An Optimal Algorithm for Changing from Longitudinal to Latitudinal Formation of Autonomous Aircraft Squadrons

This work presents an algorithm for changing from latitudinal to longitudinal formation of autonomous aircraft squadrons. The maneuvers are defined dynamically by using a predefined set of 3D basic maneuvers. This formation change is necessary when the squadron has to perform tasks which demand both formations, such as lift off, georeferencing, obstacle avoidance and landing. Simulations show that the formation change is done without collision. The time complexity analysis of the transformation algorithm reveals that its efficiency is optimal, and the proof of correctness ensures its longitudinal formation features.

Flying in a prescribed formation in an agile manner remains a challenging problem in the field of UAVs, particularly when following highly-demanding trajectories that require flight at platform limits. We address this problem by proposing a novel decentralized approach to formation flight along a given path that integrates formation maintenance into the MPCC framework, allowing UAVs to adapt their progression along complex paths while respecting individual dynamic constraints and maintaining the desired formation. To this end, we introduce a novel reparametrization and synchronization method for dynamic formation geometries together with a decentralized approach to determine the desired positions for the individual UAVs. The proposed approach allows the formation to coordinate high-speed path following without compromising formation integrity. The proposed approach is validated through extensive simulation and real-world experiments involving scenarios with varying complexity of paths and changes of required formation shape on the fly. In comparison to time-parameterized trajectory tracking, we demonstrate improved formation maintenance by 65% in high-speed flight with velocities up to 21 m/s, while achieving comparable times required to reach the goal.

We propose a method for the collective maneuvering of affine formations in the plane by modifying the original weights of the Laplacian matrix used to achieve static formations of robot swarms. Specifically, the resulting collective motion is characterized as a time-varying affine transformation of a reference configuration, or shape. Unlike the traditional leader-follower strategy, our leaderless scheme allows agents to maintain distinct and possibly time-varying velocities, enabling a broader range of collective motions, including all the linear combinations of translations, rotations, scaling and shearing of a reference shape. Our analysis provides the analytic solution governing the resulting collective motion, explicitly designing the eigenvectors and eigenvalues that define this motion as a function of the modified weights in the new Laplacian matrix. To facilitate a more tractable analysis and design of affine formations in 2D, we propose the use of complex numbers to represent all relevant information. Simulations with up to 20 agents validate the theoretical results.