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借鉴自然界流水避石现象,提出一种基于流体计算的无人机(UAV)三维(3D)航路规划方法。首先介绍了球心位于坐标原点时,球形障碍三维绕流问题的解析解。之后采用旋转平移矩阵与流线数据叠加方法生成了任意位置多障碍同时存在的三维流线。为验证解析解的有效性同时给出该方法基于数值模拟的计算过程,对适合无人机三维航路规划的流体模型和数值求解方法进行了分析,并给出了通过数值模拟求解航路的方法。最后,根据无人机机动约束对流线进行处理得到可飞航路,将航路长度、纵向和横侧向机动次数作为子目标函数对航路进行综合评价。仿真结果表明:解析法航路规划中,圆球障碍的地形建模简单计算量小,航路集中在由起点至终点的航路带间;数值法航路规划适合障碍分布复杂的地形,航路分布于规划空间中。这两种方法的航路平滑,能够满足无人机飞行约束,航路具有绕流意义的最优性,可以避免势场法的局部极小问题,并且可以提供多条备选航路。
Drawing on the phenomena of flowing water and avoiding stone in nature, this paper proposes a three-dimensional (UAV) route planning method based on fluid calculation. Firstly, the analytic solution of three-dimensional flow around a spherical obstacle is introduced when the center of the sphere is located at the origin of coordinates. After that, the three-dimensional streamline with multi-obstacle at any position is generated by using the method of rotational translation matrix and streamline data superposition. In order to verify the validity of the analytical solution and to give the calculation process of the method based on numerical simulation, the fluid model and numerical solution method suitable for UAV 3D route planning are analyzed and the method of solving the route by numerical simulation is given. Finally, according to the UAV maneuver constraint, the flight path is processed to get the flightable route, and the route length is evaluated as the sub-objective function by the route length, longitudinal and transverse maneuvering times. The simulation results show that in the analytic route planning, the terrain modeling of the ballistic barrier has a small amount of calculation and the route is concentrated in the route zone from the start point to the end point. The numerical route planning is suitable for the terrain with complicated obstacles, and the route is distributed in the planning space in. The two methods have smooth routes, which can meet the flight constraints of UAVs. The routes have the optimality of bypassing flow, avoiding the local minimum problem of potential field method and providing multiple alternate routes.