# A criterion for assessing obstacle-induced environmental complexity in multi-robot coverage exploration

## TL;DR

This paper introduces a new way to measure how complex an environment is for multi-robot exploration based on obstacles.

## Contribution

A novel criterion for quantifying obstacle-induced environmental complexity in multi-robot coverage exploration is proposed.

## Key findings

- The criterion assigns a numerical value between 0 and 1 to represent environmental complexity.
- The metric is independent of robot hardware and algorithm specifics, allowing for fair comparisons.
- Statistical analysis confirms the effectiveness of the proposed criterion.

## Abstract

In many applications, such as coverage exploration and search and rescue missions, accurately assessing environmental complexity is valuable for performance evaluation and algorithm adjustments. Despite this, in the context of multi-robot systems, quantifying environmental complexity caused by obstacles when using autonomous ground robots presents significant challenges. This research proposes a criterion for measuring environments’ obstacle-induced complexity in the context of autonomous multi-robot coverage exploration. The criterion rates the environment’s complexity numerically, where 0 denotes obstacle-free setups, and the value increases with obstacle-related effects, reaching a maximum of 1, representing the highest measurable complexity for the criterion. The proposed criterion is independent of robot hardware specifications and algorithm-specific aspects. Furthermore, it is independent of the environment’s size and the ratio of the area occupied by obstacles, enabling comparisons across various environments. Statistical analysis shows the metric performs well both on average and in single-case comparisons.