Lattice-based artificial endocrine system model and its ... - Springer Link

SCIENCE CHINA Information Sciences

. RESEARCH PAPERS .

April 2011 Vol. 54 No. 4: 795–811 doi: 10.1007/s11432-010-4157-8

Lattice-based artificial endocrine system model and its application in robotic swarms XU QingZheng1,2 & WANG Lei1 ∗ 1School

of Computer Science and Engineering, Xi’an University of Technology, Xi’an 710048, China; 2Xi’an Communication Institute, Xi’an 710106, China Received February 1, 2010; accepted July 22, 2010; published online February 17, 2011

Abstract To solve the problem of controlling robot swarms in a distributed manner, we propose a novel latticebased artificial endocrine system (LAES) model, inspired by modern endocrinology theory. Based on a latticed environment, relying on cell intelligentization, connected by cumulative hormones, and directed by target cells, the LAES model can finally adapt to the continuous volatility of the external environment and maintain the relevant stability of the internal dynamics of the system, thus exhibiting the self-organizing and self-repairing features of the biological endocrine system. Experiments show that the LAES model enables a robotic swarm to search an unfamiliar space and seize multiple targets automatically without using unique global identifiers or a centralized control strategy for the individual robots. This demonstrates that the model can reliably be used to simulate large scale swarm behavior through wireless communication. Keywords artificial endocrine system, robotic swarms, endocrine cell, hormone, self organization, self repair, searching and seizing Citation Xu Q Z, Wang L. Lattice-based artificial endocrine system model and its application in robotic swarms. Sci China Inf Sci, 2011, 54: 795–811, doi: 10.1007/s11432-010-4157-8

1

Introduction

Until recently, it was thought that the major regulating systems of the human body—the cerebral nervous system, the immune system and the endocrine system—functioned independently of one another. Bolstered by modern scientific research, it is now known that they are, in fact, all integrated into a single system of information communication. With bidirectional information transmission between cytokines, neurotransmitters and hormones, these systems interact and cooperate with one another to organize a cubic intelligent regulatory network. We have reason to believe that the structure of these regulatory systems may affect metabolism, growth, development, reproduction, thinking and motion in most mammals, including humans, and may also be responsible for responding adaptively to maintain the long-term dynamic equilibrium of the organism and organization when the internal and external environments change rapidly and the physiological balance is unexpectedly disturbed. Enormous achievements in the theory, modeling and application of artificial neural network [1–3] and artificial immune system [4–6] have shown the significant theoretical meaning and practical application value of intelligent systems research based on a biological information processing approach. At the same time, they have inspired and guided the ∗ Corresponding

author (email: [email protected])

c Science China Press and Springer-Verlag Berlin Heidelberg 2011

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Figure 1

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April 2011 Vol. 54 No. 4

Diagrammatic representation of hormonal sensitization of the response of sets of neurons [10].

interest and enthusiasm in research on other biological information processing systems including the endocrine system. Making slow progress, comparatively speaking, research on artificial endocrine system (AES) is at the discipline creation and preliminary exploration stage, and a great many challenges still remain with respect to the theoretical model and engineering application thereof. An autonomous decentralized system (ADS) proposed by Mori in 1984 is perhaps the earliest attempt at using hormone-inspired methodology to build distributed functional systems with properties of online expansion, online maintenance, robustness and flexibility [7, 8]. In the ADS, the content code communication protocol has been developed for autonomous systems to communicate through a semantics-based system, and not a conventional syntax-based system. The ADS technology has been applied in various systems to control trains, multi-stage dams, water supplies, and production [9]. The hormone computational model is a theoretical AES model with obvious biological significance. As the theoretical foundation, the principle of mutual interaction between hormones, neurohormones and the nervous system to control the complicated combined behavior of lobsters was first addressed by Kravitz [10], as illustrated in Figure 1. The underlying idea behind the hormone computational model is that an activation level depicts behavior activation rank [11]. Based on the hormone computational model, a robotic swarm can exhibit perfect survival ability and high efficiency, and avoid collision behavior within a behavior selection process. However, there are some unresolved issues, such as improvement and enhancement in terms of learning capacity and flexibility. Later, based on the identical principles of biological systems, a regulation model of hormones was proposed by Avila-Garcia and Canamero [12, 13]. They considered fully the effective significance in behavior decisions, resulting in an ideal solution for dealing with internal and external stimuli to choose the appropriate behavior. Shen [14–16] proposed the digital hormone model (DHM) as a distributed control method for robot swarming behavior. The model integrates the advantages of Turing’s reaction-diffusion model, stochastic reasoning and action, dynamic network reconfiguration, distributed control, self-organization, and active learning techniques. Mathematically speaking, the DHM has three components: a dynamic network, a specification of a probabilistic function for individual robot behavior, and a set of equations for hormone reaction, diffusion, and dissipation. The DHM has identified a number of potential features such as simple structure, complete mathematical description, and extensive application areas [17–19], and it will quite likely become the general theoretical model for AES. However, it lacks a coordination and cooperation mechanism among endocrine cells, which may result in difficulties in overcoming interference from complicated external environments, such as multi-target and barriers. Perhaps the most extensive application of artificial endocrine systems to date is in the robotics field.

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Under the leadership of the Director, Dr. Shen, researchers and engineers in the Polymorphic Robotic Laboratory at the University of Southern California have conducted research on self-reconfigurable, autonomous, and adaptive robots with meaningful achievements. One of their main contributions is a biological hormone-inspired decentralized control mechanism [20–24], the fundamental idea of which is that the self-reconfigurable system can be seen as a network. In the network, where contact and communication is through hormone information, each node is, in fact, an individual autonomous robot with its own energy, flow, accelerators, sensors and connectors. A hormone is the signal to trigger different modules and thus, different behaviors. Once triggered, the corresponding modules execute the behavior on their own. Mendao [25] utilized hormone signals to coordinate the completion of several tasks at one time by an individual autonomous robot. Each task is imagined to be a gland, which can release hormones into a hormone pool at a fixed speed. Once the hormone concentrations in the hormone pool are greater than the pre-determined threshold, they are released as free hormones and disseminated over the whole network. Free hormones with a maximum concentration motivate behavior-controlling modules to implement the corresponding task, at which time the gland stops releasing hormones. This model was later expanded by Walker to a task assignment system for multiple autonomous robots [26]. Each task is assigned dynamically to an autonomous robot with low complexity, and every robot can automatically choose an appropriate response to sustained changes in all the robots and/or the external environment. However, this system may over-react to minor environmental changes and parameter adjustments. As a result, this may directly affect the system’s overall performance. In recent years, artificial endocrine systems have been widely used in human-machine communication of emotions [27–29], multiprocessor system control [30–32], decoupling control [33–35], management systems in autonomic networks [36], and real-time task allocation in heterogeneous processing systems [37–39]. Due to additional research findings in modern endocrinology and continued development and expansion of the artificial endocrine system, its core idea and key techniques are now more deeply understood and some inherent faults are gradually being discovered as discussed below. First, hormones in our body are divided into more than 200 distinct species that have hitherto been detected and recognized. These hormones with complex sources and distinguished functions are widely distributed in the blood, tissue fluid, intercellular fluid, intracellular fluid, or gaps of ganglion vesicle and other parts. In the models and algorithms described above, all endocrine cells have the same physiological function and the nature of all hormones is identical, and thus, the models cannot reflect the diversity of hormones and complexity of the interaction between them. Second, the effective hormone concentrations are determined collectively by the speed of synthesis and release and by the speed of degradation and conversion, which are exquisitely regulated by the cerebral nervous system so as to keep the hormone concentrations at normal levels. For some unknown reason, the authors make the assumption that all hormones can degrade or convert to other forms very quickly and completely in most of the above models and algorithms. As a result of this, hormone concentrations are only related to the current distribution of endocrine cells, and have nothing to do with their past distribution. Finally, only certain local features of biological endocrine systems are highlighted and mimicked in all models, while global features, such as self-organizing and self-repairing, are totally neglected. To address these problems, and inspired by information processing mechanisms in the endocrine system, particularly the coordinated effect of hormones, we present the lattice-based AES in this paper.

2

Overview of endocrine system

A most interesting observation is that, as an independent discipline, endocrinology is less than 100 years old, despite our ancestors having access to preliminary knowledge about endocrine phenomena a long time ago. In recent years, revolutionary changes have taken place in modern endocrinology under the influence of new theories and technologies in molecular biology, cytobiology, immunology, genetics, ecology, psychology, and clinical medicine [40–42]. At the same time, we have a more in-depth and comprehensive understanding of the information processing strategies in the endocrine system.

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Endocrine system structure

It is well-known that the endocrine system is an important regulatory system in mammals. To be more specific, the system comprises various endocrine glands and histiocytes, which are widely spread throughout different parts of the body, and has a crucial role in cell growth, differentiation, and apoptosis, as well as in preserving stability of the internal environment in mammals with the help of hormones. According to the classic definition, hormones are efficient bio-active substances, secreted by endocrine cells and transported by the blood circulatory system to remote organ tissues, where they adjust cell functions. Through the process of transcription, translation and post-translation, protein and peptide hormones are synthesized. Having been stimulated by a hormone cell, vesicles combine with the cell membrane, and then the hormones stored in the vesicles are set free from the endocrine cell. On the other hand, amines and steroid hormones use tyrosine and cholesterol as raw materials, which are transported to a certain kind of steroid hormones with the help of a serial enzymatic reaction. Because these are highly soluble in lipids, they can exocytose with a simple diffusion action and transit immediately in the circulatory system. The hormone release process is staged; in other words, most of the process takes place in seconds and then there are few or no hormones in the interval between two release processes. As a result, the hormone concentrations in plasma fluctuate in a short period of time. The path of hormone transport may be long or short with diversity of forms and functions. In the blood circulatory process, various hormones are combined with specific plasma protein to varying degrees. The other hormones are transported at dissociative states in the blood circulatory system. It should be noted that combined hormones are not active; only dissociative ones are. The entire metabolism process between release and consumption of the hormones can be either long or short. In general, we use a half-life to measure the validity period of hormones. The half-life of peptide hormones is short, between 3 and 7 min. On the other hand, the half-life of steroid hormones depends mainly on the molecular type and structure and changes over a period of a few hours or a few weeks in some cases. Nevertheless, it is longer than that of peptide hormones. 2.2

Types of hormone effect

Modern endocrinology research has found that the function of hormones is not isolated, but interrelated. All endocrine glands scattered across different parts of the body are included in the endocrine system that adjusts all the basic life processes. It is also well-known that the regulatory system is so precise that it is equipped with strong variability, accurate rating, and extreme safety factors. It is generally agreed that there are various types of hormone effects as discussed below. i) Single hormone, multiple effects. Most hormones have different roles in different tissues and even different life cycles of the same tissue. For example, testosterone can accelerate the sex differentiation of a male embryo, influence the growth of the male genito-urinary system, adjust the speed of sperm generation and erythropoietin synthesis, promote the development and growth of pubes and body hair, and strengthen prostatic hypertrophy. From the perspective of modern gene and molecular biology, all these different roles of a single hormone have the same mechanism. ii) Multiple hormones, single effect, that is, the synergistic effect. Almost all physiological functions and pathological responses are the result of combined control and action among many hormones and cytokines. For example, hyperglycemia is the result of the direct effect of glucagon, adrenalin, norepinephrine, cortisol and growth hormone, and the indirect effect of the thyroid hormone influencing orexis, somatostatin restraining insulin, and glucagon. iii) Two hormones, opposite effect. For instance, the parathyroid gland increases blood calcium, while calcitonin decreases it. iv) Empowerment effect. Hormones can merely increase sensitivity of the tissue in terms of certain physiological information, such as nervous impulses or metabolites, and have no physiological effect on

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Activating endocrine cell

Repulsion hormone


799

Inhibiting endocrine cell

Attraction hormone

Target cell

Figure 2

Lattice-based artificial endocrine system.

organs or cells. That is a necessary condition for other hormones to have a physiological effect, such as the effect of norepinephrine versus cortisol on blood pressure. Last but not least, there may be a neutral effect, that is, no effect between hormones.

3

LAES model

The fundamental idea of the LAES is that a swarm is a network of endocrine cells that are dynamically distributed and move freely within the latticed network. These endocrine cells utilize cumulative hormone information to communicate, collaborate, and accomplish a particular task under the guidance of the target cells. The cumulative hormone information is similar, but not identical, to content-based information. A cell does not have an address, but propagates through the swarm within the entire latticed network. Each endocrine cell decides the next action autonomously relying on its hormone information, the local topological structure, and its own state. Mathematically speaking, the LAES can be abstracted as a quintuple model, LAES=(Ld , EC, TC, H, A), where LAES denotes the lattice-based artificial endocrine system, comprising five components: the environment space Ld , endocrine cells EC, target cells TC, hormones H, and an algorithm A [43]. The first four components are discussed in the next section, while the algorithm is described alone until section 3.2. 3.1

Design of LAES

In our model, all the LAES elements live, communicate, move, and die within a bounded square, called the environment space Ld , where positive integer d is the dimension of the environment space. Here, we first explore the simplest case, with d = 2, and then we extend the mature research ideas, methodology and achievements to the higher dimensional cases at the appropriate time. In the human body, as is well known, the endocrine system with its very complex functions has a vital role in an extensive action domain, and all endocrine cells are diffused freely in continuous space occupying a given position. First, for simplicity, we employ a two-dimensional environment space that is discrete or latticed. Obviously, the smaller the discrete scale, the greater the number of lattice units is. There is no restriction on the lattice form and a standard square is widely used, as shown in the background in Figure 2. We let Lxy denote the use status of the lattice unit at row x and column y. Nothing occupies this unit if Lxy = 0,

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while obstacles such as walls, bars, doors, or rivers occupy the space when Lxy = −1. It is noted that each lattice can only contain one endocrine cell. The endocrine cell EC, also known as a unit cell or elementary cell, is the most fundamental component of the LAES model. Considering low cost and complexity, each endocrine cell should be as simple as possible. In this paper, each endocrine cell is equipped with one sensor AE , which is responsible for perceiving the hormone concentrations of neighboring lattices, and one releaser BE . Modern endocrinology tells us that the hormone release process is staged and that the activity period is very short compared with its lifetime. Thus, we make the assumption that the hormone release process is discrete and the releaser BE is responsible for releasing a certain quantity of the hormone at a suitable time. In addition, it is well known that there are a variety of hormones with different functions in our body. Hence, according to the variation in hormone concentration in the lattice, endocrine cells are divided into two kinds, referred to as activating endocrine cells ECA and inhibiting endocrine cells ECI , respectively, in this paper. When the hormone concentration in the lattice is increased, the cell occupying the lattice is an ECA and Lxy = 1, as shown in the upper left in Figure 2. On the contrary, as the concentration decreases, the cell occupying the lattice is an ECI and Lxy = 2, as shown in the upper right in Figure 2. The target cell TC is an organ or cell that can accept stimulation from endocrine cells. Its receptor has the ability to bind directly with a specific hormone. Generally, the target cell is identified as the target to be seized and task to be accomplished in our paper. A target cell is abstracted as a simple releaser BT that constantly releases hormones with an appropriate concentration to attract the surrounding endocrine cells, as shown at the bottom in Figure 2. It is important to note that, it is unlikely that endocrine cells will generate without foundation, or fade away. Instead, they communicate with each other and move according to the move rule. When an endocrine cell arrives at the position of the target cell and thus achieves the established target, the particular target cell dies and stops releasing hormones immediately. Hormones are efficient bio-active substances, secreted by endocrine cells and endocrine glands. They have an important role in effecting physiological function and adjusting the metabolism of tissue cells in our body. In this paper, hormones, H, are classified as repulsion hormones Hr or attraction hormones Ha , as shown in the middle in Figure 2. Generally, target cells only release attraction hormones, thereby helping endocrine cells to find and seize them. On the contrary, inhibiting endocrine cells only release repulsion hormones, thereby holding back others from searching the same or a similar area. Activating endocrine cells release more attraction hormones than repulsion hormones, which mean that others are likely to search the similar area, thereby increasing the probability of seizing the target cell. It should be noted that the action sphere of hormones is limited to a spatial domain, called the neighborhood. In principle, the size and form of the neighborhood have no limit. Furthermore, influenced by the cellular automata model, we have chosen an extended Moore type as the hormone action sphere in this paper [44]. This is expressed as follows: N Moore-r = {(Nx , Ny )||Nx − x| r, |Ny − y| r, (Nx , Ny ) ∈ Z2 },

(1)

where Nx and Ny are the row and column coordinates of the neighborhood, respectively, x and y are the row and column coordinates of the centrocyte, respectively, and r is the neighborhood radius. In biological endocrine systems, after being synthesized and released in endocrine cells, hormones move into a corresponding neighborhood through the blood circulatory system with the max transportation distance determined by the neighborhood radius r. In the blood circulatory system, hormones exist for a long time in two forms: inactivity combined hormones and activity dissociative hormones. Therefore, we assume that activity hormone concentrations at different locations follow a normal distribution during transportation. The ith type of hormones released from endocrine cell j at position Lab ((a, b) ∈ NMoore-r ) at time t are transferred to position Lxy through the blood circulatory system, and the concentration of dissociative hormones at this position can be expressed as follows: 2

2

ai (x−a) 2σ+(y−b) 2 i Hij (x, y, t) = e , 2πσi2

|x − a| r,

|y − b| r,

(2)

where σi2 is the standard deviation representing the transportation loss, and ai is a constant representing the activity hormone ratio.

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As time goes by, hormones may run out as a result of conversion or degradation, and the hormone concentrations will naturally decline. Thus, endocrine cells are required to synthesize and release new hormones so as to maintain the natural equilibrium of hormone concentrations in the organism. After metabolism, the cumulative hormone concentration at Lxy is equal to the sum of the remaining concentration of activity hormones and the concentration of newly synthesized and released hormones. This can be expressed as follows: ⎧ m n ⎪ ⎪ ⎪ Hij (x, y, t) + H (x, y, t), t > 1, ⎪ ⎨ j=1 i=1 (3) H(x, y, t) = n m ⎪ ⎪ ⎪ H (x, y, t), t = 1, ij ⎪ ⎩ j=1 i=1

H (x, y, t) = (1 − α)H(x, y, t − 1),

(4)

where m is the number of endocrine cells in the action sphere, n is the type number of the hormones, and α is the metabolism extinction coefficient. 3.2

Algorithm design

Algorithm A is an iterative process in which all fundamental elements of the LAES can communicate, move and finish the designated task. The pseudocode for algorithm A is given in Figure 3. An endocrine cell in the LAES chooses its move direction and distance based on move rule R, which is a dynamics function dependent on three local factors: cell condition, cumulative hormone concentrations and local topology. It is obvious that move rule R depends on local information and is homogenous for all endocrine cells in a two-dimensional plane. Even so, it can greatly influence the sophisticated behavior of the system as shown by the following experiments, and offer significant help in predicting and analyzing the global system performance. Assume that h0 is the cumulative hormone concentration of the lattice at the kth step, h1 , h2 , h3 ,. . . ,h8 are, respectively, the cumulative hormone concentrations of the surrounding eight lattices, as shown in Figure 4. Based on the above definition, move rule R can be described as follows. Step 1. Compute the select probability pi (i = 0, 1,. . . ,8) of each lattice according to the cumulative hormone concentration hi . The alternative method is a variation of eq. (5) used in our work. ⎧ 10 × hi , hi > 0, ⎪ ⎪ ⎨ hi = 0, (5) pi = 1, ⎪ 1 ⎪ ⎩− , hi < 0. hi Step 2.

Determine the next position of the endocrine cell according to the roulette selection rule.

Step 3. The endocrine cell moves in a virtual way. If several endocrine cells occupy the same lattice, then they move towards the nearest vacant lattice. This move rule not only provides a guarantee that the lattice with more attraction hormones is selected with a greater probability, but also simplifies the computation process and increases the algorithm efficiency in the long run. 3.3

Self-organization and self-repair of the LAES model

Although it is influenced and controlled by the nervous system, the endocrine system plays a main function through interaction and self-organization among its fundamental elements. On the whole, it is a highly integrated and autonomous system. As part of the complex body chain, hormones are not isolated; in fact, their quantity and influential power seem to be adjusted by other symbiotic hormones. At the same time, inadequate or plethoric function of the endocrine gland can change the speed of hormone synthesis in other glands. Many examples show that two different hormones have an opposite effect. For example,

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1 Input: initial distribution of endocrine cells: {(ECix , ECiy ), i = 1, 2, . . . , M }, initial distribution of target cells: {(TCix , TCiy ), i = 1, 2, . . . , N } and environment space Ld : Width×Length

2

3 Output: trajectory of endocrine cells 4 Algorithm: 5 Initialize 6t=0 7 while N = 0 do 8

ECA = ∅

9

ECI = ∅

10

for j = 1 : M do

11

Determine a category and add it into ECA or ECI

12

for (x, y)Nmoore−r do

13 14

Compute Hrj (x, y, t) and/or Haj (x, y, t) according to eq. (2)// transport endfor

15

endfor

16

for j = 1 : N do

17 18 19

for (x, y)Nmoore−r do Compute Haj (x, y, t) according to eq. (2) endfor

21

for i = 1 :Width do for j = 1 :Length do

23

Compute H (x, y, t) according to eq. (4)

24

Compute H(x, y, t) according to eq. (3)

25

// transport

endfor

20 22

//differentiate

// metabolism // synthesize and release

endfor

26

endfor

27

for j = 1 : M do

28

ECjx ← New ECjx according to move rule R

29

ECjy ← New ECjy according to move rule R

30

if endocrine cell j coincides with one target cell do

31

Do the job

32

N ←N −1

33

endif

34

endfor

35

t←t+1

// update position

// perform the task // target cell dies

36 endwhile Figure 3

Figure 4

Pseudocode for algorithm A.

Example of an endocrine cell moves according to the move rule.

human insulin decreases blood sugar, whereas glucagon increases it. As a further example, the anterior pituitary cells are controlled by dual-promoting pituitary hormones, one to accelerate release of the secretions, and the other to decelerate the release process thereof. In short, the endocrine system shows its homeostasis and self-organization through the local behavior of its inner subsystems. With respect to the problem of congenital aplasia and acquired diseases of the endocrine or other systems, hormone concentration levels may be higher or lower than normal. Because of the hyper or hypo function of the endocrine gland, pathosis or sub-health may occur in the body, or even endocrine system diseases. Modern molecular endocrinology shows that effective measures can be taken to maintain

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the balance of hormone concentrations and prevent diseases of the endocrine system. Fortunately, the same physiological function can be achieved in the human body by various different hormones. Usually, if a hormone is lacking, we can synthesize, transform and release more of the other alternative hormones to maintain the stability of the whole body. One aim of this paper is to test whether the LAES model is self-organizing and self-repairing. Our research questions are listed below. i) Can the LAES model enable cells to self-organize into a pattern using simple rules? ii) Will the size and shape of the final pattern be invariant with respect to the cell population size? iii) How do the quantity and distribution of hormone diffusion affect the size and shape of the final pattern? iv) Will an arbitrary parameter setting enable self-organization and pattern formation? v) Generally, what is the amount of variation in the two kinds of endocrine cells? vi) Can the LAES model maintain a pattern and self-repair any extensive unexpected damage to the external environment? To answer these questions, we carried out four experiments as explained below. The LAES model was programmed in Java and experimental data was analyzed and processed using SPSS 14.0. The execution environment was a Pentium IV 2.4 GHz with 512 MB RAM. The environment space for the LAES was a 100×100 latticed network. In the first experiment, we used the same quantity and distribution of hormone diffusion and conducted a set of simulations with different cell population sizes, ranging from 10% (∼1000 cells) to 70% (∼7000 cells). Starting with cells randomly distributed on the grids, each simulation ran for up to 500 action steps, and we recorded the configuration snapshots of endocrine cells and hormone concentrations at 1, 5, 20, 50, 100 and 500 steps. As can be seen from the results in Figure 5, cells in all simulations do indeed form a pattern. We observe that for relatively small sizes (up to 30%) the cells form isolated clusters as shown in the bottom two rows. Furthermore, it seems that the size of these clusters most likely depends on the cell population size. On the other hand, if we increase the cell population, the cells start to form striped patterns (as shown in the top two rows in Figure 5). Note that the orientation of the stripes is random, both vertical and horizontal, for the uncertain behavior of a single cell, even with the same initial cell distribution. In the second set of experiments, we started with the same cell population and hormone diffusion distribution, but varied the amount of hormone diffusion as high, moderate or low. As shown in Figure 6, with an equal quantity of the two kinds of hormones (refer to the diagonal line from the top right to bottom left), the cells clearly form a final pattern after 500 steps. If the hormone quantity of activating endocrine cells is dominant (bottom right part of the figure), the size of the final clusters increases. Moreover, as the ratio of the quantity of ECA to ECI increases, the size of the final clusters also increases. On the other hand, if the hormone quantity of inhibiting endocrine cells is dominant (upper left part of the figure), the LAES model is barely able to form any pattern. If the hormone quantity of inhibiting endocrine cells is much greater than that of activating endocrine cells, the cells will never form any pattern, regardless of how long the simulation runs. This shows that not all hormone quantities enable self-organization. In the third experiment, we used the same cell population size and hormone diffusion quantity to observe the effects of the hormone diffusion distribution on the final pattern formation results. As can be seen from the results in Figure 7, with a balanced distribution of the two kinds of hormones (as the third row), the cells form a final pattern similar to that in the first set of experiments. Moreover, as the quantity of attraction hormone increases, the size of the final clusters also increases. If the quantity becomes so high that there are only attraction hormones and no repulsion hormones present, the cells form increasingly large clusters through cluster aggregation (see the fourth row). On the contrary, when the quantity becomes so low that repulsion hormones accumulate to a greater degree than attraction hormones, the cells will never form any pattern, regardless of how long the simulation runs. This confirms that not all hormone distributions enable self-organization. In addition to investigating the size and shape of the final pattern, we also investigated the variation in quantity of the two kinds of endocrine cells. The test method used is a typical experiment, with the

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Population size

70%

50%

30%

10%

1

5

Figure 5

20

100

50

500

Steps

Pattern formation with different cell population sizes.

Hormone diffusion quantity of ECI

High

Moderate

Low

Low Figure 6

Moderate

High

Hormone diffusion quantity of ECA

Pattern formation with different quantities of hormone diffusion.

parameters chosen from the common parts of the experiments given above (see the bold parts in Figures 5–7). To eliminate random errors from the initial distribution of endocrine cells and iterations of the model itself, each experiment was independently executed 20 times. As shown in Figure 8, initially, there are no concentration variations in the lattices, but then all endocrine cells are seen as inhibiting endocrine cells. In the second step, the hormone concentrations in a great many lattices increase compared with the last step, and cells occupying these lattices convert to activating endocrine cells. Thereafter, the number of activating endocrine cells increases while the number of inhibiting endocrine cells decreases. As can be seen, after an adequate time interval (∼20 steps) the quantity of the two kinds of endocrine cells does not change dramatically and tends to a dynamic equilibrium. Many simulation experiments show that the peak value of the variation curve, duration from the beginning to dynamic equilibrium, and the final

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Hormone diffusion distribution ECA Three repulsion hormones

Two repulsion hormones

One repulsion hormone

All attraction hormones Steps 1 Figure 7

5

20

50

100

500

Pattern formation with different hormone diffusion distribution.

number of the two kinds of endocrine cells are affected by many factors. Nevertheless, the trend in the quantity variation is similar to that in the sample. Note that we obtain similar results when the initial endocrine cells are all regarded as activating endocrine cells. The aim of the fourth experiment is to demonstrate that the LAES model can self-repair unexpected damages to its organization. First, we ran the simulation and allowed the cells to form a stable pattern (see the first column in Figure 9). For some unexpected reason, a bomb exploded and damaged 15% of the cells at the center of the global pattern (see the second column in Figure 9). We then allowed the cells to continue executing for 200, 500, and 1000 steps, and observed as the cells self-repaired the hole completely and formed a new global pattern. This demonstrates that as long as the simple cell move rule is in effect, the LAES model can, without global information, repair itself even after severe damage, and transform to a new pattern. This confirms the existence of the self-repairing feature. In general, the self-repairing occurred quite quickly in the experiment (about 500–1000 simulation steps).

4

LAES model application in robotic swarms

Technological advances in the fields of large-scale integrated circuits, embedded computing and low energy cost wireless communication have enhanced the importance of robotic swarm research and the application thereof in industry, agriculture and national defense. The reason is that, compared with a single robot, swarms have several advantages, such as distribution in space, diversity in function, parallel operation, high reliability, and low cost. However, robotic swarms should build their learning and collaboration ability in interaction with the external environment and other robots, so that they can accommodate a complex unknown living space. Enabling mobile robots to search and seize targets is potentially the most important research topic with possible applications in searching dangerous environments (tunnels or a battlefront) and rescuing people after natural disasters (conflagration or earthquakes). The LAES model noted here, not only mimics the basic features of biological endocrine systems, such as self-organizing and self-repairing, but meets the requirements for robotic swarms. Despite some differences in intelligentization and communication type, there is a one-to-one correspondence between the endocrine system and robotic swarms in terms of system architecture, properties, and realization forms, as shown in Table 1.

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Figure 8

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Variation in quantity of two kinds of endocrine cells.

Steps 0

1 Figure 9

Table 1

4.1

200

500

1000

Self-repairing feature of LAES model.

Correspondence between the endocrine system and robotic swarms

Endocrine system

Robotic swarms

Living body

Environment space/Motion domain

Endocrine cell

Robot

Endocrine cell population

A swarm of robots

Hormone

Short range wireless signal (either RF or infrared)

Hormone releaser BE and BT

Signal transmitter

Hormone preceptor AE

Signal receiver

Target cell

Target for seizing

Blood circulatory system

Free space

Barriers such as other cells

Barriers such as walls and rivers

Design of algorithm for robotic swarms

In view of the above analysis, we extend the basic algorithm A described in section 3.2 to a new A-robotic algorithm for robotic swarms. The pseudocode for the A-robotic algorithm is given in Figure 10. Compared with the basic algorithm A in the LAES model, we first introduce two kinds of endocrine cells in the new A-robotic algorithm, that is, the enhanced endocrine cells and neutral endocrine cells. The enhanced endocrine cells can release attraction hormones causing neighboring robots to follow a similar path and showing an empowerment effect among endocrine cells. However, each robot moves randomly, regardless of the neighborhood hormone concentrations. The other difference between the two algorithms is that, when an endocrine cell is attracted to the target signal field, it converts to a neutral endocrine cell. By not releasing anything, a neutral endocrine cell does not have any effect on others, while at the same time, other cells cannot affect it, which illustrates the so-called neutral effect among endocrine cells in the endocrine system.

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807

1 Input: initial distribution of endocrine cells: {(ECix , ECiy ), i = 1, 2, . . . , M }, initial distribution of target cells: {(TCix , TCiy ), i = 1, 2, . . . , N } and environment space Ld : Width×Length

2

3 Output: trajectory of endocrine cells 4 Algorithm: 5 Initialize 6t=0 7 while N = 0 do 8

ECA = ∅

9

ECI = ∅

10

ECE = ∅

11

ECN = ∅

12

for j = 1 : M do

13 14 15 16

Determine a category and add it into ECA , ECI , ECE or ECN

Compute Hrj (x, y, t) and/or Haj (x, y, t) according to eq. (2)// transport endfor

17

endfor

18

for j = 1 : N do

19 20 21

for (x, y)Nmoore−r do Compute Haj (x, y, t) according to eq. (2) endfor

23

for i = 1 :Width do for j = 1 :Length do

25

Compute H (x, y, t) according to eq. (4)

26

Compute H(x, y, t) according to eq. (3)

27

// transport

endfor

22 24

// differentiate

for (x, y)Nmoore−r do

// metabolism // synthesize and release

endfor

28

endfor

29

for j = 1 : M do

30

ECjx ← New ECjx according to move rule R

31

ECjy ← New ECjy according to move rule R

32

if endocrine cell j coincides with one target cell do

// update position

33

Do the job

// perform the task

34

N ←N −1

// target cell dies

35

endif

36

endfor

37

t←t+1

38 endwhile Figure 10

4.2

Pseudocode for the A-robotic algorithm.

Experimental results

The aim of the first set of experiments was mainly to verify the ability of robotic swarms based on the LAES model to search unfamiliar environments, as shown in Figure 11. For simplicity, the whole search space was divided into three zones separated by barriers, such as walls, with each wall having two doors to connect the zones. We assumed that wireless signals can penetrate the walls. Initially, all robots were in the left zone. Driven by their hormone signals, some robots were pushed through the doors into the middle zone. These robots then gradually spread out into the right zone. This confirms that using the LAES model, the robots can automatically and evenly distribute themselves in these zones without explicitly being ordered to do so. This ability will have a positive role in reducing human loss of life when searching dangerous areas. We conducted 20 independent experiments, using the same settings, and then averaged the results, as shown in Figure 12. These results confirm that robots were able to penetrate the middle and right zones with increasing numbers as the simulation progressed.

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Steps 0

500 Figure 11

Figure 13

2000

3000

Example of searching unfamiliar environments.

Figure 12

0

1000

200

Number of endocrine cells in three zones.

400

605

788

Steps

Example of searching and seizing multiple targets.

Steps 0 Figure 14

500

1000

1500

2180

Example of bypassing the barrier and seizing a target.

In the second experiment, we assumed that two targets were located, respectively, at position (60, 10) and (60, 50) in the environment space, and could be sensed by the robots at a short distance. The task of the robotic swarm was to search and seize these targets. The simulation results are shown in Figure 13 with the robots initially concentrated in the upper left corner and distributed nearby (8, 8). Once they start moving, the robots first wander around as before, dispersing uniformly from the corner, but soon some of them are attracted to, and aggregate around, the target. Finally, the target is seized by a robot. Notice that not all robots concentrate on the same target, and there are sufficient robots still searching other potential targets in the open environment space. This automatic dynamic balancing between global searching and locally seizing a target is partly because of the non-deterministic, yet probabilistic robot behavior rule in the LAES model. The other important reason is that there are a number of enhanced endocrine cells that swarm randomly throughout the entire environment space and lead others by releasing attraction hormones.

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Table 2 Barrier

Steps

809


Comparison of system performance Number of free robots

Running time (s) Upper right

Bottom left

Middle

Total

No

1721 ± 252

118 ± 19

70 ± 8

70 ± 6

2.1 ± 1.2

142 ± 10

Yes

2286 ± 442

144 ± 40

65 ± 8

43 ± 8

1.5 ± 0.7

110 ± 14

In the process of searching and achieving their goals, a robotic swarm will inevitably face barriers or obstacles, such as houses, walls, ravines and rivers. The aim of the third experiment was mainly to verify the circumvention ability of the LAES model for robotic swarms, as shown in Figure 14. We assumed that a target was located at position (85, 85) and a pair of crossed dead-end barriers distributed nearby (35, 35) in the environment space. The robots were initially concentrated in the upper left corner and distributed nearby (8, 8). As can be seen from Figure 14, when more and more robots are trapped at a barrier, the repulsion hormone will be so strong that some robots will be pushed away towards an alternative route. These free robots will then, in turn, attract those robots trapped at the barrier. As more and more robots choose the correct path, the correct signals will become stronger and stronger, and eventually overcome the signals from the trapped robots. As the final result, the majority of robots will bypass the barrier and seize the target. In general, the attributes and distribution of barriers and traps can be arbitrarily complex and impossible to predict. Nevertheless, with the ability of self-organizing and self-repairing, a robotic swarm based on the LAES model can find a way to bypass the barrier and seize the target. We executed 20 independent trials, all with the same settings, and then averaged the results of these experiments. From the statistical results of these experiments in Table 2, we conclude that system performance, in terms of number of steps, running time, and number of free robots decreases when barriers are present in the environment, despite the robotic swarms finally finding a way around the barrier and seizing the target after a number of steps. Interestingly, our barrier setting is somewhat special, in that there are two openings, that is, at the upper right with a width of 15 and at the bottom left with a width of 5. We recorded the number of robots that were able to bypass the obstacles in different areas once the algorithm had terminated. According to the results in Table 2, the ratio of the number of free robots at the upper right to that at the bottom left is approximately 1.5; obviously not equal to 15 5 = 3. The reason for this is that, with successive steps, free robots may move regularly throughout the entire space, and robots initially distributed in different areas are gradually integrated.

5

Conclusions

The power of information processing in biological endocrine systems has provided significant inspiration in the engineering field and is exactly reflected in the research on AES. Inspired by the information processing mechanism of endocrine systems, we presented a novel LAES model in this paper. This model allows many simple cells in large-scale systems to communicate and interact with one another to form global patterns, except in a few special cases. In addition, the model is able to transform into new patterns, thereby clearly showing the self-organizing and self-repairing features of the endocrine system, without requiring unique identifiers or sophisticated control strategies for individual cells. The experimental results presented in this paper demonstrate that the advantages of the LAES model include its simplicity, robustness and selforganization, and that the LAES model is an effective tool for simulating and analyzing self-organizing and self-repairing phenomena, as well as developing and testing new hypotheses, theories and experiments for biological endocrine systems. Our future research will focus on investigating the implementation and performance of the LAES model in dynamic environments and continuous systems, such as when a barrier or target moves quickly, the number of robots or targets increases or decreases after the algorithm starts, or even when some targets call for coordination of multiple robots. In addition, a detailed comparative study with existing approaches would be interesting.

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Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 61073091, 60802056), and the Natural Science Foundation of Shaanxi Province (Grant No. 2010JM8028) and the Foundation of Excellent Doctoral Dissertation of Xi’an University of Technology (Grant No. 105-211010). We thank Dr. Shen WeiMin from the University of Southern California for his valuable assistance.

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