Power in Numbers: Primitive Algorithm for Swarm Robot Navigation in Unknown Environments

TL;DR

This study proposes a simple navigation algorithm for traversing unknown environments by utilizes the number of swarm robots and mathematically validate the proposed navigation algorithm, present numerical simulations based on the potential field method, and conduct experimental demonstrations using developed robots based on the sound fields for navigation.

Abstract

Recently, the navigation of mobile robots in unknown environments has become a particularly significant research topic. Previous studies have primarily employed real-time environmental mapping using cameras and LiDAR, along with self-localization and path generation based on those maps. Additionally, there is research on Sim-to-Real transfer, where robots acquire behaviors through pre-trained reinforcement learning and apply these learned actions in real-world navigation. However, strictly the observe action and modelling of unknown environments that change unpredictably over time with accuracy and precision is an extremely complex endeavor. This study proposes a simple navigation algorithm for traversing unknown environments by utilizes the number of swarm robots. The proposed algorithm assumes that the robot has only the simple function of sensing the direction of the goal and the relative positions of the surrounding robots. The robots can navigate an unknown environment by simply continuing towards the goal while bypassing surrounding robots. The method does not need to sense the environment, determine whether they or other robots are stuck, or do the complicated inter-robot communication. We mathematically validate the proposed navigation algorithm, present numerical simulations based on the potential field method, and conduct experimental demonstrations using developed robots based on the sound fields for navigation.

Figures (21)

• Figure 1: Diagram of problem definition for unknown environment navigation. The robot moves from the start point to the goal on a 2D plane where several areas through which the robot cannot move (impassable zones) randomly. However, we assume the existence of at least one path from the start point to the goal. Note that the robot has no prior awareness of the impassable zones.
• Figure 2: Schematic diagram of the proposed algorithm, BYCOMS (BYpassing COmpanions Method for Swarm robots navigation). The robots move toward the goal one at a time. The first robot gets stuck at the boundary of the impassable zone, and the following robots bypass the stuck robot and head toward the goal.
• Figure 3: Schematic diagram of the mathematical formulation of the guidance problem. In a 2D plane, the start point is denoted as $S$, the goal as $G$, and the impassable zone for robot $i$ as a closed region $R_i~(i=1,\cdots,n)$. The position of robot $i~(i=1,\cdots,N)$ is represented by $r_i$, and when robot $i$ gets stuck, it generates a circular closed region with radius $\epsilon$, denoted as $O_i$. The path that a robot can take from the start to the goal is represented by $Q$, while the path $P_i$ is the route for robot $i$ that avoids passing through the regions $O_{i-1}, O_{i-2}, \cdots$, generated by the previous robots.
• Figure 4: Relationship between the passable path $Q$ from the start point to the goal, the minimum distance $l$ from the stuck robot, and the robot's circumferential radius $\epsilon$. By setting $\epsilon$ such that $\epsilon < l$, the path $Q$ is maintained.
• Figure 5: When robot $i$ gets stuck, a non-zero length boundary line $C$ is newly included in $O$.