Safe Periodic Trochoidal Paths for Fixed-Wing UAVs in Confined Windy Environments

TL;DR

The paper tackles safe terminal loitering for fixed-wing UAVs in confined, windy terrain by introducing a wind-invariant set of periodic trochoidal paths and a minimum-extent formulation. It develops analytic results for some path families (RSR/LSL) and numerical methods for others (RSL/LSR, RLR/LRL), then proposes a switching strategy to minimize the worst-case path extent across wind conditions, reducing the required radius from $\pi R_{min}$ to about $1.62R_{min}$. The approach yields up to $10$-fold increases in reachable locations in mountainous terrain and expands safe regions compared to conservative baselines. These contributions offer a practical framework for wind-robust planning of fixed-wing UAVs in challenging environments, with future work focusing on robust tracking and integrated path planning under wind variability.

Abstract

Due to their energy-efficient flight characteristics, fixed-wing type UAVs are useful robotic tools for long-range and duration flight applications in large-scale environments. However, flying fixed-wing UAV in confined environments, such as mountainous regions, can be challenging due to their limited maneuverability and sensitivity to uncertain wind conditions. In this work, we first analyze periodic trochoidal paths that can be used to define wind-aware terminal loitering states. We then propose a wind-invariant safe set of trochoidal paths along with a switching strategy for selecting the corresponding minimum-extent periodic path type. Finally, we show that planning with this minimum-extent set allows us to safely reach up to 10 times more locations in mountainous terrain compared to planning with a single, conservative loitering maneuver.

Figures (9)

• Figure 1: Overview of the safe valid set and example of periodic paths given the wind direction. Our approach defines a wind invariant safe periodic set which allow the vehicle to stay within the region given any wind speed and wind direction.
• Figure 2: LSL/RSR periodic trochoidal paths with different wind ratios, tangent to the (arbitrary) initial state $\bm{x}_0 = (0.0, 0.0, 0.1\pi$). Wind direction is marked as grey arrows.
• Figure 3: LSR/RSL periodic trochoidal paths with different wind ratios, tangent to the (arbitrary) initial state $\bm{x}_0 = (0.0, 0.0, 0.1\pi)$. Wind direction is marked as grey arrows.
• Figure 4: RLR/LRL-type periodic trochoid paths with different wind ratios, tangent to the (arbitrary) initial state $\bm{x}_0 = (0.0, 0.0, 0.4\pi)$. There are no feasible paths for higher wind ratios. The wind direction is marked as grey arrows.
• Figure 5: Evolution of RSR/LSL periodic trochoidal paths with different wind ratios. The radius of maximum extent for the minimum-extent wind-invariant set is $\pi R$.

Theorems & Definitions (4)

• Definition V.1: Radius of Extent
• Definition V.2: Minimum-Extent Wind-Invariant Safe Set
• Proposition V.1: Existence of Figure Eight
• proof