We present an optimal algorithm for determining a time-minimal rectilinear path among transient rectilinear obstacles. An obstacle is transient if it exists only for a specific time interval, i.e., it appears and then disappears at specific times. Given a point robot moving with bounded speed among non-intersecting transient rectilinear obstacles and a pair of points (s, d), we determine a time-minimal, obstacle-avoiding path from s to d. Our algorithm runs in \(\varTheta (n \log n)\) time, where n is the total number of vertices in the obstacle polygons. The main challenge in solving this problem arises when the robot may be required to wait for an obstacle to disappear, before it can continue moving towards its destination. Our algorithm builds on the continuous Dijkstra paradigm, which simulates propagating a wavefront from the source point. We also present an \(O(n^2 \log n)\) time algorithm for computing the Euclidean shortest path map among transient polygonal obstacles in the plane. This decreases the time complexity of the existing algorithm (Fujimura, in: Proceedings 1992 IEEE international conference on robotics and automation, vol 2, pp 1488–1493, 1992. https://doi.org/10.1109/ROBOT.1992.220041) by a factor of n. The shortest path map can be preprocessed for point location, after which a shortest path query from s to any point d can be answered in time \(O(\log n + k)\) where, k is the number of edges in the path.

我们提出了一种确定瞬态直线障碍物中时间最小直线路径的最佳算法。如果障碍物仅在特定的时间间隔内存在，那么它就是短暂的，即障碍物在特定的时间出现然后消失。给定一个点机器人在非相交的瞬态直线障碍物和一对点（s，  d）之间以有限的速度运动，我们确定了从s到d的最小时间，避免障碍的路径。我们的算法以\（\ varTheta（n \ log n）\）时间运行，其中n是障碍物多边形中的顶点总数。当可能需要机器人等待障碍物消失之后，它才能继续向目的地移动，这是解决此问题的主要挑战。我们的算法建立在连续的Dijkstra范式的基础上，该范式模拟从源点传播波前。我们还提出了一种\（O（n ^ 2 \ log n）\）时间算法，用于计算平面中瞬态多边形障碍物之间的欧几里德最短路径图。这样可以减少现有算法的时间复杂性（Fujimura，摘自：Proceedings 1992 IEEE国际机器人技术和自动化会议，第2卷，第1488–1493页，1992年。https：//doi.org/10.1109/ROBOT.1992.220041）。n的因数。可以对最短路径图进行预处理以进行点定位，然后可以在时间\（O（\ log n + k）\）中回答从s到任意点d的最短路径查询，其中，k是路径中的边数路径。