一种针对无人机定点投放问题的规划算法

A Planning Algorithm for the Fixed-Point Delivery Problem of Unmanned Aerial Vehicles

摘要: 本文旨在研究无人机在高空定点投放物品时，不能飞到目标正上方投放，而是要适当提前投放才能命中目标，投放后由于惯性、阻力等影响，会做类平抛运动，所以要适当提前投放才能命中目标。我们分析了无人机投放距离与飞行速度、飞行高度、空气阻力等因素之间的关系，以及无人机在发射爆炸物时俯冲较角度、飞行速度、发射速度对等因素对于命中精度的影响，并通过数学建模带入数据计算给出最优策略。我们建立数学模型，描述出无人机投放距离与无人机飞行高度、飞行速度、空气阻力等之间的关系。明确假设条件，无人机以平行于水平面的方式飞行，这意味着我们可以将无人机的运动分解为水平面和竖直方向上的运动。通过类平抛运动与受力分析。之后确定物理模型：考虑无人机在发射爆炸物前的飞行轨迹，可以将其看作是一个抛体运动。根据牛顿第二定律和重力加速度的定义，可以列出抛体运动的方程组。确定目标函数和约束条件：目标函数可以设置为无人机发射距离与目标的直线距离之间的差值的平方。最后，需要建立一个稳定性与命中精度之间的关系模型，还需要在一定条件下，给出无人机的最优飞行姿态调整策略。建立稳定性与命中精度之间的关系模型，无人机的飞行稳定性可以通过无人机的姿态角来描述。在无人机的飞行过程中，姿态角不断变化，因此需要考虑无人机姿态角的变化对命中精度的影响。

Abstract: The purpose of this paper is to study the UAV cannot fly to the target is directly above the delivery, but should be properly put in advance to hit the target, due to inertia, resistance and other effects, will do flat throwing motion, so it should be properly put in advance to hit the target. We analyzed the relationship between UAV delivery distance and flight speed, flight height, air resistance and other factors, as well as the impact of diving angle, flight speed and launch speed equivalent factors on the hit accuracy of the UAV when launching explosives, and brought the optimal strategy into the data calculation through mathematical modeling. We set up a mathematical model to describe the relationship between UAV delivery distance and UAV flying height, flying speed, air resistance, etc. The explicit assumption that the drone is flying parallel to the horizontal plane means that we can break down the drone’s motion into horizontal and vertical motions. The motion and force analysis were carried out. Then the physical model is determined: consider the flight path of the drone before launching the explosive, which can be regarded as a projectile motion. According to Newton’s second law and the definition of gravitational acceleration, the equations of projectile motion can be listed. Determine the objective function and constraints: The objective function can be set to the square of the difference between the launch distance of the drone and the straight-line distance of the target. Finally, it is necessary to establish a relationship model between stability and hit accuracy, and to give the optimal flight attitude adjustment strategy of UAV under certain conditions. The relationship model between the stability and the hit accuracy is established. The flight stability of UAV can be described by the attitude angle of UAV. During the flight of UAV, the attitude angle changes constantly, so it is necessary to consider the impact of the change of attitude angle on the hit accuracy of UAV.