Meta-Module Mutual Assistance: A Bioinspired Design for Self-Assembly of Modular Space Robot

The theoretical capability of modular robots to organize the overall robot into different structures with different functions has broad prospects in space exploration. Therefore, a novel modular space robot named Space Module is developed, and a self‐assembly strategy inspired by biological cooperative and mutual assistance behaviors is proposed. First, the meta‐module method is utilized to endow nonmobile modules with the mobility. Second, the mutual assistance is presented to achieve position and posture reachability of the assembly unit while minimizing the effect of meta‐modules on granularity. Then, according to the unique motion characteristics of the meta‐module and mutual assistance, an assembly planner is designed to obtain the assembly sequences to realize the self‐manufacturing of desired configurations. Finally, the validity and feasibility of the proposed assembly strategy are further confirmed by demonstrations. An interactive preprint version of the article can be found here: https://doi.org/10.22541/au.167264888.81237462/v1.


Introduction
Cooperative nest construction by social insects, [1] such as termites and wasps, is common in the biological kingdom. Natural builders demonstrate significant degrees of cooperation ability and efficiency. These behaviors have highly heuristic meaning to the collective construction of multiagents system, which received more and more attention from scholars. [2] It is worth noting that the self-assembly behavior of modular robot is also a special multiagents construction process.
Modular robot is a class of special robot, which is composed of several homogeneous or heterogeneous modules with certain drive and sensing abilities. [3] Through combining and disassembling modules, modular robot can be organized into different structures with different functions to adapt to complex tasks and environments. [4] With the rapid development of aerospace technology, modular robot has begun to turn their attention to space exploration, [5] such as space on-orbit service 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 would 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 nonmobile. The complex mechanical structures are abandoned to reduce the failure rate of module. The electropermanent magnets are used for docking, communication, and charging. The details and advantages of Space Module are shown in Section 2.1.
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 [6] is similar to the cooperative nest construction of insects. The subtle difference between is that the modules are both transporters and materials for construction. Compared to other schemes, [7] self-assembly is not limited by system connectivity and the module number of current configurations. In the unmanned space environment, module separation caused by impact, fall, and replacement of faulty modules often occurs. Hence, self-assembly is the preferred shape-shifting method for modular space robot.
Some progresses have been obtained in the research on selfassembly of modular robot. A formation self-assembly method for Sambot modular robot was proposed to self-assemble a group of swarm robots into a single articulated structure. [8] A chain type, homogenous, mobile, and modular multirobot system (ULGEN) was presented in ref. [9], which has the mobility and sensors to realize the self-assembly of desired configurations. A directional self-assembly control model was proposed in ref. [6], which utilized the seed module and docking module to perform the self-assembly experiments. A suite of algorithms for REPLICATOR modular robot were proposed in ref. [10], which includes a reversible graph grammar and broadcast communication and can drastically speed up self-assembly process.
However, these assembly strategies are proposed based on the full locomotion capability of mobile modules, which are more like the simplified path planning of multiagents. [11] In addition, the complex mobile mechanics of mobile modules would increase the redundancy of modular robot structures and reduce the robustness, which is not suitable for the unmanned requirements in space tasks. The research on the self-assembly of nonmobile modules is almost nonexistent, and the fundamental problem is the mobility of nonmobile modules. The design of self-assembly using external forces such as water and magnetism in ref. [12] is still far from producing application value.
Meta-modular method is an important breakthrough in modular robot self-reconfiguration and flow motion, which can give nonmobile 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 module number and docking mode. A reconfiguration algorithm was studied based on a 2 Â 2 Â 2 cubic meta-module for heterogeneous lattice modular robots with linear operation time cost. [13] A new meta-module design for two important classes of modular robots was proposed in ref. [14], which can perform the scrunch, relax and transfer moves that are necessary in any tunneling-based reconfiguration algorithm. A 2D meta-module for the ATRON robot was presented in ref. [15], which simplifies the motion constraints significantly, and utilizes a simple distributed algorithm to achieve efficient cluster flow locomotion. A novel selfconfiguration strategy based on the concept of meta-module was proposed in ref. [16], which can make every meta-module self-configure in the system by itself and effectively reduce the global constraints. Those results provide inspiration for the self-assembly of nonmobile modules, but the meta-module method also have a negative impact. To obtain sufficient locomotion ability, it is necessary to increase the number of modules that make up the meta-module. Consequently, the assembly granularity would become irregular and oversized, which significantly impairs organizable configurations' diversity. Hence, it is critical to solving the conflict between locomotion ability of metamodule and assembly granularity.
Biological mutual assistance is a type of social behavior, which is widely found in the biological world. An intuitive example is two people climbing a high platform, one person supports the other to climb up, and then the upper person pulls the lower person up. Through mutual assistance, individuals do not need to be powerful enough to accomplish their tasks, which has substantial reference value for solving the conflict between locomotion ability of meta-module and assembly granularity. 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 position, which can achieve position and posture reachability of assembly unit and minimize the impact of meta-modules on granularity. Then an efficient assembly planner is designed based on the motion characteristics of meta-module mutual assistance to obtain the assembly sequence. The self-manufacturing of a class of configurations can be realized. Finally, several simulation examples are given to demonstrate the feasibility and effectiveness of the selfassembly strategy.
This paper is organized as follows. Section 2 describes the Space Module and its basic motions. Section 3 introduces the self-assembly strategy, which include the meta-module mutual assistance and assembly planner. Section 4 gives assembly simulation examples. Section 5 discusses the self-assembly strategy and the results of simulations. The conclusions and future work are summarized in Section 6.

Module Design
As shown in Figure 1a-e, Space Module is a 100 Â 100 Â 100 mm cube. Each module has a lithium-ion polymer battery, a micro-controller, and a 2.4 GHz NRF24L01 transceiver module unit. The docking method adopts electropermanent magnet. The cluster of modules is controlled by a central computer running a Python program that sends serial commands to control the degrees of freedom, magnet on/off and communication of each module. The wireless network is provided by a wireless serial port with a range of about 20 m, allowing high-speed communication between the modules and the host computer. In addition, each module has an infrared sensor and an IMU to measure distance and feedback acceleration.
The structure of Space Module is regular and compact. Homogeneous modules enhance the fault tolerance and selfrepair ability, and robustness can be guaranteed in face of the complex and dangerous space environment. Each module has four connection surfaces and one degree of freedom, which can be used to form different robot configurations with different functions. Therefore, the modular robot system has sufficient versatility and adaptability to deal with the complex and diverse missions in space exploration.
The docking method is efficient and quick. Compared with the traditional mechanical structure and electromagnet, electropermanent magnet consumes very little energy during the connection and separation of modules. The effect of magnetic force is amplified in micro-gravity environment, which can guide the docking of the modules without emphasizing the positional accuracy. In addition, the electropermanent magnets can be used for posture judgment and communication between the connected modules. 70 N attachment force can be maintained by the electropermanent magnets, which is sufficient in micro-gravity environment.

Basic Motions
For the convenience of description, the module is simplified into a combination of two L-shaped surfaces and a rotation axis, as shown in Figure 1c. In the absence of obstacles, each L-shaped surface can revolve around the axis. Two L-shaped surfaces cannot move at the same time, and it must be ensured that one of the L-shaped surfaces is fixed. Hence, Space Module is a typical nonmobile module.
Since each surface can be docked to other modules, two types of interactive motion exist. Define the surface paralleling to the axis in the L-shaped surface as S1 and the surface intersecting the axis as S2. S1 can carry a module to revolve around the axis, and S2 can rotate a module. The former is divided into S2 is fixed and S1 is fixed, as shown in Figure 1f,g, and the latter is shown in Figure 1h.

Problem Description
The self-assembly process consists of two steps: 1) determining the assembly sequence of positions in the desired configuration and 2) moving the assembly units to the target positions with appropriate postures. Unfortunately, Space Module does not have any mobility, which means the step 2 cannot be completed. Hence, we proposed the meta-module mutual assistance to solve this problem. Meta-module method is to endow assembly unit with certain mobility, and mutual assistance would compensate for the motion defects to achieve position and posture reachability, that is moving to the target position with the appropriate posture. Although the meta-module mutual assistance is proposed to complete step 2, it also requires to be taken into consideration in step 1. Hence, a planner is designed to plan the self-assembly process and obtain the assembly sequence according to the motion characteristics of meta-module mutual assistance.

Meta-Module
The connected structure of a group of modules can provide more mobility than an individual module, which is the basis of meta-module method. By analyzing the basic motions of Space Module, two types of meta-module are designed in this section, which are shown as follows: Mover: The meta-module Mover is formed by horizontally docking S1 of two opposite direction modules, as shown in Figure 2a.
By alternately using the basic motion shown in Figure 1f, Mover has the ability to walk in a 2D plane, as shown in Figure 2b.
To facilitate planning the path, Mover adopts grid motion, which means the absolute value of joint rotation angle is restricted to a multiple of 90. Hence, A* algorithm can be utilized to plan the path.
Tumbler: The meta-module Tumbler is formed by vertically docking S1 of two same direction modules, as shown in Figure 2c. By alternately using the basic motion shown in Figure 1g, Tumbler has the ability to walk in straight line, as shown in Figure 2d.
The design of Mover and Tumbler endows the assembly unit with a certain mobility, but it is not sufficient to achieve position and posture reachability. Mover cannot rotate itself and Tumbler cannot change its forward direction. Docking more modules to the meta-module can obtain more mobility, but the granularity would become oversized and irregular. However, it is exciting that the meta-modules can complement each other to compensate for the deficiencies in mobility. Thus, sufficient mobility to achieve position and posture reachability can be obtained.

Mutual Assistance
Mutual assistance is common in social animals, which can help individuals accomplish the tasks far beyond their capability. d) Simplified simulation model. e) Exploded view of space module. f ) Module basic motion: S1 carries a module to revolve around the axis and S2 is fixed. g) Module basic motion: S1 carries a module to revolve around the axis and S1 is fixed. h) Module basic motion: S2 rotates a module. (The size of the blue grid in f, g, and h is 100 Â 100 mm, and the size of the meta-module is 100 Â 200 Â 100 mm.).
www.advancedsciencenews.com www.advintellsyst.com Inspired by this, meta-module mutual assistance approach was proposed. Through the superposition of the basic motions, meta-modules can provide assistance to others. Specifically, Mover can help Tumbler change direction and Tumbler can help Mover rotate.
Since the Space Module is designed based on the premise of working in a micro-gravity environment, the mutual assistance motion cannot be completed in the gravity environment. However, it can be found that the auxiliary meta-module only interacts with one part of Tumble or Mover in the mutual assistance, which is marked with yellow in Figure 3a,c, and the other part neither facilitates nor hinders the mutual assistance. Hence, the meta-module can be replaced by the yellow part to demonstrate the mutual assistance and prove that the mutual assistance is feasible in principle, as shown in Figure 3b,d.
Direction Change: Tumbler cannot change its forward direction, as shown in Figure 3a. The superposition of the basic motion ( Figure 1f ) and the mobility of the base allow the Mover's end surfaces to rotate at any angle. Furthermore, the connectivity of the end surfaces allows Mover to provide assistance. The process of direction change is shown in Figure 3b. First, Mover reaches the appropriate position and connects the module that needs assistance. Second, Mover rotates the end surface to change the direction of the module.
Rotation: Mover cannot rotate itself, as shown in Figure 3c. Through the superposition of the motions (Figure 1g,h), Tumbler can help a modules to rotate. The process of rotation is shown in Figure 3d. First, the upper module of Tumbler connects the module that needs assistance and lifts it to rotate. Second, Tumbler puts it down to achieve rotation.
In the assembly of modular robot, the rotated mover is named Rotated Mover. Note that the motion of Rotated Mover is the same as Tumbler. Hence, the Mover can be rotated by Tumbler in an appropriate position and roll to the target position when the desired configuration needs Rotated Mover.
In order to determine more intuitively whether the metamodule needs assistance, the following criterion is given where o c is the rotated angle around the R-axis from the initial position to the current position, o g is the rotated angle around the R-axis from the initial position to the target position, and the R-axis is the solid blue arrow shown in Figure 3a,c. When f ¼ 0, the movement of the meta-module does not require www.advancedsciencenews.com www.advintellsyst.com assistance, and when f 6 ¼ 0, the movement of the meta-module would trigger the mutual assistance. Through meta-module mutual assistance, assembly unit can reach the target position with the desired orientation, but the joints posture cannot be guaranteed. As shown in Figure 3e, it is difficult for Tumbler and Rotated Mover to reach the target position with this joints posture, unless there are reliable connected surfaces in one of the black areas. The joints adjustment example is shown in Figure 3f. Since the connectivity of target configuration, the adjacent structural meta-modules in configuration can provide reliable connection surfaces. Hence, it is stipulated that joints posture adjustment starts only when all meta-modules have reached the target positions. In addition, a redundant Mover can also be used to provide a connection surface in some extreme cases.
The two types of meta-module are composed of only two modules, and the structures are compact and regular, which have little effect on the granularity of configuration. At the same time, the meta-module mutual assistance enables them to achieve position and posture reachability. Hence, the designed metamodules are suitable for assembling the desired configuration as the basic unit.
Although meta-module mutual assistance can achieve the 3D position and posture reachability, the self-assembly of 3D initial configuration cannot be realized. Because a module has only four surfaces, there are not enough surfaces to support the 3D motion of meta-modules. Hence, the target configurations have a feature that all meta-modules can have a common surface by adjusting joints.
To sum up, the assembly configurations applicable to the meta-module mutual assistance strategy must satisfy two www.advancedsciencenews.com www.advintellsyst.com constraints. One is that the configuration must be composed of meta-modules, and the other is that all the meta-modules in the configuration can be coplanar.

Self-Assembly Planner
After realizing position and posture reachability of assembly unit, it is crucial to establish a pragmatic and effective planner to avoid collisions and achieve self-assembly. The tasks of the planner consists of two aspects. The first one is obtaining the appropriate assembly sequence and corresponding auxiliary sequence. The second one is obtaining the information for mutual assistance, including the positions, target directions, etc.

Assembly and Auxiliary Sequence
The obtaining of assembly and auxiliary sequence requires consideration of the configuration information, the meta-module motion characteristics, and the mutual assistance characteristics. A bubble algorithm is proposed, whose principle is replacing the order of the assembly blocked position to the front, and continuously updating the whole assembly sequence until a suitable order is found. The flowchart is shown in Figure 4. First, the assembly sequence is preordered according to the layout characteristics of target configuration. Then the meta-modules are matched with the assembly positions one by one to obtain a assembly sequences without considering the motion constraints of meta-module mutual assistance. Specifically, a coordinate system parallel to the common surface of configuration is defined first, then the assembly positions are sorted according to the y-axis coordinates from large to small and the x-axis coordinates from large to small. By this way, an initial assembly sequence is obtained.
Second, the initial assembly sequence is traversed and metamodule mutual assistance constrains are checked. The first check is whether there is motion blockage or assembly obstacle when Mover assists Tumbler. The second check is whether there is effective assistance when Tumbler assists Mover. If a metamodule cannot satisfy those constraints, the assembly priority of this meta-module's position would be raised above the position of the meta-module that blocks it or can assist it. Then the traversal of assembly sequence would continue until all positions are traversed. Once traversal is trapped in a dead loop, the redundant meta-module assist mechanism would be activated to ensure that the assembly process proceeds.
The configuration information, constraints, and redundant meta-module assist mechanism mentioned earlier are shown as follows: Configuration Information: The information of each metamodule in the configuration includes type, position, orientation, joints posture, etc. Connector graph has been widely used for representing modular robot topologies. [17] Compared with other methods such as incidence matrix, [18] it is more intuitive and would not cause dimensional explosion due to the increase of the module's number. Hence, a configuration representation based on the characteristics of Space Module and connector graph method is proposed. The morphology of modular robots is modeled by the combinatorial topology of edges and vertices. Each vertex contains a number, a superscript, and a subscript, representing the meta-module's ID, type, and joints information. Edges denote connection between meta-modules by a 3-tuple, representing the docking information. The details are shown in Supporting Information.
Mutual-Assistance Constraints: The characteristics of metamodule mutual assistance are mainly reflected in the movement constraints, which would cause blockages and collisions. The constraints are as follows: When Tumbler needs to change the direction with the assistance of Mover, it must satisfy Positionðm, MÞ or PositionðM, mÞ and ExistðtpÞ (2) When Mover needs to rotate with the assistance of Tumbler, it must satisfy PositionðT, mÞ and CrossðT, tpÞ  where m represents the meta-module needed to be assisted, M represents the existence of a Mover in the assembly sequence, T represents the existence of a Tumbler in the assembly sequence, tp represents the target position, Positionðx, yÞ represents that x precedes y in the assembly sequence, or y precedes x, which depends on the position of m in the function. Specify the direction corresponding to the long side of the meta-module as the extension direction and the area passing along this direction as the extension area, ExistðtpÞ represents no obstacle in the extension area in at least one extension directions of the target position, as shown in the shaded area in Figure 5a. Crossðt, tpÞ represents that there is an intersection between the extension area of the Tumbler and the extension area of the target position, and the area extending to two unit positions after the intersection along the intersection direction is unobstructed, as shown in the shaded area in Figure 5b. Redundant Meta-Module-Assist Mechanism: Although the constraints mentioned earlier may not be satisfied, the assembly can still proceed. The reason is that the library of meta-modules used for assembly is bound to have a large number of redundant meta-modules for subsequent multiple tasks, hence a redundant meta-module can be chosen directly for assistance. This mechanism is usually triggered when a meta-module cannot get assistance from the meta-modules that make up the configuration to reach the assembly position. At this time, the redundant metamodules would come out temporarily to provide corresponding assistance.
The corresponding pseudo-codes of the bubble algorithm are shown in Supporting Information.

Information for Mutual Assistance
After obtaining the assembly sequence and the auxiliary sequence, the planner would send the target position and orientation information to the corresponding meta-module to perform the assembly task. Once the assistance happened, the planner should provide the information about the assistance to the auxiliary meta-module. Details are as follows: The Information Acquisition of Mover Assisting Tumbler: When Mover assists Tumbler in changing direction, Mover needs to get the position information and target direction information of Tumbler. Due to the linear motion of Tumbler and the grid motion of Mover, Tumbler needs to pass through an inflection point to reach the target position. In the inflection point, Tumbler would complete the direction adjustment with the assistance of Mover. Three cases should be noted: 1) the inflection point may coincide with the start point or the end point; 2) the start point and the end point may also need to change direction; and 3) the assistance cannot occur at the end point in order to avoid collision. For this purpose, a backward planning method is adopted to obtain auxiliary information, as shown later: Step 1: Move Δx=Δy from the end point along the end direction to the inflection point; Step 2: If the initial direction is the same as the end, the middle direction of inflection point would select a different direction. If opposite, the middle direction would select the initial direction. Then Tumbler would change direction from the end to the middle by the assistance of Mover; Step 3: Move Δy=Δx from the inflection point along the middle direction to the start point and adjudge the current direction to the initial direction if necessary; Step 4: According to the different choice of Δx and Δy, there are two paths, choose the one with the least movement of Mover.
where Δx is the x-axis difference from the start point to the end point in the absolute coordinate, Δy is the y-axis difference from the start point to the end point in the absolute coordinate. By this way, the position and direction information is obtained and transmitted to Mover, which can move to the target position and assist Tumbler.
The Information Acquisition of Tumbler Assisting Mover: According to Figure 5b, the position of Tumbler assisting Mover is the intersection point in the figure. Hence, the position of the intersection point can be obtained during the planning process of the assembly sequence. When this information is obtained, the Mover and the Tumbler would move to this position and complete the rotation. Then the Mover becomes the Rotated Mover, which would roll to the assembly position.
With the designed planner, the orderly assembly of various configurations can be realized, blockages and obstacles can be avoided. Then, the specific modular robots' assembly would be used to verify the effectiveness of the meta-module mutual assistance self-assembly strategy.

Results
In this section, the self-assembly processes based on metamodule mutual assistance and assembly planner are demonstrated in simulations. The initial positions of meta-modules only affect the matching of the meta-modules to the assembly positions. Hence, the impact of whether the meta-modules are scattered or gathered together on the feasibility verification of the self-assembly strategy can be ignored. Based on the premise assumption that it is necessary to place the cargo in a centralized and regular manner during the rocket launch process, the initial stacking form of meta-modules is shown in Figure 6a, with Movers in Area A and Tumblers in Area B. Meta-modules are driven out from both sides for autonomous assembly. Although they are stacked together, the meta-modules are separated from each other, which is not fundamentally different from the scattered distribution, and would not affect the self-assembly process.

Super Redundant Manipulator
As a kind of special robot, the joint space dimension of super redundant manipulator is much more than the task space dimension, which can meet the posture requirements during operation. As shown in Figure 6b, it is a super redundant manipulator configuration composed of meta-modules. Figure 6c is the assembly configuration graph, it can be seen that all metamodules have a common surface. Figure 6d is the connector graph, which includes the configuration information, details about parameters can be seen in Supporting Information. Through analysis, the following assembly conflicts and auxiliary requirements can be found in Table 1 and 2.
Then, the configuration information is input into the assembly planner to get a suitable assembly sequence, which is as follow and the auxiliary sequence is where B represents the movement of this meta-module that does not need assistance. In addition, meta-modules 2, 4, and 6 need connection surfaces to adjust posture. Utilize meta-module mutual assistance to execute the assembly and auxiliary sequence. Experiment in simulation is shown in Figure 6e. The final result is a super redundant manipulator that can be used for handling, welding, machining, assembly, etc.

Quadruped Robot
The quadruped robot has the characteristics of high stability and adaptability and can be used for environmental detection and transportation. As shown in Figure 6f, it is a quadruped robot configuration composed of meta-modules. Figure 6g is the assembly configuration graph, it can be seen that all metamodules have a common surface. Figure 6h is the connector graph, which includes the configuration information. Through analysis, the following assembly conflicts and auxiliary requirements can be found in Table 3 and 4.
Then, the configuration information is input into assembly planner to get a suitable assembly sequence, which is as follow 7 ! 8 ! 5 ! 2 ! 4 ! 6 ! 1 ! 3 (6) and the auxiliary sequence is where M represents a redundant meta-module Mover in the meta-module library. In addition, meta-modules 4 and 6 need connection surfaces to adjust posture. Utilize meta-module mutual assistance to execute the assembly and auxiliary sequence. Experiment in simulation as shown in Figure 6i. The final result is a quadruped robot that can be used for environmental exploration, item transportation, moving base of robotic arm, etc.

Humanoid Robot
The humanoid robots are adapted to the human working environment and can replace astronauts to complete some delicate operations. As shown in Figure 6j, it is a humanoid robot configuration composed of meta-modules. Figure 6k is the assembly configuration graph, it can be seen that all meta-modules have a common surface. Figure 6L is the connector graph, which includes the configuration information. Through analysis, the following assembly conflicts and auxiliary requirements can be found in Table 5 and 6.
Then, the configuration information is input into assembly planner to get a suitable assembly sequence, which is as follows and the auxiliary sequence is In addition, meta-modules 3, 4, 6, 7, 8, and 9 need connection surfaces to adjust posture.
Utilize meta-module mutual assistance to execute the assembly and auxiliary sequence. Experiment in simulation is shown in Figure 6m. The final result is a humanoid robot that can replace astronauts in performing some of the space operation tasks.

Meta-Module Mutual Assistance
In the past researches, there is a tendency to add enough designs to make the unit robot omnipotent. The most direct manifestation in the meta-module is the increasing number of modules, but its structure would become oversize and irregular. Table 7 shows the characteristics of some representative metamodules.
Through comparison, it can be clearly seen that the granularity of the meta-module proposed by our group is optimal. It is composed of only two basic modules, with regular and compact shape and strong motion ability. Since the different module structure and target tasks, such a comparison is unfair, but it can be seen the superiority of the mutual assistance. In order to meet the carrier weight and space requirements of launch vehicle and reduce the potential for mechanical failure, space module was designed www.advancedsciencenews.com www.advintellsyst.com to be extremely simple, with only two L-shaped surfaces and a revolute joint. Sufficient mobility is a huge challenge for the self-assembly of Space Module. The meta-module method alleviates this problem to a certain extent, but the increased granularity caused by meta-module raises a new obstacle. Through mutual assistance, full mobility can be achieved, and the granularity of the meta-modules remains at the size of two modules. The conflict between locomotion ability of meta-module and assembly granularity is solved. Therefore, mutual assistance is of great significance to the research of nonmobile modules, which is a further improvement on the meta-module method.

Self-Assembly of Space Module
In the self-assembly process, as shown in Figure 6e,i,m, the required meta-modules are driven out from the library in turn and move to the assembly position assigned to them. During the movement, there would be corresponding meta-modules to assist them in changing direction or rotating. When all meta-modules reach the target positions, joint postures are adjusted uniformly to ensure the existence of reliable connection surfaces. Finally, the assembly configuration in Figure 6c,g,k can be assembled, and then the quadruped robot, humanoid robot and robot in Figure 6b,f,j are formed by adjusting the joint angles.
The situations contained in the experiments are comprehensive. First, it contains all the motion forms of the meta-modules, including the tumbling motion of Tumbler, the movement of Mover, and the tumbling motion of Rotated Mover. Second, it contains all forms of mutual assistance, including Mover assisting Tumbler in changing its forward direction and Tumbler assisting Mover in rotating. Finally, it contains various positions and postures in the target configurations, including horizontal or vertical placement and different rotation angles. Hence, the above experiments are a strong proof for the effectiveness of the self-assembly strategy.
As mentioned in Section 3.3, a complete mutual assistance experiment cannot be done in the gravity environment, hence the hardware experiment of self-assembly cannot be completed either. To address this problem, we are currently developing an underwater weightless experimental platform that would use the buoyancy of water to counteract the gravity of the module. It is a feasible but extremely time-consuming work, which requires continuous iterative analysis of the modules subtle structures based on issues such as sealing and counterweight. At present, we have completed the preliminary work on the sealing, and other works are still in order. However, the innovation point of this paper mainly focuses on the strategy, the simulation experiments can equally prove the effectiveness of the strategy when the basic motions (Section 2.2) of the module is unchanged, and the meta-module motion (Section 3.2) and mutual assistance motion (Section 3.3) are feasible in principle.      Move along negative y-axis is hindered by 10 9 Move along negative y-axis is hindered by 11 10 Move along positive y-axis is hindered by 7

11
Move along positive y-axis is hindered by 9 A simple application demonstration of the self-assembly strategy is shown in Figure 7. The task is installing solar panels. After receiving the task, the stacked meta-modules would be selfassembled into a manipulator and a quadruped robot through the self-assembly strategy. The former would place the solar panels on the quadruped, and then the quadruped would move to the target location for installation. This demonstration may not be rigorous in its details, but it shows the great potential of modular robots and self-assembly strategy in tackling unmanned, customized tasks, which has broad prospects in space exploration.

Summary and Prospect
The concept of meta-modules mutual assistance is proposed inspired by biological cooperation and mutual assistance, which makes nonmobile modules no longer need to seek a balance between granularity and mobility. Then an assembly planner is designed to achieve autonomous assembly while avoiding assembly conflicts and positional blockage. Some experiments demonstrate the effectiveness of the method. Through this method, the self-manufacturing of various robots can be realized, which will make a good start for the application of modular robots in space exploration.
In the next work, hardware experiments will be realized and an attempt will be make to complete a specific task. Then the assembly strategy will be further optimized to reduce the constraint of the configuration by using the configuration decomposition and component assembly method. In addition, the meta-module mutual assistance has high application value in the fields of self-reconfiguration and self-repair, which is worth further exploration.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.