# Multi-Robot Exploration Employing Harmonic Map Transformations
## 1 Introduction
### Related Works  
A vast array of methods have been suggested and implemented for autonomous exploration using a single robot. A well-studied and common approach is that of frontierbased methods. In [2], [PERSON] introduced the idea of frontier detection, i.e., the edges between explored and unknown areas, and then used a depth-first search to navigate to the frontier location, while using reactive obstacle avoidance. In [3], an improved algorithm is proposed for faster frontier detection. In [4], the authors eliminated the need for tuning in frontier clustering with the employment of a histogram. In recent years, artificial intelligence and particularly Deep Reinforcement Learning (DRL) has shown promising results in the field of exploration. Particularly, in [5], DRL is combined with frontier exploration to allow for the exploration of unknown cluttered environments, aiming for use in urban search and rescue missions. In [6], an algorithm that utilizes DRL is used to predict an efficient long-term visiting order for unexplored regions, obtaining knowledge from information derived from a training set of office blueprints. Another popular approach is using sampling-based algorithms to search and select areas to be explored. In [7], a method called UFOExplorer is proposed that continuously expands a dense undirected graph, optimized for fast and efficient exploration. Rapidly-exploring Random Tree (RRT) and its variants are mainstream among various sampling-based exploration methods. In [8], a novel method is presented where the robot is guided to the unexplored region using multiple RRTs, removing the requirement for frontier exploration. Artificial Potential Fields have been utilized in the field of robotic exploration, such as in [9; 10], where a harmonic potential field function is used for navigating to frontiers. Due to the clear advantages of employing multiple robots for exploration, most methods used in single robot exploration have been extended to multi-robot setups. In [11], [PERSON] first expanded the concept of frontier-based robotic exploration to multiple robots. In this method, each robot exchanged information with others but kept a local copy of its map to maintain robustness. In [12], a more sophisticated approach was taken for multi-robot exploration, as frontier target selection considered both cost and utility. In [13], a modified A* search algorithm for multi-agent exploration is presented that attempts to minimize the energy consumption during the exploration process. Similarly, the RRT approach has been extended to multi-robot systems as well. In [14], local and global RRT-based detectors are used for multi-robot exploration. Additionally, [15] proposes a novel frontier detection algorithm called Hybrid Multi-Strategy RRT to improve the efficiency and reliability of multi-robot exploration. Their method consists of an adaptive incremental distance strategy, a sub-region sampling strategy, and a greedy frontier-based exploration strategy. In [16], a decentralized and computationally efficient frontier allocation method favoring a well-balanced spatial distribution of robots in the environment was introduced. A wavefront propagation algorithm constructs Artificial Potential Fields used for the path planning process. In [17], multi-robot multi-target Potential Fields are used for exploration, an approach that eliminates local minima for multi-robot Artificial Potential Fields. In the same vein, artificial harmonic potential fields were employed in [18], leading to a reactive algorithm for autonomous exploration for multiple autonomous multi-rotor robots. In [19], a collaborative multi-robot exploration method is proposed. Utilizing Voronoi-based exploration strategies, each robot is assigned a target location for exploration. The robots then navigate to the target location with the use of a DRL collision avoidance algorithm. In [20], a Gaussian Process and relative localization belief information are used to generate a map and determine the unexplored region.