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.

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