Trajectory Planning and Control for Differentially Flat Fixed-Wing Aerial Systems

TL;DR

This paper tackles real-time trajectory planning and control for fixed-wing UAVs with non-holonomic, coordinated-flight dynamics. It leverages differential flatness to map flat outputs to full state-and-input trajectories and uses online Bernstein-polynomial trajectory optimization, formulated as a convex quadratic program to minimize jerk while enforcing velocity, acceleration, and curvature constraints. The approach supports continuous replanning, enabling dynamically feasible, curvature-bounded paths over long ranges, and is validated through both PX4 SITL-Gazebo simulations and real outdoor flights under wind disturbances. The results demonstrate accurate trajectory tracking, scalable onboard computation, and a practical path to real-world deployment for fixed-wing platforms.

Abstract

Efficient real-time trajectory planning and control for fixed-wing unmanned aerial vehicles is challenging due to their non-holonomic nature, complex dynamics, and the additional uncertainties introduced by unknown aerodynamic effects. In this paper, we present a fast and efficient real-time trajectory planning and control approach for fixed-wing unmanned aerial vehicles, leveraging the differential flatness property of fixed-wing aircraft in coordinated flight conditions to generate dynamically feasible trajectories. The approach provides the ability to continuously replan trajectories, which we show is useful to dynamically account for the curvature constraint as the aircraft advances along its path. Extensive simulations and real-world experiments validate our approach, showcasing its effectiveness in generating trajectories even in challenging conditions for small FW such as wind disturbances.

Figures (8)

• Figure 1: Continuous, online trajectory replanning between multiple waypoints during a sample real-world flight.
• Figure 2: Frames' visualization and convention. The Velocity frame $\mathcal{V}$ differs from the Body frame $\mathcal{B}$ by the angles $\alpha$ and $\beta$, whereas $\mathcal{I}$ defines the Inertial fixed frame.
• Figure 3: Architecture overview. The trajectory generated by our planner is forwarded to the Differential Flatness Block, which computes the desired inputs to control the attitude and the longitudinal thrust of the simulated or real robot.
• Figure 4: Planned Mission: Two loiter trajectories (yellow) and centered in $L_1$ and $L_2$ are linked together by two Bernstein trajectories passing through the set of waypoints $S_{\mathcal{B}_1} = [B_1, \dots, B_4]$ and $S_{\mathcal{B}_2} =[B_5, \dots, B_7]$ with a visualization of the replanning strategy (top right).
• Figure 5: The average optimization computation time $\bar{t}_{opt}$ increases linearly with the number of waypoints remaining unaffected by the trajectory length.