Due to the limited online computational resources and the inherent probability of hardware and software failures of real-world robots, large-scale formation planning faces two common challenges: computational intractability and agent failures. Based on the theory of sparse graphs and the maximum clique, we achieve a resilient and efficient formation planning (RE-Formation) to address these issues. To improve the computational efficiency of trajectory planning while ensuring flexible formation maneuvers, we introduce sparse graphs to describe connection relationships and present a sparse graph construction method with closed-form solutions. The sparse graphs ensure theGlobalRigidity for uniquely corresponding to a geometric shape andPreserve the mainFeatures of complete graphs, denoted as the GRPF sparse graph. To prevent the impact of abnormal agents, the problem of eliminating abnormal agents is transformed into an outlier rejection problem that can be solved by computing the maximum clique. We approximate the maximum clique by periodically triggering the calculation of the maximumk-coreto meet the real-time computational demands of large-scale swarms. We validate the performance through real-world experiments and implement formation planning with 100 drones in simulation. Benchmark comparisons and ablation experiments demonstrate the effectiveness of our method.

Formation flight has a vast potential for aerial robot swarms in various applications. However, the 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 article 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 article 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.

For aerial swarms, navigation in a prescribed formation is widely practiced in various scenarios. However, the associated planning strategies typically lack the capability of avoiding obstacles in cluttered environments. To address this deficiency, we present an optimization-based method that ensures collision-free trajectory generation for formation flight. In this paper, a novel differentiable metric is proposed to quantify the overall similarity distance between formations. We then formulate this metric into an optimization framework, which achieves spatial-temporal planning using polynomial trajectories. Minimization over collision penalty is also incorporated into the framework, so that formation preservation and obstacle avoidance can be handled simultaneously. To validate the efficiency of our method, we conduct benchmark comparisons with other cutting-edge works. Integrated with an autonomous distributed aerial swarm system, the proposed method demonstrates its efficiency and robustness in real-world experiments with obstacle-rich surroundings11https://www.youtube.com/watch?v=lFumtOrJci4. We will release the source code for the reference of the community22https://github.com/ZJU-FAST-Lab/Swarm-Formation.

The quadrotor is popularly used in challenging environments due to its superior agility and flexibility. In these scenarios, trajectory planning plays a vital role in generating safe motions to avoid obstacles while ensuring flight smoothness. Although many works on quadrotor planning have been proposed, a research gap exists in incorporating self-adaptation into a planning framework to enable a drone to automatically fly slower in denser environments and increase its speed in a safer area. In this paper, we propose an environmental adaptive planner to adjust the flight aggressiveness effectively based on the obstacle distribution and quadrotor state. Firstly, we design an environmental adaptive safety aware method to assign the priority of the surrounding obstacles according to the environmental risk level and instantaneous motion tendency. Then, we apply it into a multi-layered model predictive contouring control (Multi-MPCC) framework to generate adaptive, safe, and dynamical feasible local trajectories. Extensive simulations and real-world experiments verify the efficiency and robustness of our planning framework. Benchmark comparison also shows superior performances of our method with another advanced environmental adaptive planning algorithm. Moreover, we release our planning framework as open-source ros-packages1.