Ten Problems in Geobotics

TL;DR

This paper reviews ten challenging problems in Geobotics, highlighting the geometric algorithmic difficulties in robotics and automation, and emphasizing the need for new techniques with quality guarantees.

Contribution

It identifies and discusses ten key open problems at the intersection of robotics and computational geometry, emphasizing their complexity and the gap in existing algorithmic solutions.

Findings

Most existing algorithms lack quality guarantees for these problems.

Addressing these problems can improve understanding of computation in robotics.

Many problems remain open and challenging for future research.

Abstract

Robots sense, move and act in the physical world. It is therefore natural that algorithmic problems in robotics and automation have a geometric component, often central to the problem. Below we review ten challenging problems at the intersection of robotics and computational geometry -- let's call this intersection Geobotics. What is common to most of these problems is that the prevalent algorithmic techniques used in robotics do not seem suitable for solving them, or at least do not suggest quality guarantees for the solution. Solving some of them, even partially, can shed light on less well-understood aspects of computation in robotics.