Trajectory generation for quadrotors with limited field-of-view sensors has numerous applications such as aerial exploration, coverage, inspection, videography, and target tracking. Most previous works simplify the task of optimizing yaw trajectories by either aligning the heading of the robot with its velocity, or potentially restricting the feasible space of candidate trajectories by using a limited yaw domain to circumvent angular singularities. In this paper, we propose a novel \textit{global} yaw parameterization method for trajectory optimization that allows a 360-degree yaw variation as demanded by the underlying algorithm. This approach effectively bypasses inherent singularities by including supplementary quadratic constraints and transforming the final decision variables into the desired state representation. This method significantly reduces the needed control effort, and improves optimization feasibility. Furthermore, we apply the method to several examples of different applications that require jointly optimizing over both the yaw and position trajectories. Ultimately, we present a comprehensive numerical analysis and evaluation of our proposed method in both simulation and real-world experiments.

翻译：受限视场传感器四旋翼飞行器的轨迹生成在诸如空中探索、覆盖、巡检、摄影及目标追踪等多种应用中具有重要作用。以往大多数研究通过将机器人航向与其速度对齐来简化偏航轨迹优化任务，或通过限制偏航域以避免角度奇异性，从而可能缩小候选轨迹的可行空间。本文提出一种新颖的全局偏航参数化方法用于轨迹优化，该方法允许根据底层算法需求实现360度偏航变化。通过引入辅助二次约束并将最终决策变量转换为所需的状态表示，该方法有效规避了固有奇异性。此方法显著减少了所需控制代价，并提高了优化可行性。此外，我们将该方法应用于需要同时优化偏航与位置轨迹的多种不同应用实例。最后，我们在仿真和真实世界实验中进行了全面的数值分析与评估。