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Robot Coverage Path planning (i.e., provide full coverage of a given domainby one or multiple robots) is a classical problem in the field of robotics andmotion planning. The goal is to provide nearly full coverage while alsominimize duplicately visited area. In this paper we focus on the scenario ofpath planning on general surfaces including planar domains with complextopology, complex terrain or general surface in 3D space. The main idea is toadopt a natural, intrinsic and global parametrization of the surface for robotpath planning, namely the holomorphic quadratic differentials. Except for asmall number of zero points (singularities), each point on the surface is givena uv-coordinates naturally represented by a complex number. We show thatnatural, efficient robot paths can be obtained by using such coordinatesystems. The method is based on intrinsic geometry and thus can be adapted togeneral surface exploration in 3D.

Robot Coverage Path Planning for General Surfaces Using Quadratic Differentials