Pure Hamiltonian mechanics plus active braking for swarm formation control: 9 UAVs hold 2.5 m buffers and 0.9 m spacing in undulating-terrain simulation

It embeds an analytical Rimon-Koditschek navigation potential, modified with anisotropic vertical tracking scaling, into a pseudo-Hamiltonian dynamical framework, mapping potential-field gradients directly into smooth acceleration profiles so agents keep agile open-space flight paths. Where traditional multi-agent artificial potential field controllers frequently fail in cluttered environments due to spurious local minima that can destabilize the formation or cause collisions, this framework replaces pure potential descent with Hamiltonian-style dynamics, changing how trajectories are generated. Evidence comes from the paper's own method construction and numerical simulations; the loaded text reports no quantitative comparison table against an APF baseline or ablation data.

It implements an active kinematic preview and deflection layer on the virtual target's trajectory: the target monitors an expanded activation zone and generates d_target_extra_buffer = 6.5 m of lateral clearance around obstacles, pre-deconflicting narrow bottlenecks before the trailing formation arrives. Obstacle-avoidance decisions are moved forward to the leading virtual target rather than each agent reacting independently, making this a formation-level pre-deconfliction mechanism. The text gives the concrete 6.5 m parameter and uses a simulation of N=9 agents crossing a sinusoidal terrain cluster as the validation scenario.

It uses a coordinate-free formation engine that projects rigid, parameterized spatial offsets onto individual agents via a dynamic SO(3) rotation matrix, maintaining a robust, symmetric V-shape configuration. Rotation-matrix projection replaces formation descriptions that depend on a global coordinate frame, keeping the configuration consistent under attitude changes. Evidence is the method description plus V-shape maintenance in simulation; the text reports no statistics on configuration error.

It introduces a spatial decay braking force F_brake modulated by the normal gradient of the workspace topology, draining kinetic energy only within safety envelopes to counteract momentum-driven overshoot; in simulation the swarm strictly respects d_buffer = 2.5 m, z_buffer = 2.0 m, and d_spacing = 0.9 m. Braking is confined to safety envelopes and tied to the terrain normal gradient, linking energy dissipation directly to geometric boundaries. Evidence is numerical simulation metrics for N=9 agents on an undulating sinusoidal terrain cluster, where the text states the hard safety margins are met under strict kinematic bounds.

The result targets multi-UAV operations that must hold rigid formations and satisfy hard safety margins over unstructured, non-flat terrain, such as autonomous multi-UAV flight missions. It lets follow-up work build a clearer interface between Hamiltonian-style dynamics and potential-field navigation, and move avoidance decisions forward to the virtual-target layer; for researchers reusing the framework, the parameters of 6.5 m target extra buffer, 2.5 m and 2.0 m safety buffers, and 0.9 m spacing provide a directly referenceable calibration starting point.

The reading scope is incomplete and covers only abstract-level content, so figures, baseline comparisons, and ablations in the body cannot be assessed here; the metrics above should therefore be treated as the paper's own statements rather than independently verified. Readers should still watch: behavior under denser or dynamic obstacles and limited communication; how transferable the 6.5 m extra buffer and 0.9 m spacing are across different vehicle sizes and speed envelopes; and whether the kinematic-bound and braking energy-dissipation assumptions hold when moving from simulation to real flight.