A Time-Sweeping Approach for Determining Shortest Paths in a Dynamic, 2-D Environment with Multiple, Moving Goals

In this paper we study the problem of determining optimal paths in a dynamic, 2-D environment. We present a novel cell decomposition approach which generates optimal paths based on a number of di erent optimality criteria, including time-optimal, distance-optimal (shortest paths), and costoptimal paths based on a combination of time and distance. After mapping the dynamic, 2-D environment to a static, 3-D workspace, we propagate a path planning wave through the workspace to obtain distance transform values in an accurate and e cient manner. Our approach uses a computational geometry technique for sweeping a 3-D space with a plane, called time-sweeping. Furthermore, our approach allows us to generate these optimal paths much more e ciently than could be obtained with traditional shortest path planning algorithms.