IROS2019国际学术会议论文集Segregation and Flow of Modules in a Robot Swarm Utilising the Brazil Nut Effect

Segregation and Flow of Modules in a Robot Swarm Utilising the Brazil Nut Effect Devwrat Joshi1, Masahiro Shimizu2and Koh Hosoda3 AbstractA lot of research has been conducted on swarm and modular robots and their reconfi guration. For this kind of robot system, it is best to simplify each individual module in order to avoid making the swarm system too complex in the interest of reducing the computing power necessary for a task. This paper proposes a swarm robot system capable of self- segregation by changing the size of each agent, utilising the Brazil Nut Effect. The self-segregation allowed by this effect lead to the simplifi cation of the control protocol necessary for the swarm. We simulated a swarm robot system consisting of circular modules capable of changing their radius and, with the aid of externally supplied vibrations, utilising the Brazil Nut Effect to achieve segregation of the swarm. The effect also allowed for the migration of individual modules through the swarm. Additionally, we harnessed this segregation effect in simulation to create a fl ow of modules within the swarm, whilst the swarm was confi ned within a vibrating container. Lastly, we took the fi rst steps toward physical verifi cation of the experimental results by designing and building a prototype for a circular robot module capable of changing its radius in a manner inspired by a spiral torsion spring. I. INTRODUCTION In this paper, we consider the case of what are called heterogeneous swarms, consisting of n robot modules each of which belong to one or many of k n groups within the swarm. This type of swarm model, initially suggested through work on CEBOT, the pioneering work on modular robots by Fukuda et al. 1, by virtue of distribution of functionality across its constituent groups, would fecilitate the simplifi cation of each individual module, and thus allow for smaller, less complicated modules as a whole. This is as opposed to the most of the works related to swarm robots or modular robots where swarms tend to be homogeneous, made up of identical modules with the same capabilities, such as in works about the modular robots PolyBot by Yim et al. 2 or the SMORES by Davey et al. 3. The individual location of a single module in the swarm is considered to be irrelevent as long as the swarm as a whole can perform the task at hand. A particular example of possible distributed *This work was supported by JSPS KAKENHI Grant Numbers JP18H05467, JP15H02763, JP17K1997 1 Devwrat Joshi is an undergraduate student in the fi nal year of the course offered by the School of Engineering Science, System Science faculty, Osaka University, Japan, and is affi liated with the Hosoda Laboratory. joshi.devwratarl.sys.es.osaka-u.ac.jp 2Masahiro Shimizu is the Associate Professor of the Hosoda Laboratory, affi liated with the School of Engineering Science, System Science faculty, Osaka University, Japanshimizusys.es.osaka-u.ac.jp 3 Koh Hosoda is the Professor of the Hosoda Laboratory, affi liated with the School of Engineering Science, System Science faculty, Osaka University, Japanhosodasys.es.osaka-u.ac.jp functionality might be equipping different groups of modules with different types of sensors responsive to different stimulii or actuators capable of a variety of actuation. In such a swarm, given that not all modules have the same capabilities, it might become necessary for a certain type of module to be in a certain part of the swarm to perform a given task. It would therefore be useful for modules in a swarm to be able to segregate based on module capability. There exist works in the fi eld which attempt to solve this segregation problem for heterogeneous swarms 4 5. Most of these works however rely on the concept of different artifi cial potential between modules of different groups for segre- gation effects. While these models are certainly effective for segregation of heterogeneous swarms, they require inter- module communication in order to be replicated in the real world. If this was replaced by a physical effect relying on physical module interactions, it might allow the design of simple modules that can segregate by nothing more than inter-module collisions. The physical self-segregation effect considered in this paper is the Brazil Nut Effect. The Brazil Nut Effect (BNE) 6 7 8 9 10refers to the emergent segregation of particles by size in a granular mixture subjected to vibrations. The advantage of the BNE is that it offers complex and variable internal reconfi guration of a swarm without the need for a proportionately complex control mechanism. Of the studies surveyed, some were found to take advantage of BNE for swarm. In one such study, by Sugawara et al., a system of vibrating circular active modules was simulated. Rather than the vibration energy being provided externally, as in most BNE related studies 6 7, the modules themselves vibrated 11. This work attempted to solve the box-pushing problem 12, moving a passive load larger in diameter than the active modules in the opposite direction of a global force by taking advantage of BNE. In a study by Groet al, an algorithm was developed for swarm robot segregation for robots simulated in a horizontal plane 13 based on the BNE. In a continuation of that study, Chen et al produced a physical realization of the algorithm making use of 20 DD e-Puck robots 14. The studies managed to make the robots assume an annular formation centered around an overhead light source with the smaller robots in the middle and the larger robots around the outside 15. However, a majority of these studies focus on reconfi g- uration of the robot swarm in a 2D plane in the absense of gravitational effects. We feel that in order to take full advantage of the emergent properties that would come with the Brazil Nut Effect, it would be necessary to allow the 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Macau, China, November 4-8, 2019 978-1-7281-4003-2/19/$31.00 2019 IEEE4080 effects of gravity on the interacting modules and let seg- regation take place due to actual inter-module collisions as well as interactions with the bounding container. This paper therefore, will attempt to achieve segregation of a robot swarm based on the Brazil Nut Effect where the segregation of modules by size will occur in the vertical plane. In addition to achieve module segregation based on size, we consider the possibility of creating a fl ow of modules within the swarm as another method of movement for the modules within the swarm. The motivation for creating this fl ow is the same as that for swarm segregation. We feel that being able to control the internal dynamics of the swarm by stimulating fl ows with the aid of the Brazil Nut Effect would be worth investigating, as it might lead to further methodologies for internal reconfi guration of the swarm and restructuring of local groups of modules within it. This paper is organised in the following way: Initially in Section II, we provide a concrete idea of the scope of this paper and the motivation behind it. This is followed by an account of the simulation experiments conducted in Section III. In Section IV, an application of the swarm segregation using the Brazil Nut Effect is presented and a summary of the characteristics of the prototype robot module constructed is presented in Section V. Finally, the conclusions and future work are noted in Section VI. II. PROPOSEDSWARMROBOTMODEL The most important contribution of this work is that individual modules within a robot swarm migrate within the swarm independent of initial position. For a heteroge- neous swarm consisting of different groups of modules with different capabilities and on-board sensors, this means that modules equipped with the same kind of sensor migrate towards a particular section of the swarm and congregate there in response to external stimulus specifi c to that sensor. For example, modules equipped with an infrared light sensor could move toward the source of infrared radiation incident on the swarm, while modules not equipped with the sensor would not react to it. For this work, we propose a 2D swarm robot system consisting of a number of circular modules. Each module is capable of changing its radius via an on-board motor. The swarm will be constrained to move in a bounded plane under the infl uence of gravity. Unlike in other studies surveyed that take advantage of BNE for swarm segregation 13 15, we focus on using gravity as the biasing force and seek to segregate the robots in a vertical plane. This work will attempt to produce a system of swarm robots where each circular module can change its radius in response to an external stimulus unique to that module or a group of modules and rise to the top of the swarm in response to external vibration, effectively segregating the swarm into large and small modules. In order to move from one end of the swarm to the other, the module would only need to change its radius. Segregation would be acheived through nothing but local interactions between modules without the need for a complex control protocol. We feel this approach would greatly be useful for heterogeneous swarms of robots. As pointed out in 16, particularly in the case of swarm robotics, as the number of robots in a system increase, simu- lation results may diverge from real-world results. Therefore, a real world verifi cation of the relationship between these investigated factors and the properties of the Brazil Nut Effect of the swarm is essential. To verify the smulation results, a physical prototype of a module capable of chaging its radius is produced. III. SIMULATIONS Simulations were conducted to demonstrate the Brazil Nut Effect in the case of modules with variable radius. As described above, several studies researching the Brazil Nut Effect investigate the rise time of a single large intruder through a bed of smaller particles. A common pattern has been to investigate the change in the rise time of a sin- gle intruder in response to change of parameters such as amplitude or frequency of vibration. However, the swarm proposed in this work assumes groups of robots containing multiple member modules, all of which would change their size in response to an external stimulus. Rise time is not useful to determine the effectiveness of the Brazil Nut Effect in this case. This is partly because it is unclear at what point all the members of the group can be considered to have “risen” (either when a single large module enters the top layer of the swarm or when a certain fraction of large modules are at least above the mean height of the swarm etc). Therefore, in place of rise time, a dimensionless parameter was used to determine the degree of segregaton of the swarm. Simulations were conducted to determine the change in with change in frequency and amplitude. In addition to segregation, another objective of this re- search was to attempt to generate fl ows of modules in predictable directions within the swarm. This was meant to be in aid of reconfi guring the internal structure of the swarm, allowing a particular module to move to a particular location in the swarm rather than merely upward as in segregation. Simulations were conducted to attempt to generate such a fl ow and to control its direction. The simulations were conducted in 2 dimensions using a java-ported version of the Box2D library (jBox2D). In all simulations, the coeffi cient of restitution of the modules was set to 0.85, the coeffi cient of friction between the the side walls and the modules was set to 0.4 and between modules was set to 0.3. The modules were considered to have 2 possible states, “large state” and “small state”, with the diameter ratio of large state to small state set to 2. The density ratio of the large modules to that of the small modules was set to 0.25, maintaining a constant mass when the module increased in size. The total number of modules in the swarm was N = 100 for segregation simulations and N = 50 for fl ow simulations. A. Segregation Experiments was defi ned as = (Cs Cl)/H., where Csis the height of the center of mass of the small modules, Clis 4081 the height of the center of mass of large modules and H is the height of the swarm. Positive therefore indicates a state where small particles are higher than large particles, near 0 indicates a mixed bed and a negative indicates a bed where large modules are higher than small modules. The change in lambda with changing frequency of vibration and amplitude was investigated. The frequency was taken to be between 15 Hz and 40 Hz. The amplitude was taken between 0.03dsand 0.25ds, where dsis the diameter of the small modules. The total number of large module was kept constant throughout the segregation simulations at 10 modules, or 10% of the total. Each simulation was conducted for 20000 steps (approximately 100 seconds). The simulations were run and the results were plotted using a frequency-amplitude- graph. The graph can be seen in Fig.1. Fig. 1.Graph of frequency-ampltude-segregation parameter . Red cells indicate a positive while blue cells indicate a negative . Increase in frequency and amplitude can be seen to improve segregation due to the Brazil Nut Effect. As can be seen from the graph, the degree of segregation is seen to improve with increasing frequency and amplitude. Increase in amplitude can be seen to have a greater infl uence on than change in frequency. B. Flow Experiments In the previous section, segregation of modules based on the Brazil Nut Effect was discussed. The objective of segregation within the swarm is to enable the modules to move independently of their local group and navigate through the swarm. Under normal conditions, when a mixture of large and small modules of fi xed size (where the modules are unable to change their radius), are subjected to vertical vibrations, the larger modules tend to rise to the top of the swarm. This was demonstrated in the segregation experi- ments. Once the two groups of modules segregated, there is no signifi cant change of the distribution of the modules even after continuing to subject the swarm to vibrations. In other words, the groups of large and small robots tend to remain segregated once seperated in the case of the modules being of constant size. However, the modules proposed in this work have variable radii. If the radius of the modules is controlled according to their relative location in the swarm, they could be made to move contnuously through the swarm driven by the Brazil Nut Effect. In an example of this, the modules in the swarm were controlled such as their radius became large at the bottom of the swarm, and small when they reached the top of the swarm. Due to the Brazil Nut Effect, the modules that become large at the bottom of the swarm would tend to rise to the top of the swarm, where they would decrease their radius and then fall to the bottom of the swarm as larger modules coming from the bottom took their place. Further, in order to control the direction of the resulting fl ow, we set up 2 “zones” within the container, one for large robots and one for small robots. When a module enters the large zone, it increases in size and, conversely, decreases in size when it enters the small zone. By changing the boundary conditions between these zones, changes in the nature of this fl ow were observed. In this group of experiments, we attempted to determine the nature of the fl ow of modules within the container. In order to create a fl ow of modules in, say, the clockwise direction, we would need to set up a path profi le that went upward on the left side of the swarm, and downward on the right side of the swarm. An example of such a profi le is shown in Fig.2. In the fi gure, the purple line indicates the boundary line between the large and small zones. Due to the modules only being large in the large zone, the Brazil Nut Effect only took place in this section of the container. The voids created due to this upward movement of large modules would be occuped by small modules from the other zone. As seen in the fi gure, there are 4 phases to the velocity diagram. They will be detailed below: Phase A: Large modules move upward due to the Brazil Nut Effect. Phase B: Modules fall to the other side of the container. Phase C: Modules decrease in size and tend to move dwnwards through the swarm. Phase D: Modules move in through the small zone to occupy the voids left by the modules in Phase A Fig. 2. The path profi le for modules in a clockwise fl ow within the swarm 1) Flow for a horizontal boundary line: For this set of simulations, we attempted to investigate the generation of 4082 fl ow for a horizontal boundary line. In the case of normal Brazil Nut Effect simulations, certain modules in the swarm increase their radius, and the time to rise through the swarm is calculated. However in this case, the objective was not merely to cause segregation, but also to cause a stochastic but predictable fl ow of modules in the swarm. In aid of that, it was necessary for modules to become large in order to move upward and small in order to be able to move downward in the swarm. A screenshot from the simulation in progress can be seen in the Fig.3. A certain percentage of modules below the lower bound were made to increase in size. In the simulation, we set up a lower boundary line below which a certain percentage of modules would become large, and an upper boundary line above which the large modules would become small. All modules maintained their sizes between these two bounds. In order to evaluate the kind of fl ow occuring, the position of one of the modules was monitored during the duration of the simulation. This module is shown in red in the fi gure. The two boundary lines are shown in orange. Fig. 3.Screenshot of the simulation with horizontal b