Operating unmanned aerial vehicles (UAVs) in complex environments that feature dynamic obstacles and external disturbances poses significant challenges, primarily due to the inherent uncertainty in such scenarios. Additionally, inaccurate robot localization and modeling errors further exacerbate these challenges. Recent research on UAV motion planning in static environments has been unable to cope with the rapidly changing surroundings, resulting in trajectories that may not be feasible. Moreover, previous approaches that have addressed dynamic obstacles or external disturbances in isolation are insufficient to handle the complexities of such environments. This paper proposes a reliable motion planning framework for UAVs, integrating various uncertainties into a chance constraint that characterizes the uncertainty in a probabilistic manner. The chance constraint provides a probabilistic safety certificate by calculating the collision probability between the robot's Gaussian-distributed forward reachable set and states of obstacles. To reduce the conservatism of the planned trajectory, we propose a tight upper bound of the collision probability and evaluate it both exactly and approximately. The approximated solution is used to generate motion primitives as a reference trajectory, while the exact solution is leveraged to iteratively optimize the trajectory for better results. Our method is thoroughly tested in simulation and real-world experiments, verifying its reliability and effectiveness in uncertain environments.

翻译：在具有动态障碍物和外部扰动的复杂环境中操作无人机（UAV）面临重大挑战，这主要源于此类场景下固有的不确定性。此外，不精确的机器人定位和建模误差进一步加剧了这些挑战。针对静态环境下无人机运动规划的现有研究无法应对快速变化的环境，导致生成的轨迹可能不可行。同时，以往单独处理动态障碍物或外部扰动的方法不足以应对此类环境的复杂性。本文提出了一种可靠的无人机运动规划框架，将各种不确定性整合为机会约束，以概率方式表征不确定性。该机会约束通过计算机器人高斯分布的前向可达集与障碍物状态之间的碰撞概率，提供概率安全保证。为降低规划轨迹的保守性，我们提出了碰撞概率的紧上界，并对其进行了精确解和近似解的评估。近似解用于生成运动基元作为参考轨迹，而精确解则用于迭代优化轨迹以获得更优结果。我们的方法在仿真和真实实验中进行了全面测试，验证了其在不确定环境中的可靠性和有效性。