Optimal competitive online ray search with an error-prone robot

TL;DR

This paper investigates optimal strategies for a blind robot searching for a door along a wall, accounting for movement errors, and proposes strategies that outperform the traditional doubling approach under error conditions.

Contribution

It introduces new optimal competitive strategies for error-prone robot search problems, extending the classic doubling strategy to scenarios with movement inaccuracies.

Findings

Optimal strategies depend on the error model used.

The proposed strategies outperform the classic doubling strategy under errors.

Analysis techniques are adaptable to various error models.

Abstract

We consider the problem of finding a door along a wall with a blind robot that neither knows the distance to the door nor the direction towards of the door. This problem can be solved with the well-known doubling strategy yielding an optimal competitive factor of 9 with the assumption that the robot does not make any errors during its movements. We study the case that the robot's movement is erroneous. In this case the doubling strategy is no longer optimal. We present optimal competitive strategies that take the error assumption into account. The analysis technique can be applied to different error models.