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Two Dimensional Self-Assembling/Self-Repairing Machine

1. Introduction

Contemporary civilization is supported by many artificial systems. The artificial systems such as transportation systems or communication systems compose very important part of our infrastructure. Those systems have a tendency to become more and more complicated, and cost of design, production and maintenance of such systems turned into a grave issue. In our research activity, we would like to focus attention on the maintenance issue of large scale mechanical systems, and propose a novel methodology to construct a reliable complex system.

2. Idea - Moving LEGO

We propose a concept of self-repairable machine which consists of homogeneous mechanical units. In a sense, the system has the ultimate redundancy, namely, the system is made of only one kind of units (component redundancy) and it can change functionality by changing its shape (functional redundancy). The unit is an active robotic unit with some mobility to change local connection. Each unit has an onboard microprocessor for information processing and communication. This figure illustrates how the self-repairable machine works. It can form arbitrary shape from random initial condition by using the ability of local connection change of the unit. This process is called "self-assembly." When the system detects some failure, it cuts off the faulty units, and transports spare units to faulty part to restore the original shape. The process of repair is done by cooperation of the units without any outside help, thus is called "self-repair."

3. Mechanical Unit "Fractum"

　 Based on this concept, we have built several prototype models of self-repairing system. The first prototype is a two-dimensional system is called "Fracta System" using electro-magnet as an actuator. It has six connection arms actuated by combination of electro-magnets and permanent magnets. A microprocessor (Z80) installed onboard controls polarity of three electro-magnets. It also has a communication channel through all of six connecting arms by using optical communication device. The actuator part of the unit has three layers; permanent magnets are embedded in the top and the bottom layers and electro-magnets are installed in the middle layer. Connection between two units is established when an electro-magnet of one unit is pulled into a gap between permanent magnets of the other unit. To release the connection, simply reverse the polarity of the electro-magnet. A group of fracta can change local connective situation by repeating this basic procedure(Photos of Fracta）
　
An onboard CPU is installed to control the inter-unit connection. Software for the CPU is written on an EPROM.
　
Optical devises for communication are embedded in each connection mechanism. By using this, the unit can exchange digital information with neighboring units.
　
The inter-unit connection is realized by a special mechanism using a pair of permanent magnets and an electro-magnet. The electro-magnet is pulled into a gap between the permanent magnets or pushed out from the gap according to the current direction. By repeating this process, a group of the unit can reconfigure its global shape. (Procedure of Reconfiguration）

4. Distributed Software for Self-Assembly

　Our first target of software development is to realize "self-assembly" functionality, in other words, to form desired global configuration based on local information. Information available on each unit is local connective situation around the unit. It is recognized by checking each of six connecting arms. (The onboard CPU sends a message to all the direction, and if it receives an answer from a neighbor, it can recognize the arm is connected.) The neighbor units also can exchange the data of the connective situation. The following self-assembly algorithm is based on these basic information about local connective situation. Possible connective situations of a unit can be classified into 12 connection types ( Figure). A hexagon denotes the unit, and short bar in it indicates that the arm is connected to a neighbor. We use the connection type to describe the desired goal shape. Each unit recognizes its own connection type and neighbor's connection types through communication, and then, a unit can compare its current situation to the statements in goal shape description. Difference between the current and goal situation is evaluated by using the distance defined on the connection types. If the distance to one of the goal statements becomes zero, the unit recognizes that it achieved a part of goal shape, and does not move while this condition is satisfied. Otherwise, it moves to random direction by some probability related to its evaluated distance. Namely, if the unit judges its current situation is close enough to goal, it doesn't try to move, but when the distance seems to be large, it moves frequently to get better position. (Self-Assembly Algorithm）

5. Experiment

　We conducted an experiment to evaluate feasibility of the above software. In this experiment, an extended version of self-assembly algorithm is examined. This algorithm is capable of primitive self-repair with one spare unit. We embedded two target shapes; one for a triangular shape made of 10 units, and another is for the triangle plus one spare unit. The former has priority, thus the system try to make a triangle without a spare unit. At the initial time, the system contains 11 units, thus it cannot achieve the former target, and converges to the latter target. After the convergence, we cut off power for an arbitrary unit in the configuration to mimic a situation with a faulty unit. The faulty unit is detected by inter-unit communication (the faulty unit cannot reply to calls from neighbors). It is ejected by the surrounding units and the self-assembly process resumed.(Experiments)
　

6. Future Works

Many important issues related to the self-repairing system remained for future work. Firstly, it is essential to develop a smaller and simpler mechanical module with self-reconfiguration ability. Micro fabrication technology may be a key to provide a feasible solution. Secondly, a method to construct a reliable system out of unreliable elements is very important. Although this issue stems from von Neumann's work [1] for almost a half century ago, there is no such man-made artifacts so far. In order to realize truly flexible system like living things, we need a deeper understanding of complex homogeneous system.

[1] J. von Neumann: Theory of self-reproducing automata, Univ. Illinois Press (1966).

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