使用活动角自动进行避碰几何证明
Automating Geometric Proofs of Collision Avoidance with Active Corners
摘要：
避免障碍物与汽车、机器人或飞机等车辆之间的碰撞对于自动化和自主性的发展至关重要。为了简化问题，许多避碰算法和证明将车辆视为质点，尽管实际车辆不是点。本文考虑了一个具有非零面积的凸多边形车辆沿二维轨迹运动的问题。我们推导出一个易于检查的，无量化器的公式来检查是否有一个给定的障碍物将碰撞的车辆上移动的规划轨迹。我们将我们的方法应用到两个案例研究的飞机防撞，并研究其性能。
英文摘要：
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.
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