Safe Periodic Trochoidal Paths for Fixed-Wing UA Vs in Confined Windy Environments Jaeyoung Lim 1, David Rohr 1, Thomas Stastny 1, Roland Siegwart 1 Abstract -- Due to their energy-efficient flight characteristics, fixed-wing type uncrewed aerial vehicles (UA Vs) are useful robotic tools for long-range and duration flight applications in large-scale environments. However, flying fixed-wing UA V 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 . I. INTRODUCTION Uncrewed aerial vehicles (UA Vs) have become crucial tools for information-gathering applications, such as surveying and inspection [1], search and rescue [2], and environment monitoring [3], [4]. For large-scale coverage or long-range applications, fixed-wing type UA Vs are preferred over rotary-wing type systems due to their high endurance and speed. While the wing-borne aerodynamic lift enables energy-efficient flight, it also poses challenges for operating safely.

The distributed consensus protocol (CP) presented in [1] enables a connected swarm of agents, modelled as single integrators, to trace repeated geometric paths in both 2-dimensional (2-D) and 3-D spaces. The parameters of the protocol, the connection topology of the swarm, and the initial positions of the agents define the characteristics of the generated paths. The applications of agents, or robots, tracing such paths have been well identified in the literature, for example, persistent coverage and surveillance of a region, guarding an asset, and target detection; the cited references provide an exhaustive list. In such applications, the issues of collisions between robots, communication range, feasibility of path tracking, and time taken to trace the path, have to be considered explicitly. Further, in applications involving guarding a specific region or an asset, the path should be defined by making the asset the centre of rotation (CoR). In this paper, the protocol is designed for a connected swarm of 3 unicycle-robots of finite size moving in a 2-D Cartesian space; the use of 3 robots leads to the generation of trochoidal paths, where each robot traces a unique trochoid. For a given communication topology, design of the trochoidal paths involves the selection of 3 scalars for the CP, a positive integer,k, with magnitudek 2, and the initial coordinates of the 3 robots inX Y space, thus leading to a total of 10 design variables.