Robot Coverage Path planning for general surfaces using quadratic differentials

Robot Coverage Path planning (i.e., the process of providing full coverage of a given domain by one or multiple robots) is a classical problem in the field of robotics and motion planning. The goal of such planning is to provide nearly full coverage while also minimize duplicately visited area. In this paper, we focus on the scenario of path planning on general surface, including planar domains with complex topology, complex terrain, and general surface in 3D space. Our approach described in this paper adopts a natural, intrinsic and global parametrization of the surface for robot path planning, namely the holomorphic quadratic differentials. We give each point on the surface a uv-coordinates naturally represented by a complex number, except for a small number of zero points (singularities). We show that natural, efficient robot paths can be obtained by using such coordinate systems. The method is based on intrinsic geometry and thus can be adapted to general surface exploration in 3D.