# Robot Coverage Path Planning for General Surfaces Using Quadratic Differentials

arXiv: https://arxiv.org/abs/1701.07549 · HTML: https://mlsanity.com/paper/1701.07549/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2017.

## Built on by (most cited first, 3 of 3)

- [Reinforcement Learning-Based Coverage Path Planning with Implicit Cellular Decomposition](https://mlsanity.com/paper/2110.09018/) (2021)
- [An Efficient Drifters Deployment Strategy to Evaluate Water Current Velocity Fields](https://mlsanity.com/paper/2301.04216/) (2023)
- [Coverage Path Planning: Classical Foundations, Recent Advances, and Future Directions](https://mlsanity.com/paper/2607.10649/) (2026)

## Abstract (arXiv)

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.