From theory to flight: formation flight, crosswind navigation and autonomous aerobatics on real drones.
Fixed-wing drones are efficient but hard to coordinate: they cannot stop, and their airspeed is tightly bounded. I implement and test our algorithms onboard real aircraft running Palomo, our modified version of the open-source Paparazzi autopilot (not yet public) - distributed formation flight that needs no speed actuation, guidance that keeps the trajectory in strong crosswinds, and fully autonomous aerobatics with guiding vector fields on SO(3).
This paper develops a singularity-free guiding vector field (SF-GVF) for path following on the special orthogonal group SO(3). First, we lift the Euclidean SF-GVF construction to SO(3), integrating the augmented-state approach with the intrinsic Lie-group geometry and obtaining a closed-form geometric guidance law whose integral curves converge to a designer-specified attitude path. The field is defined on a dense open subset of SO(3), excluding only the measure-zero antipodal set — a manifestation of the topological obstruction to continuous global stabilization on SO(3). The construction requires no per-step optimization and produces a control input intrinsically in mathfrakso(3) as body angular rates. Second, we formalize the progression behavior along the path as a designer-supplied function nu(xi), promoting the parametric speed from an implicitly resolved degree of freedom to a first-class design specification. In contrast to the Euclidean condition v = 0, which excludes vehicles with minimum-speed constraints, the corresponding condition omega = 0 on SO(3) is physically admissible for most platforms with active attitude control, making the progression behavior a design freedom structurally available on SO(3) but absent in the Euclidean setting. The framework's structural results are established under a bi-invariant Riemannian metric and hold uniformly across choices of path, progression, and Lyapunov gain. The framework is illustrated in simulation on self-intersecting paths under both constant and point-convergence progression behaviors.
The autonomous formation flight of fixed-wing drones is hard when the coordination requires the actuation over their speeds since they are critically bounded and aircraft are mostly designed to fly at a nominal airspeed. This paper proposes an algorithm to achieve formation flights of fixed-wing drones without requiring any actuation over their speed. In particular, we guide all the drones to travel over specific paths, e.g., parallel straight lines, and we superpose an oscillatory behavior onto the guiding vector field that drives the drones to the paths. This oscillation enables control over the average velocity along the path, thereby facilitating inter-drone coordination. Each drone adjusts its oscillation amplitude distributively in a closed-loop manner by communicating with neighboring agents in an undirected and connected graph. A novel consensus algorithm is introduced, leveraging a non-negative, asymmetric saturation function. This unconventional saturation is justified since negative amplitudes do not make drones travel backward or have a negative velocity along the path. Rigorous theoretical analysis of the algorithm is complemented by validation through numerical simulations and a real-world formation flight.
