# Robot Coverage Path Planning for General Surfaces Using Quadratic Differentials

## TL;DR

This paper introduces a novel surface parametrization method using quadratic differentials for robot coverage path planning on complex 3D surfaces, enabling efficient and intrinsic exploration.

## Contribution

It presents a new approach leveraging quadratic differentials for intrinsic surface parametrization to improve robot coverage path planning on general 3D surfaces.

## Key findings

- Efficient paths are generated using quadratic differentials.
- Method adapts to complex topologies and terrains.
- Intrinsic geometry-based approach enhances surface exploration.

## Abstract

Robot Coverage Path planning (i.e., provide 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 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 surfaces including planar domains with complex topology, complex terrain or general surface in 3D space. The main idea is to adopt a natural, intrinsic and global parametrization of the surface for robot path planning, namely the holomorphic quadratic differentials. Except for a small number of zero points (singularities), each point on the surface is given a uv-coordinates naturally represented by a complex number. 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.