A robust method for fast exploration of environments with moving obstacles

Abstract

Exploring environments with static and moving obstacles is a fundamental problem with numerous applications in physics and engineering. The Fast Marching Method (FMM) offers a computationally efficient numerical solution to the Eikonal equation, which describes a wavefront propagating through a medium. The FMM is effective in media with static obstacles, but, as we show, it fails in the presence of moving ones. We introduce a novel, robust method for wave exploration of environments of arbitrary dimension and complexity, and prove its convergence numerically. The method accurately handles both dynamic and static obstacles while preserving the computational efficiency of the FMM, ensuring a fast and reliable global search for collisionfree trajectories. The algorithm can also serve as an interception strategy for catching a moving target among many obstacles.