To greatly extend the capabilities of unmanned aerial vehicles, automation systems for the various piloting functions are being developed. However, the development of these auto-systems is not without challenges. One of these challenges is the ability to prove the robustness of an autonomous system against unpredicted events. For the navigation task, this means to prove that the system can recover safely after a deviation from the original plan. In a decoupled scheme where the planner generates a plan online and the controller executes the plan, it is difficult to prove the safety of a system exhaustively. Conversely, using a feedback motion plan generated off-line, it is possible to pre-verify and pre-approve a large number of cases simultaneously. Therefore, it is easier to prove system safety. In this work, this approach is utilized to integrate the guidance toward a target location or a target path with geofence avoidance and recovery for a fully autonomous fixed-wing aircraft. Our formulation extends the wavefront expansion to the case of vehicles having minimum turning radius constraints. The solution is suitable for both single goal missions and path following problems in presence of geofences that can have both convex and non-convex shape. The main novelties introduced in the proposed method are the followings: (1) path following in presence of obstacles having an arbitrary shape, (2) definition of a transition function for the rotation of the flow around the predefined path, (3) use of a Gaussian filter to smooth the vector field. Simulation and experimental results demonstrate the effectiveness of the proposed method.

中文翻译：

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在最小转弯半径约束下用于二维导航的离散矢量场

为了极大地扩展无人机的能力，正在开发用于各种驾驶功能的自动化系统。但是，这些自动系统的开发并非没有挑战。这些挑战之一是要证明自主系统对意外事件的鲁棒性。对于导航任务，这意味着证明系统可以在偏离原始计划后安全恢复。在计划者在线生成计划并且控制器执行计划的分离方案中，很难详尽地证明系统的安全性。相反，使用离线生成的反馈运动计划，可以同时预验证和批准大量案例。因此，更容易证明系统安全性。在这项工作中 这种方法被用于将指向目标位置或目标路径的导航与地理围栏避免和完全自主固定翼飞机的恢复结合起来。我们的公式扩展了波前扩展到具有最小转弯半径约束的车辆的情况。该解决方案既适用于单目标任务，又适用于存在既可以具有凸形也可以具有非凸形的地理围栏的路径跟踪问题。所提出的方法中引入的主要新颖性如下：（1）在存在具有任意形状的障碍物的情况下遵循的路径；（2）定义用于绕预定路径旋转的流的转换函数；（3）使用高斯滤波器以平滑矢量场。仿真和实验结果证明了该方法的有效性。