Avoiding collisions between obstacles and vehicles such as cars, robots or aircraft is essential to the development of automation and autonomy. To simplify the problem, many collision avoidance algorithms and proofs consider vehicles to be a point mass, though the actual vehicles are not points. In this paper, we consider a convex polygonal vehicle with nonzero area traveling along a 2-dimensional trajectory. We derive an easily-checkable, quantifier-free formula to check whether a given obstacle will collide with the vehicle moving on the planned trajectory. We apply our method to two case studies of aircraft collision avoidance and study its performance.
翻译:为简化问题,许多避免碰撞的算法和证据都认为车辆是一个点质量,尽管实际车辆不是点;在本文件中,我们认为是一条非零区域、沿二维轨道飞行的锥形多边形车辆;我们得出一个容易检查、无限定的公式,以检查某一障碍是否会与移动在计划轨道上的车辆相撞。我们采用的方法是,对避免飞机碰撞的两个案例研究进行研究,并研究其性能。