Robotics and Autonomous Systems 54 (2006) 142–149 www.elsevier.com/locate/robot
Self-reconfigurable M-TRAN structures and walker generation H. Kurokawa a,∗ , E. Yoshida a , K. Tomita a , A. Kamimura a , S. Murata b , S. Kokaji a a National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba, Ibaraki 305-8564, Japan b Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama, 226-8502, Japan
Received 22 November 2004; accepted 13 September 2005 Available online 28 November 2005
Abstract The M-TRAN is a modular robot capable of both three-dimensional self-reconfiguration and whole body locomotion. Introducing regularity in allowed structures reduced difficulties of its reconfiguration problems. Several locomotion patterns in various structures were designed systematically using a CPG controller model and GA optimization. Then they were verified by experimentation. Results showed a feasible scenario of operation with multiple M-TRAN modules, which is presented herein, including metamorphosis of a regular structure, generation of walkers from the structure, walker locomotion, and reassembling of walkers to the structure. c 2005 Elsevier B.V. All rights reserved.
Keywords: Modular robot; Autonomous distributed system; Self-reconfiguration; Metamorphosis
1. Introduction Several modular robots are under development that can change their configuration independently or perform locomotion in various structures. Their modules’ design differs in the number of DOFs, geometric arrangement of DOFs, connector design, information processing and controller, and communication capability with other modules. A comprehensive system of connected modules forms an autonomous distributed system. Software problems include feasible tasks and their representation, reconfiguration algorithms, a centralized or decentralized controller, and coordination between modules. Most three-dimensional (3D) modular robots are classifiable into two types: a lattice type [1–4] and a linear (or string, or chain) type [5,6]. Self-reconfiguration problems, such as self-assembly, i.e., metamorphosis from one configuration to another, and a cluster flow motion by repetitive local reconfiguration, have been investigated mainly using the former type of system. Whole body locomotion has typically been studied using the latter type of system. ∗ Corresponding author.
E-mail addresses:
[email protected] (H. Kurokawa),
[email protected] (E. Yoshida),
[email protected] (K. Tomita),
[email protected] (A. Kamimura),
[email protected] (S. Murata),
[email protected] (S. Kokaji). c 2005 Elsevier B.V. All rights reserved. 0921-8890/$ - see front matter doi:10.1016/j.robot.2005.09.023
The modular transformer (M-TRAN), which was developed at AIST, was designed to offer features of both lattice and linear types [7]. It can form various self-reconfigurable lattice structures. Once a specific structure is produced, each rotational joint can be driven powerfully to realize robotic motion as a whole. Therefore, both self-reconfiguration and whole body locomotion can be studied using the same M-TRAN hardware. Regarding self-reconfiguration, several difficulties arise in sequence design and control algorithms. Transformation between arbitrary configurations is a difficult problem, even considering an omni-mobile module and by a centralized algorithm. Distributed algorithms are suitable for cluster flow motions, but they require several methods of maintaining total connection, collision avoidance, and multi-module cooperation. Constraints of respective actual hardware design complicate the problem. The M-TRAN has numerous kinematic and hardware constraints. For that reason, general self-reconfiguration obstacles are extremely difficult to surmount [7]. We have manually designed reconfiguration sequences for experimentation. Fewer than 10 modules were used in these experiments, including the experiment illustrating transformation from a four-legged walker to a caterpillar structure [8]. For systematic reconfiguration of a larger structure, we introduced types of structural regularity and developed a centralized planner to find a reconfiguration sequence [9].
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Fig. 1. M-TRAN module design.
Locomotion is another research subject of modular robots. Systematic designs of distributed locomotion control have been proposed for specific topology having symmetry [10,11]. We have developed a systematic design method for locomotion of several M-TRAN structures and verified it by experiments [12]. In most studies above, two problems – self-reconfiguration and whole body locomotion – are dealt with for different size structures, i.e., self-reconfiguration, especially cluster flow motions, for a larger structure and whole body locomotion for a smaller structure. We have shown an example in which a small walker is generated from a structure of many modules [7]. This process of sub-structure generation combines two problems. Therefore, we can draw a big scenario of M-TRAN operation in which a structure with many modules metamorphoses to form a given structure or generates a cluster-flow motion that conforms to the environment: it generates many walkers; the walkers then leave and gather to reassemble another structure. Section 2 describes principles and the current M-TRAN hardware. An operation scenario is presented in Section 3, followed by past research results of self-reconfiguration and whole body locomotion. Section 4 presents a detailed evaluation of the feasibility of the scenario using several examples of walker generation by self-reconfigurable structures and metamorphosis between walkers. Future work and the conclusion are included in Section 5. 2. Modular transformer (M-TRAN) 2.1. Module design and motion The M-TRAN module comprises two blocks, half cubic and half cylindrical, and a link (Fig. 1) [4]. The module has two DOF rotational actuation and six connection surfaces. Each actuated angle ranges ±90 degrees; when all the angles are controlled as 0 or ±90 degrees, all blocks of connected modules are lined up into a regular cubic lattice. By this property, precise positioning between two neighbor modules is not required for a reconfiguration operation. Because the two actuated axes are parallel, reconfiguration of the M-TRAN module structure usually requires cooperation of multiple modules, especially the carrying of one module by another. This renders the reconfiguration process difficult from a design perspective.
Fig. 2. M-TRAN II.
2.2. Hardware We have developed second-generation hardware called M-TRAN II, as shown in Fig. 2 [8] based on the first prototype [7]. Its motors and connections are sufficiently strong to support and manipulate one or two other modules under gravity. It has sufficient controllability of connection for selfreconfiguration and sufficient actuation power and speed for locomotion. Each module has three micro-controllers that allow it to perform precise angular control, connection, and disconnection. The main controllers of connected modules form a computer network that is suitable for synchronization and cooperation. Installation of a battery in each module allows stand-alone wireless operation. This is an important feature because wires typically obstruct the self-reconfiguration process and interfere with locomotion. One module has an RF receiver, with which an operator sends a command to the modules. 3. Operation scenario, self-reconfiguration and locomotion 3.1. Operation scenario We have conducted various simulations and experiments to verify both self-reconfiguration ability and whole body locomotion of the M-TRAN system [8,12]. They include metamorphosis of large structures, generation of a walker from a structure, locomotion in variously shaped walkers, and metamorphosis from walkers to caterpillar-like robots. Combining those results, we can infer a scenario of multi-MTRAN operation that is useful for several applications such as search-and-rescue operations (Fig. 3). Among several motions, self-reconfiguration (Fig. 3(a)) and whole body locomotion (Fig. 3(b)) have been well examined. Past research results of those motions by the M-TRAN system are summarized and evaluated hereafter. 3.2. Self-reconfiguration Various studies have addressed self-reconfiguration of modular robotic systems. Tasks vary from self-assembly, i.e.,
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Fig. 3. Operation Scenario of the Multi-M-TRAN System. (a) Metamorphosis as a cluster flow motion by repetitive local reconfiguration, (b) locomotion in small structure, (c) walker generation, (d) metamorphosis between walkers, and (e) reassembly by connection of separate structures.
(a) Basic structure.
(b) Contracting. Fig. 4. Meta-module by M-TRAN.
transformation between configurations, to cluster flow motions by repetitive local reconfigurations. Distributed algorithms have been mostly sought. General problems of self-reconfiguration include maintaining total connection, collision avoidance, etc. The M-TRAN system has its own difficulties caused by its mechanism [7]. The salient problem for reconfiguration between arbitrary configurations is engendered by the fact that we cannot define an appropriate metric function – a distance measure – for similarity of configurations. Merely identifying configurations is a problem of graph-matching, which is known to be intractable (NP-hard). No heuristic search can be applied without a metric function. A blind search induces computational explosion. We have conducted two approaches, design by humans and introduction of regularity in structure, to cope with these difficulties. Humans can find reconfiguration sequences by trial and error if the problem size is sufficiently small. We have manually produced several examples of reconfiguration, including metamorphosis from a four-legged walker configuration to a linear configuration [8]. We have made a program to support this design process. It displays a configuration in 3D, stores and plays back a sequence, and checks total connection, collision, and stability under
gravity. The current revision supports a structured programming language that is suitable for reuse of acquired sequences, dynamics, and simulation utilities based on Vortex and ODE. For larger size problems, it is better to introduce logical layers or macro-scale regularity in structure. A “meta-module” is a construction of mutually connected modules that functions as a larger module [4]. Reconfiguration between meta-module structures becomes an easier task if the meta-module is more manipulable than a single module, especially if it can change its position to any neighboring macro-position. Fig. 4 shows an example of a meta-module by eight M-TRAN modules. It can perform the same motion as a model of a crystalline atom [3]. This meta-module functions only in two dimensions. Using a different idea from the meta-module, we designed three regular structure families and have been developing reconfiguration algorithms. Each structure is assembled mostly through the use of identical building blocks that are made of some similar modules with a meta-module structure. Such building blocks do not function as a meta-module by themselves, but they can change their position or orientation with the help of other modules and thereby maintain their regularity after a predefined sequence of motions. Several such sequences are necessary for flexible reconfiguration.
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(a) Basic structure.
(b) Climbing over obstacle.
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(c) Turning.
Fig. 5. Type-1 regular structure.
Fig. 6. Vertical transportation of modules.
(a) Basic structure with converters.
(b) Cluster flow motions. Fig. 7. Type-2 regular structure.
To the extent that they are used, general problems of self-reconfiguration such as those with connectivity and collision are solved automatically. Currently, we are producing adequate sequences for flexible reconfiguration for myriad structures [13]. The first type of structure, shown in Fig. 5, is called Type1 hereafter. It is based on a parallel linear structure with two additional modules, called converters. This structure can move straight, up, or down along a terrain by transferring tail modules to the head [7]. It can change its direction using converters (Fig. 5(c)). Moreover, it can generate caterpillar and crawler motions, and assume a tower structure [14]. Vertical transportation of modules as in Fig. 5(b) was verified using an experiment, as shown in Fig. 6. Fig. 7 shows another type of configuration, called Type2 hereafter, which comprises four module blocks with two additional modules, called converters. It functions more flexibly
than the first type. This structure can move straight and make an orthogonal turn in any direction by moving a tail block to the head. It can also make branches. We have developed a centralized planning method for generating sequences of such reconfiguration [9]. An experiment of this type of reconfiguration was performed for a two-block structure laid on the floor [7]. Though decentralized algorithms of cluster flow have been proposed only for a simplified subset of this problem [15,16], a decentralized algorithm for the full problem of three-dimensional cluster flow is feasible by designing sufficient numbers of subroutines (Fig. 7(c)). The third type of structure in Fig. 8(a), called Type-3 hereafter, is a planar structure made of four module building blocks (forming either a square or a cross shape). It can move along a plane by (1) lifting two modules up from an edge, (2) carrying them on the structure, and (3) placing them down at another edge (Fig. 8(b)). Such a cluster flow motion on
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(a) Planar structure.
(b) Transformation.
(c) Direction change.
Fig. 8. Type-3 regular structure.
(a) Four legged walker (L4a).
(b) Mini four legged walker (L4S).
(c) Caterpillar (SL1).
(d) Six legged walker (L6).
Fig. 9. Locomotion experiments.
Fig. 10. Walker generation from Type-2 structure. (1) H-shaped sub-structure, (2) crawler, (3) four-legged walker.
the horizontal plane can turn up along the vertical direction as in Fig. 8(c), but only further experimentation can clarify whether all the intermediate structures have sufficient structural strength. 3.3. Locomotion Locomotion is another research topic of modular robots. Overwhelmingly, the literature includes robotics studies on bipedal or multi-legged robots and on other typical forms such as crawlers, caterpillars, and snakes. Those results are useful, but locomotion by modular robots has unique qualities. A usual robot can be designed to be suitable for locomotion, but modular robots sometimes cannot be. Modular robots can form various structures, some of which resemble neither a robot nor any living creature. In addition, distributed control methods have been sought for a modular robot to gain scalability [10, 11]. We have developed a method of designing an appropriate
locomotion pattern that is suitable for distributed control and is applicable to an arbitrary configuration of M-TRAN modules [12]. The method uses a generalized Central Pattern Generator (CPG) network as a locomotion controller and the Genetic Algorithm to optimize network parameters. By this method, we designed various locomotions and carried out experiments [12]. Fig. 9 shows some examples of module configurations for locomotion. See [17] for motion videos of experiments and simulations. 4. Feasibility of operation scenario This section sketches a clearer scenario of Section 3.1. Motions (a) and (b) in Fig. 3, cluster flow type reconfiguration and whole body locomotion, have been well studied individually as above. Other motions in the scenario and feasibility in total are examined here.
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(a) L4b.
(b) L4c.
(c) L4L.
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(d) Sidewinder.
Fig. 11. Four-legged walkers and sidewinder.
(a) Type-2 structure.
(b) Reconfiguring.
(c) L4S walker generated.
Fig. 12. Snap shot of generation sequence of L4S from Type-2 structure.
4.1. Walker generation We have produced a sample sequence showing the construction of a four-legged walking robot (Fig. 9(a)) out of a Type-2 regular structure, as shown in Fig. 10 [7]. Various possibilities of walker generation from the three types of regular structures (operation (c) in Fig. 3) are examined here. Candidates for walking robots are selected and labeled as four-legged walkers (L4a: Fig. 9(a), L4b: Fig. 11(a), L4c: Fig. 11(b), L4S: Fig. 9(b), L4L: Fig. 11(c)), a caterpillarlike serial link (SL1: Fig. 9(c)), and a six-legged walker (L6: Fig. 9(d)). The first three, L4a, L4b and L4c, are almost identical except for one or two modules connecting the four legs. The L4S comprises four modules; simply adding a module to each leg of the L4S produces an L4L. The SL1 is a serial link with the same joint axis direction; the L6 is made of nine modules, all of which have the same joint direction. Table 1 lists the feasibility of walker generation. Each feasible case is valid if there are enough modules in the structure. This table is made by a geometric and kinematic model of the module, hence is incomplete because the feasibility of reconfiguration depends critically on the feasibility of each module motion, which in turn depends on the modules’ hardware. Because the main part of Type-1 has an identical axis direction, substructures are made by the two converter modules, which function as a manipulator to carry other modules. Fig. 10 shows that generating a walker from a Type-2 structure is rather complicated. Transferring modules one by one produces a linear structure: SL1. Similarly, three parallel lines are made, which change to L4a or L6 after separation. Both L4b and L4c are produced by slight modifications.
Fig. 13. Experiment of locomotion control.
Generation of L4S from a Type-2 structure requires a different sequence, but it is possible, as shown in Fig. 12. Generation of L4S from a Type-3 structure involves a simple separation. Generation of L4L is possible by a similar sequence of a Type-3 cluster flow motion, as shown in Fig. 8(b). 4.2. Versatility and metamorphosis of walkers The walkers described above, except SL1, have sufficient versatility of locomotion. The L4a, L4b, and L4c have the same performance of walking to go straight and round and making a turn (Fig. 13). The L4S can go along four directions and the L4L can walk and turn more flexibly [18]. Some of them can metamorphose to others [8]. Both L4a and L4b can form a crawler configuration, whereas both L4b and L4c can metamorphose into linear configurations similar to SL1 capable of caterpillar-like locomotion. L4L can metamorphose into a linear configuration (Fig. 11(d)), which can make a sidewinding motion. Table 2 lists those results.
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Table 1 Feasibility of walker generation: feasibility of generating a walker (column) from a structure (row)
Type-1 Type-2 Type-3
L4a
L4b
L4c
L4S
L4L
SL1
L6
– Feasible –
– Feasible –
– Feasible –
Feasible Feasible Feasible
– – Feasible
Feasible Feasible –
Feasible Feasible –
–: Unknown
Table 2 Feasibility of transformation between configurations
Crawler Caterpillar Side-winder
L4a
L4b
L4c
L4S
L4L
SL1
L6
Feasible × ×
× Feasible –
Feasible Feasible –
× × –
× × Feasible
× × ×
× × ×
–: Unknown, ×: Impossible
(a) Two separate walkers.
(b) Alignment of position and orientation.
(c) Connected.
Fig. 14. Reconnection experiment.
4.3. Reassembly With the current hardware, an operator sends a command via an RF transmitter and the modules either switch their motion accordingly with stored data or change a locomotion pattern. Reconnection of separated modules is possible under such human operation. Fig. 14 shows results of a preliminary experiment in which two four-legged walkers were controlled to align and connect with each other by remote operation. The process of reconnection can be automated, though not easily, with appropriate sensors to measure its position and orientation and with a proper controller. Operation (e) in Fig. 3 is a reverse process of (c), but it is not simple. Table 1 does not guarantee the feasibility of this reversal process. By those sequences of walker generation, a single walker is generated from a large structure, but some length of structure must remain after repetitive generation of walkers because the converters and a supporting structure are always necessary for walker generation, such as that in Figs. 10 and 12. Only in the case of metamorphosis from a Type-3 structure to either L4S or L4L can the generation sequence be reversed. The whole operation scenario requires sequences where multiple walkers gather and form a regular target structure without the help of another structure. 5. Future works and concluding remarks Future efforts will complete and expand Tables 1 and 2 with other configurations and transformations.
Hardware problems remain. Current M-TRAN II hardware is insufficient for a large-scale reconfiguration experiment because each operation of connection or detachment is too slow and consumes too much battery power. We are developing new module hardware using mechanical connections and infrared sensors. By constructing new modules and by developing actual algorithms, we will attempt experiments of a cluster flow motion and walker generation. Moreover, sensors, communication between separate modules and an integrated control method will be investigated to enhance inter-module cooperation. The scenario in this paper serves as a guide for future research exploring modular robots toward use in applications such as search-and-rescue operations. The M-TRAN system can generate a flow motion of the structure, climb a step by transporting modules one by one, and then produce a tower structure to look down. It can generate multiple walkers that present similar advantages to those of swarm robots. Some walkers can metamorphose into a linear structure that is suitable to enter a narrow space; multiple walkers can gather and form a larger structure again. Acknowledgement This study was partly supported by Grants-In-Aid for Scientific Research from Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.
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Eiichi Yoshida received M.E and Dr.Eng degree from Graduate School of Engineering, the University of Tokyo in 1993 and 1996, respectively. From 1990 to 1991, he joined the Department of Microtechnique at Swiss Federal Institute of Technology at Lausanne (EPFL). He joined the Mechanical Engineering Laboratory, MITI in 1996, and since 2001, he has been conducting research in National Institute of Advanced Industrial Science and Technology (AIST). His research interests include decentralized autonomous systems and modular robotics. He received the Best Paper Award in 1998 International Symposium on Distributed Autonomous Robotic Systems (DARS’98). Kohji Tomita received the B.E., M.E. and Ph.D. from University of Tsukuba in 1988, 1990 and 1997, respectively. He joined the Mechanical Engineering Laboratory, MITI in 1990, and has been conducting research in National Institute of Advanced Industrial Science and Technology (AIST) as senior research scientist since 2001. He was a visiting researcher in Dartmouth College from 2000 to 2001. His research interests include modular robots, distributed software systems and graph automata. Akiya Kamimura received M.E and Dr.Eng degree from Graduate School of Engineering, the University of Tokyo in 1997 and 2000, respectively. He joined the Mechanical Engineering Laboratory, MITI in 2000, and has been conducting research in National Institute of Advanced Industrial Science and Technology (AIST) since 2001. His research interests include modular robotics and rapid prototyping systems. He received the Best Paper Award in 2002 International Symposium on Distributed Autonomous Robotic Systems (DARS’02). Satoshi Murata received the B.E., M.E and Dr. Eng degrees in aeronautical engineering from Nagoya University, Nagoya, Japan, in 1984, 1986 and 1997 respectively. In 1986, he joined the Mechanical Engineering Laboratory, MITI. From 2001, he is an associate professor in Tokyo Institute of Technology. His interest includes distributed mechanical system, modular robotics and graph automata. He received IEEE-IE Outstanding Paper Award and SICE Outstanding Paper Award in 1991 and 1996 respectively. He is a member of IEEE, SICE, RSJ and JSME. Shigeru Kokaji received B.E, M.E and Dr.Eng in Precision Machinery Engineering from the University of Tokyo in 1970, 1972 and 1986 respectively. He is currently the Deputy Director of Intelligent Systems Institute, National Institute of Advanced Industrial Science and Technology (AIST). His research interest includes distributed control of mechanical/robotic systems.
