A New Application of Discrete Morse Theory to Optimizing Safe Motion Planning Paths

We present a novel method for extracting geometric and topological features from a robot's configuration space. To accomplish this, we define a discrete Morse function on the Vietoris-Rips simplicial complex to identify critical points on the surface of obstacles present. These critical points serve as waypoints for determining feasible bounds near an identified obstacle. This work builds on previous work that provides a method to approximate the number of samples required to generate pathways. Our results achieve near-optimal paths with a low computation time and reduced path distance in this work. We conduct experiments in different environments and with various robots, including the Kuka YouBot and PR2 robots in simulation, and demonstrate the performance gains compared to state-of-the-art methods.