Introduction

Cooperative nest construction by social insects \cite{hansell2007built,invernizzi2019deconstructing} such as termites and wasps is common in biological kingdom, natural builders demonstrate significant degrees of cooperation ability and efficiency. These behaviors have highly heuristic meaning to collective construction of multi-agents system, which received more and more attention from scholars \cite{zhang2022aerial,petersen2019review}. It is worth noting that the self-assembly behavior of modular robots is also a special construction process of multi-agents.
Modular robot is a class of special robot, which is composed of several homogeneous or heterogeneous modules with certain drive and sensing ability \cite{holdcroft2022hybrid}. Through the combining and disassembling modules, modular robot can be organized into different structures with different functions to adapt to complex tasks and environments \cite{yang2022modular,zhang2020modular}. With the rapid development of aerospace technology, modular robot has begun to turn their attention to space exploration \cite{sayed2022modular,toglia2011cooperative}, such as building the adaptive and unmanned robotic system for lunar base. The special micro-gravity environment can help modular robot get rid of the limitations of module size on joint drive capability, which will make large-scale module movement and reconfiguration possible. At the same time, the complex space environment and diverse customizable tasks also make the advantages of modular robots useful. Therefore, we develop a novel modular robot named Space Module for the special space environment. Constrained by the payload capacity of spacecraft, Space Module is designed with a light and regular structure and is non-mobile. To reduce the failure rate of module, the complex mechanical structures are abandoned, and the electropermanent magnets are used for docking, communication and charging.
Self-assembly is one of the ways for modular robot to realize shape-shifting. The autonomous aggregation of dispersed, initially-detached modules into desired morphologies \cite{wei2012self} is similar to the cooperative nest construction of insects, with the subtle difference that the modules are both transporters and materials for construction. Compared to other schemes \cite{bie2019natural,gerbl2022self,luo2022adaptive}, self-assembly is not limited by system connectivity and the module number of current configurations. Therefore, considering the possible dilemmas suffered by robotic systems in unmanned operating environments, such as module separation due to impact or fall, autonomous disengagement and replacement of faulty modules, self-assembly is the preferred shape-shifting method for modular space robots.
Some results have been obtained for the research on self-assembly of modular robot. \cite{li2016response}  proposed a formation self-assembly method for Sambot modular robot, which can self-assemble a group of swarm robots into a single articulated structure; \cite{ercan2016design} presented a chain type, homogenous, mobile and modular multi-robot system (ULGEN), and used the mobility and sensors of modules to realize the self-assembly of desired configurations; \cite{wei2012self} proposed a directional self-assembly control model which utilized the seed module and docking module to perform the self-assembly experiments; \cite{rai2011self} proposed a suite of algorithms for REPLICATOR modular robot, including a reversible graph grammar and broadcast communication, which can drastically speed up self-assembly process. Noted that these methods are proposed based on mobile modules, which have full locomotion capability and can mobile independently. Hence, the self-assembly methods of mobile module are more like simplified path planning of multi-agents \cite{del2018toward}. However, the complex mobile mechanics of mobile modules will increase the redundancy of modular robot structures and reduce the robustness, which is not suitable for unmanned space work requirements. The research on self-assembly of non-mobile modules is almost non-existent, and the fundamental problem is the mobility of non-mobile modules. The design of self-assembly using external forces such as water and magnetism in \cite{zhu2013precision,yun2011optimal,haghighat2017automatic} is still a long way from producing application value.
Meta-modular method is an important breakthrough in modular robot self-reconfiguration and flow motion proposed to give non-mobile modules the ability to move. Meta-module is an intelligent unit of a small group of basic modules, and the locomotion ability of meta-modules is related to the number of modules and docking mode. \cite{kawano2019distributed} studied a reconfiguration algorithm for heterogeneous lattice modular robots with linear operation time cost based on a 2x2x2 cubic meta-module; \cite{parada2021new} proposed a new meta-module design for two important classes of modular robots, which can perform the scrunch, relax and transfer moves that are necessary in any tunneling-based reconfiguration algorithm; \cite{brandt2007new} presented a 2D meta-module for the ATRON robot, which simplifies the motion constraints significantly, and utilized a simple distributed algorithm to achieve efficient cluster flow locomotion; \cite{yang2018unit} proposed a novel self-configuration strategy based on the concept of meta-module, which can make every meta-module self-configure in the system by itself and the global constraints are effectively reduced at the same time. Those results provide inspiration for the self-assembly of non-mobile modules, but there are still some problems. In order to obtain sufficient locomotion ability, it is necessary to increase the assembled granularity, hence the meta-module is irregular and oversize, which will severely affect the diversity of organizable configurations.
Biological mutual assistance is an interesting phenomenon in social animals, organisms help each other to achieve tasks that cannot be completed by each other alone, so as to achieve a win-win situation. For example, when two people want to climb a high platform, the most appropriate measure is that one person first supports the other person to climb up, and then the upper person pulls the lower person up. Inspired by this, a mutual assistance assembly scheme based on meta-module is proposed. Meta-modules receive or provide assistance to each other while traveling to the assembly site, which can be used to help meta-modules designed compensate for the lack of mobility and minimize the impact of meta-modules on granularity. Then an efficient assembly planner is designed based on the motion characteristics of meta-module and mutual assistance to obtain the assembly sequence of target configuration and realize the self-manufacturing of a class of configurations. This meta-module mutual assistance method will make a good start for the building of adaptive and unmanned robotic system for lunar base. Finally, several simulation examples are given to demonstrate the feasibility and effectiveness.

Experimental Section/Methods

1. Space Module