Mean-Shift Theory and Its Applications in Swarm Robotics: A New Way to Enhance the Efficiency of Multi-Robot Collaboration

TL;DR

This article presents a tutorial review on recent advances in assignment-free collaboration of robot swarms, focusing on the problem of shape formation, and discusses three important applications of the mean-shift exploration strategy, including precise shape formation, area coverage formation, and maneuvering formation.

Abstract

Swarms evolving from collective behaviors among multiple individuals are commonly seen in nature, which enables biological systems to exhibit more efficient and robust collaboration. Creating similar swarm intelligence in engineered robots poses challenges to the design of collaborative algorithms that can be programmed at large scales. The assignment-based method has played an eminent role for a very long time in solving collaboration problems of robot swarms. However, it faces fundamental limitations in terms of efficiency and robustness due to its unscalability to swarm variants. This article presents a tutorial review on recent advances in assignment-free collaboration of robot swarms, focusing on the problem of shape formation. A key theoretical component is the recently developed \emph{mean-shift exploration} strategy, which improves the collaboration efficiency of large-scale swarms by dozens of times. Further, the efficiency improvement is more significant as the swarm scale increases. Finally, this article discusses three important applications of the mean-shift exploration strategy, including precise shape formation, area coverage formation, and maneuvering formation, as well as their corresponding industrial scenarios in smart warehousing, area exploration, and cargo transportation.

Figures (6)

• Figure 1: An overview of mean-shift collaboration. (a) Precise shape formation. (b) Area coverage formation. (c) Maneuvering formation.
• Figure 2: An illustration of the mean-shift process.
• Figure 3: Results of precise formation. (a) Comparison between the mean-shift method Zhang2024RAL and assignment-based methods Chu2023TASEWang2020TRO. There are 300 robots forming a shape "G". The definitions of convergence rate and convergence time refer to Zhang2024RAL. Another metric is the average distance traveled by all the robots from the initial moment to the convergence moment. (b) Simulation of 32 robots transferring products from picking stations to work stations. The parameters of (a) and (b) are listed as: $r_{\rm sense}=1.3$, $v_{\rm max}=2$, $c_1=1$, $c_2=0.4$, $\sigma=0.22$, $\kappa_1=3$, $\kappa_2=10$, and $\kappa_3=1$. (c) Experiment results of 10 real robots forming different shapes in a sequence. The parameters can be found in Zhang2024RAL.
• Figure 4: Results of coverage formation. (a) Experiment results of 50 robots forming a snowflake shape. The definition of coverage rate refers to Sun2023NC. (b) Comparison between the mean-shift method Sun2023NC and the assignment-based method Wang2020TRO. There are 300 robots forming a shape "M". The definitions of convergence rate and convergence time refer to Sun2023NC. (c) Experiment results of 50 robots forming a starfish shape. Even as robots are sequentially removed from the shape, the rest of the robots can form a new starfish shape. (d) Experiment results of 36 robots exploring a complex maze without getting deadlocks at any corners. The simulation parameters of (b) are listed as: $r_{\rm sense}=1.3$, $v_{\rm max}=2$, $q_{\varrho_o}=[11.1, 11.1]^{\rm T}$, $\sigma_1=2$, $\sigma_2=10$, $\kappa_2=4$, and $\kappa_3=20$. The experiment parameters of (a), (c), and (d) can be found in Sun2023NC.
• Figure 5: Results of maneuvering formation. (a) Simulation results of 128 robots tracking moving shapes in a sequence. (b) Experiment results of 8 robots forming different shapes, including wedge, rectangle, line, and semi-enclosed shapes, in a sequence. (c) Cargo transportation by a group of 8 real robots. The simulation and experiment parameters are consistent with those in Figure \ref{['Fig_coverage']}. The negotiation parameters are listed as: $c_1=c_2=c_3=c_4=1.6$, and $\sigma=0.8$.

Theorems & Definitions (2)

• Definition 1: Profile
• Definition 2: Sample Mean