale formation flight in dense outdoor environments.
