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Parallel asynchronous control strategy for target search with


									Parallel asynchronous control
strategy for target search with
swarm robots
XUE Songdong
Division of System Simulation & Computer Application,
Taiyuan University of Science & Technology, Taiyuan 030024, P. R. China

ZENG Jianchao*
Division of System Simulation & Computer Application,
Taiyuan University of Science & Technology, Taiyuan 030024, P. R. China
*Corresponding author

ZHANG Jianhua
Division of System Simulation & Computer Application,
Taiyuan University of Science & Technology, Taiyuan 030024, P. R. China

Abstract: Upon mapping swarm robots search to particle swarm optimization (PSO), we
extend PSO algorithm to model and control swarm robots for target search at an abstract
level. At first, we analytically compare the characteristics of different versions of PSO to
facilitate design of robots control algorithm by tailoring and transferring parallel
asynchronous property of PSO into case of swarm search. Next, a concept of time-varying
character swarm is proposed to afford decision-making on the best-found position
according to swarm intelligence principles. Based on control principle of expected
evolution position of individual robot, an asynchronous communication policy for swarm
search is presented. In this case, each robot detects and fuses real-time heterogeneous target
signals propagating over search environment in parallel fashion as fitness evaluate in PSO
every time step. Accordingly, a series of expected evolution positions of each individual
robot can be decided. Thus, each robot moves respectively toward its current expected
position, controlled under related control laws. The need for number of time steps depends
on kinematics and dynamics constraints of real robot. Meanwhile each robot evaluates
those positions in which it is situated every time step, updating its cognition as soon as a
better finding of itself has been found, and updating the shared information and
broadcasting this message all over the character swarm if a better finding of swarm has
been found. At the same time, each robot listens to the change of shared information. Either
knowing change caused by certain neighbour or arriving at the current expected position,
robot starts to compute new expected position and turn out next round of control at once.
Simulation results indicate that the presented evolution position-based asynchronous
communication strategy has advantage over the popular control strategy in search efficiency.

Keywords: swarm robots; target search; particle swarm optimization algorithm; parallel
asynchronous control; communication strategy.

Reference to this paper should be made as follows: Xue, S D and Zeng, J C. (2009)
‘Parallel asynchronous control strategy for target search with swarm robots’, Int. J. of Bio-
Inspired Computation, Vol. 1, No. 1, pp. xx–xx.

Biographical notes: Xue S D received his MSc in System Engineering from Taiyuan
University of Science and Technology in 2004. He is currently Associate Professor at the
Department of Computer Science and Technology, TUST, Taiyuan, P. R. China. He is now
pursuing his PhD degree in Control Theory and Control Engineering at Lanzhou University
of Technology. His current research interest includes industrial control, swarm intelligence
and swarm robotics.
                                                Zeng J C is a Professor and Tutor of Ph.D. students at the Department of Computer
                                                Science and Technology, Taiyuan University of Science and Technology, Taiyuan, P. R.
                                                China. He is now a Vice-President of TUST. He received his MSc and PhD in System
                                                Engineering from Xi’an Jiaotong University in 1985 and 1990, respectively. His current
                                                research focuses on modelling and control of complex systems, intelligent computation,
                                                swarm intelligence and swarm robotics. He has published more than 200 international
                                                journal and conference papers. From 1990s, he has been an invited reviewer of several
                                                famous scientific journals.

                                                Zhang J H received his MSc in Applied Computer Technology from North University of
                                                China in 2003. He is currently Lecturer at the School of Electronics and Computer
                                                Science and Technology, North University of China, Taiyuan, P. R. China. He is now
                                                pursuing his PhD degree in Control Theory and Control Engineering at Lanzhou
                                                University of Technology. His current research interest includes evolution computation
                                                and swarm robotics.

1   INTRODUCTION                                                         On the other hand, those evolutionary algorithms carried
                                                                     out in asynchronous manner possess special computation
Particle swarm optimization (PSO) is a global, stochastic            merits. Koh et al (2006) once point out that asynchronous
search algorithm and evolutionary computation method first           algorithm is capable of improving efficiency in the
proposed by Kennedy and Eberhart, being derivative-free              heterogeneous environment. For instance, the asynchronous
and population-based (Schutte et al, 2004; Zeng et al, 2004).        PSO proposed by Luo and Zhong (2005) makes each
As one of efficient tools of modelling and control as well as        particle acted as an independent individual and the search of
simulation, it can be used to model swam robotic systems at          population performed asynchronously. Aiming at the
a high abstract level and to control swarm robots                    differences of heterogeneous computing environments and
cooperatively (Pugh and Martinoli, 2007). Bio-inspiringly,           the time cost of fitness-evaluate, Venter and Sobieszczanki-
the original version of PSO algorithm works in parallel              Sobieksi (2006) introduce asynchronous pattern into PSO to
fashion in nature. As for those traditional parallel algorithms,     try to enhance the speedup. In like manner, we have to take
they can be classified according to granularity (Xu and Zeng,        the problem of asynchronous control over swarm robots into
2005). The same applies to the taxonomy of different                 consideration when designing control algorithm because
versions of PSO. Wang et al (2007) present a parallel                robots in real world communicate asynchronously.
version of PSO based on parallel model with controller. The             In some researchers’ opinion, being special type of multi-
communication cycle of algorithm influences on the                   robotics, swarm robots inevitably involve asynchronous
speedup significantly. Huang and Fan (2006) propose a                parallel operation too (Henrich and Honiger, 1997). As one
version of parallel PSO with island population model. It             of novel tools of modelling and control to swarm robotic
partitions the evolution group into several sub-groups and           systems, PSO can be extended and used to model at an
places them respectively on different processors to evolve,          abstract level and control swarm robots cooperatively (Pugh
communicating at any time in the evolution procedures.               and Martinoli, 2007). No doubt that the above-mentioned
Zhao et al (2005) introduce an idea of migration into PSO            extended PSO approach has to take parallelism into account.
algorithm and present a parallel version based on multi-             The individual robots distributing in search space makes
groups. All sub-groups are collected to get the optima by            cooperation control algorithms parallel in nature. Besides,
comparison after evolved for several generations. Then the           differences in sampling frequency of sensors independently
particle having best fitness is transferred into all sub-groups      carried by individual robot and communication delays make
as a migration and used to take place of arbitrary a particle        it more realistic to control swarm robots in an asynchronous
randomly. These above-mentioned algorithms are all                   fashion. How to move nature-inspired algorithms to parallel,
attributed to coarse-grained parallelism. To the contrary, the       asynchronous and decentralized environment (Ridge et al,
fine-grained parallel algorithms are characteristic with             2005)? There has so far been fairly little research in this area.
majority advantages, i.e., maintaining diversity of groups,          Within the field of swarm robotic systems, one area that has
restraining pre-mature and holding the highest degree of             received more attention is target searching, where a group of
parallelism, etc. Therefore, Schutte et al (2004) develop an         autonomous mobile robots work together to localize one or
approach to implement parallel PSO on multi-processors               more potential targets. Especially, swarm robots may be
computation environment. In particular, to overcome the              used to carry out the dangerous, dirty and dull missions
communication bottle-neck due to massively increasing in             taking the place of human being for search and localize in
size of fine-grained PSO (Li et al, 2006), Chang et al (2005)        disaster scenarios, e.g., searching for victims in coal and gas
design three types of communication strategies according to          outburst accidents. Operation on the spot can be done
the degree of correlation between algorithmic parameters.            massively in parallel, significantly decreasing the time taken
These above-mentioned parallel versions of PSO are all               to locate the targets and improving robustness against
synchronous ones. As for control of swarm robots search, its         failure of single agents by redundancy as well as individual
footstone is attributed to swarm intelligence so that we may         simplicity. Consequently, the problem of asynchronous
deal with in similar way.                                            parallel control over swarm robots is proposed.
  This paper is organized as follows: Section 2 analytically       cognition of particle, i.e., individual experience of particle
compares the properties of different versions of PSO,              and social experience respectively. The variable wk is the
indicating that the parallel asynchronous implementation           inertia coefficient which can slow down over time to
mode is perfect among four modes. Section 3 maps the case          prevent explosions of the swarm and ensure ultimate
of target search with swarm robots to PSO using idealizer.         convergence. In addition, r1, r2 are sampling of uniformly-
Also, upon extending PSO and simplifying the kinematics            distributed random variable in [0, 1]. And c1, c2 are positive
and dynamics properties of robot in real world, an abstract        cognition and social acceleration constants, respectively.
mathematical model of swarm robotic system is given.
Based on this, an asynchronous communication strategy for
                                                                   2.2   Running properties
interactions among character swarm members is introduced.
In Section 4, we show the simulation results and discuss the       To explore the characteristics of different versions of PSO,
related implications and draw conclusions on our presented         we can start in accordance with some main aspects such as
parallel asynchronous communication strategy and control           fitness evaluate in a serial or parallel way, sensing and
algorithm. Finally, we conclude the paper in Section 5.            reacting to companions and environment synchronously or
                                                                   asynchronously as well as velocity adjusting and position
                                                                   update, etc. As a consequence, we can divide the different
2 PROPERTIES OF DIFFERENT VERSIONS OF                              versions of PSO into four modes according to the different
PARTICLE SWARM OPTIMIZATION ALGORITHM                              combinations of properties to facilitate the comparison of
                                                                   them and draw our conclusions.
The standard particle swarm optimization algorithm has a
key idea about velocity and position of particle (Zeng et al,      2.2.1 Mode I: serial evaluate + synchronous update
2004), which is used to optimize nonlinear functions at the
                                                                   Particle swarm optimization algorithm is traditionally
beginning of development and is expanded to more
                                                                   considered to be implemented serially and synchronously on
applications gradually. The algorithm tries to find potential
                                                                   the single-processor computing environment. The execution
solutions of problem by imitating behaviours of social
                                                                   procedure can be described with the following pseudo code
creature, e.g., birds flying over space. Taking fitness of
                                                                   (Koh et al, 2006):
given function as evaluate metrics, this algorithm adjusts the
velocities and positions of particles representing solutions of    INITIALIZE CONSTANTS
problem to obtain optimum eventually. PSO is based on              INITIALIZE VELOCITIES & POSITIONS
possessing many desirable properties that we would like to         PERFORM ALGORITHM
transfer to our swarm robotic systems. One of them is that             For k = 1, num. of iterations
PSO operates in parallel and asynchronously (Ridge et al,                  For i = 1, num. of particles
2005), which is consistent with the biological significance                      Evaluate cost function f ( x k )
of swarm algorithm.                                                        End
                                                                           Check convergence
                                                                                     i    g     i        i
                                                                           Update p k , p k , v k +1 , x k +1
2.1   Particle Swarm Optimization
Particle swarm optimization is based on the sociological           OUTPUT RESULT
behaviour associated with bird flocking and other animals’
                                                                   It can be seen that fitness-evaluate of all particles is carried
moving (Zeng et al, 2004). Each particle is capacitated to
                                                                   out by sending them to the single-processor environment
fly over the space with changeable velocity. And a series of
                                                                   and calculating one by one in optimization process using
positions in which particles are situated are viewed as
                                                                   cost function. And the best-found positions of particle itself
potential solutions of problem. Then, the best position of
                                                                   and of swarm are determined by fitness comparison in the
particle itself and swarm respectively having the best fitness
                                                                   same way. The update of all velocities as well as positions
can be decided. Farther, the behaviour of particle can be
                                                                   occurs simultaneously at each iteration after completing
adjusted according to its inertia, individual experience
                                                                   fitness evaluate on all particles.
(cognition) and social experience (learn). The velocity and
position update equations of standard PSO at time kt+1 are         2.2.2 Mode II: serial evaluate + asynchronous update
executed as follows:
                                                                   Similar to Mode I, fitness evaluating in serial manner with
v k +1 = wk v k + c1r1 (p k − x k ) + c2 r2 (p k − x k )
  i           i           i     i             g      i
                                                            (1)    cost function. But the update of memory about individual
                                                                   and society occurs asynchronously. Immediately updates on
x k +1 = x k + v k +1
 i        i       i
                                                                   velocity, position of certain particle as well as its history
where x is the position vector of particle i at time kt, and
                                                                   cognition and the best of swarm are carried out as soon as
 v k is the corresponding vector of velocity, the subscript k is   completing fitness evaluate on the cost function of this
the abbreviation of time increment kt. Note that the two           individual. The procedure can be elaborated with the
vectors have the same dimensional variables. While p k and         following pseudo code (Koh et al, 2006). It is clear that
 p k are the best-found positions of particle i itself and the     fitness evaluation and process of information update on
swarm before time k respectively. They represent history           different particles are not completed at the same time.
INITIALIZE CONSTANTS                                                           the asynchronous evolution approach does not need a
INITIALIZE VELOCITIES & POSITIONS                                              synchronous point to determine new velocities and positions
PERFORM ALGORITHM                                                              in the process of iterations, as showed in Figure 2 (Koh et al,
    For k = 1, num. of iterations                                              2006). The optimization can proceed to the next iteration
        For i = 1, num. of particles                                           without waiting for the completion of all function evaluate
              Evaluate cost function f ( x k )                                 from the current.
              Check convergence
                        i    g     i        i                                  2.2.5 Comparison of running efficiency
              Update p k , p k , v k +1 , x k +1
        End                                                                    As stated above, different versions of PSO have different
    End                                                                        algorithmic properties in implementation. But the most
OUTPUT RESULT                                                                  desirable properties that we would like to transfer to our
                                                                               swarm robotic systems may be controlling in parallel and
2.2.3 Mode III: parallel evaluate + synchronous update
                                                                               asynchronously (Ridge et al, 2005). Indeed, as one of
The most popular implementation of parallel PSO is to                          nature-inspired algorithms, parallel asynchronous version of
simplify fitness evaluate on particles within iteration in                     PSO makes algorithm more efficient and parallel running in
parallel, without changing the overall logic of the algorithm                  performing. In order to illustrate this useful aspect, we can
itself (Venter and Sobieszczanki-Sobieksi, 2006). And the                      analytically compare the different properties obtained in
property of synchronous refers to all particles being sent to                  previous sub-sections on their efficiency of time operations
parallel computation environment and moving from the                           in single generation of evolution.
current iteration to the next only if the fitness of all particles                 Consider the need of elapsing time for one generation of
has been gotten (Schutte et al, 2004). To demonstrate the                      evolution and the completed tasks within this time duration.
internal relationship of algorithmic logic better, we illustrate               Assume that the process of one generation of evolution
with flow chart rather than pseudo code, as showed in                          consists of fitness evaluate, waiting for update and update,
Figure 1 (Koh et al, 2006). In this case, the existence of load                whose required time be t , teval , t wait and tupd , respectively.
imbalance in computation environment may significantly                         But the update time may nearly be considered to be 0, that is
influence on its parallel performance. These impacting                          tupd ≈ 0 . The following formula thereupon can be gotten
factors include: (1) a heterogeneous distributed computing
environment where processors with varying computational                        ti = ti _ eval + ti _ wait , i = 1, 2,                         ,N                     (3)
speed are combined into a parallel computing environment;
                                                                               Suppose that particle k consumes the maximum evaluate
(2) time spent in fitness evaluation, i.e., using a numerical
                                                                               time and the synchronous update assigned on basis of time
simulation to evaluate each particle, where the required
                                                                               tk_eval. And then
simulation elapsed time depends on the particle being
analyzed; (3) the number of particles cannot be equally                        t k _ wait = 0                                                                        (4)
distributed among the processors in the computation
environment, i.e., having a swarm size that is not an integer                  But
multiple of the number of processors (Koh et al, 2006).
                                                                               t j _ wait > 0 ( j ≠ k )                                                              (5)
                                                                               t k _ eval          max ti _ eval = tk , i , k = 1, 2,                           ,N   (6)
                                          # of Particles
                                                                                  Upon holding the above definitions, we can compare the
                                                                               four modes on their algorithm efficiency, i.e., required time
                                                                               and amount of completed tasks within one single generation
                                                f(x)       f(x)     …   f(x)   of particle evolution.
                                                                                  1) Mode I. The required time of evolving for only one
           # of Iterations

                                                                               generation is as follows
                                                                                            N                      k −1              N

                                                                               t ss = ∑ ti _ eval = ∑ ti _ eval +                  ∑t
                                                       Convergence                                                                            i _ eval
                                                                                                                                                         + tk        (7)
                                                                                            i =1                   i =1            i = k +1

                                                           Update              The completed tasks consists of fitness evaluate and update
                                                                               of this generation. And the average elapsing time of all
                                                                               particles from completing evaluate to update is as follows
                              Figure 1 Parallel synchronous PSO                                    N       N

                                                                               t ss _ wait =       ∑∑t             j _ eval
                                                                                                                              /N                                     (8)
                                                                                                   i =1 j = i +1
2.2.4 Mode IV: parallel evaluate + asynchronous update
Parallel asynchronous implementations can enhance running                        2) Mode II. The required time of evolving for only one
                                                                               generation is as follows
efficiency (Venter and Sobieszczanki-Sobieksi, 2006). Also,
                Initialize                                                                               Table 1 Comparison of Properties of four modes

                                 # of Particles
                                                                                               Mode               Required Time              Completed Tasks

                                                                                                    I              ∑t      i _ eval
                                                                                                                                      > tk     N × (Eva+Upd)
                                                                                                                    i =1

                                                               f(x)       …                        II              ∑t      i _ eval
                                                                                                                                      > tk     N × (Eva+Upd)
                                                                                                                    i =1
                                                                                                   III                       tk                N × (Eva+Upd)
                                                                                                                                             N × (Eva+Upd)          ∗
                & Update                                                                           IV                        tk
                                                               f(x)                                                                          +α × ( N − 1) × Εva2

                                                                                             Note: 0 < α < 1 , and Eva2 in the last row and column represents
                                                                                                   part of fitness evaluate task that the next generation needs.

                                                                                             2.3        Mapping swarm search to PSO


                        Figure 2 Parallel asynchronous PSO                                   The swarm intelligence is inspired from the phenomena of
                                                                                             individuals in social creature following simple behaviour
         N                                                                                   rules and emerging intelligence by local interactions. In
t sa = ∑ ti _ eval                                                                     (9)   general, PSO is viewed as a useful tool to optimize
        i =1                                                                                 nonlinear functions. The virtual particles are guided by the
The completed tasks consists of fitness evaluate and update                                  best-found positions having optimal fitness, iterating the
of this generation. Clearly, this mode eliminates the waiting                                velocities and positions and approaching step by step to the
time in Mode I. However, the required fitness evaluate in                                    optima of given functions. Here, particles have perfect
the next generation is not able to be done in a single-                                      information about itself and neighbours’ positions. Based on
processor computing environment when this processor is                                       actual background, swarm robots study extends the swarm
used to the tasks of current generation.                                                     intelligence and its optimization algorithms. The individuals
   3) Mode III. The required time of evolving for only one                                   follow the simple behaviour rules too, searching for one or
generation is as follows                                                                     more potential targets by local interactions. The difference
t ps = tk < t ss                                                                      (10)   between PSO and swarm robots search lies in the conditions
                                                                                             of environment and the complexity caused by idealizing
The completed tasks in this generation of evolution consists                                 degrees or extents. Consider the effect factors, we can get
of fitness evaluate and update of this generation. Of all                                    the mapping between the two cases, see Figure 3. These
particles, N-1 individuals except particle k have to wait for                                factors are as follows (Pugh and Martinoli, 2007):
update at some synchronous point. The average waiting
                                                                                             2.3.1 Physical property
time of N-1 particles is as follows
                 k −1                      N
                                                                                             In PSO, particles have infinite acceleration and no intrinsic
t ps _ wait = ( ∑ (t k − ti _ eval ) +   ∑ (t         k
                                                          − ti _ eval )) / N                 limitations on velocity. In real world, robots have limits to
                 i =1                    i = k +1                                            how quickly they can move. In most robot search scenarios,
                                                                                      (11)   it would take a substantial amount of time for a robot to

         = t k − ∑ ti _ eval / N = t k − t ss / N                                            cross the search environment at maximum velocity.
                        i =1
                                                                                             2.3.2 Search space
  4) Mode IV. The required time of evolving for only one
generation is as follows                                                                     Robot moving depends on both its sense and the best
                                                                                             experience among its neighbours. That is, there is no fitness
t pa = t k < t sa                                                                     (12)   function in our algorithm. In the first step of our work, we
                                                                                             simply assume each robot has a sensor to detect the intensity
The completed tasks in the generation of evolution consists                                  of the target signals, which has computational significance
of fitness evaluate and update of this generation. In addition,                              only but has nothing to do with the third party fitness
this mode eliminates the waiting time in Mode III. At the                                    function in the process of target search.
same time, those N-1 particles having completed evaluate
tasks prior to particle k have also carried out part of evaluate                             2.3.3 Fitness evaluate
task of the next generation before moment t k in advance. In                                 PSO algorithm works by having particles to update their
a sense, Mode IV possesses the most desirable advantages                                     positions within the closed search space when iteration of
among all four modes.                                                                        algorithm occurs. Robot search operates in continuous time.
  In summary, we can numerically compare the serial/                                         We can approximate this jump by having the robot to move
parallel and synchronous/asynchronous properties for four                                    for a fixed amount of time (time step) at the proper velocity
modes (see Table 1).                                                                         towards its desired position.
                                                                     3     TARGET SEARCH WITH SWARM ROBOTS
          Swarm Search                               PSO
                               Idealize                              When working miners are confronted with natural forces or
                  continuous              discrete
                                                                     man-made disasters, e.g., gas outburst accidents in closed
        local                                              global
                  relative                absolute
                                                                     laneways, they would be likely to lose touch with outside
       signal                                              fitness   and be trapped underground. Unfortunately, such search
                       robot              particle                   operations here tend to be very difficult. Swarm robots may
        plan                                               update    therefore be used to carry out missions taking the place of
                   …                                  …              human beings. Extending PSO to model swarm robotic
                                                                     systems, Pugh and Martinoli (2007) investigate the problem
                                                                     of target search. However, robot there is assumed to have
                                                                     only one sensor to detect the intensity (concentration) of the
        Figure 3 Mapping swarm robots search to PSO                  ideal signal emitted by potential target. This is of theoretical
2.3.4 Discrete iteration & continuous control                        significance only because the work is based on the
                                                                     assumption of continuous sense to one source signal. As a
The particles in PSO have perfect knowledge about space              matter of fact, there are real-time multiple types of signals
positions. They can also get positions of other particles via        in search environment. As for the control swarm robots in
virtual communication, i.e., the localization mechanism is           search-and-rescue operation in coal mines, there exist
global there. Although robot can localize itself and its             several heterogeneous signals, including continuous gas,
neighbours in global fashion, it is more reasonable to               intermittent cry-for-help as well as periodic RF waves. To
localize both itself and obstacles in environment by making          accomplish the search task, there is need to fuse the real-
use of systems similar to Spears et al (2006). In particular,        time heterogeneous signals appropriately to determine the
those global localization systems similar to GPS mechanism           decision sensor under different sensory conditions (Xue and
usually fail in indoor environment.                                  Zeng, 2008c). In addition, the inherent parallel property
2.3.5 Neighbourhood                                                  caused by spatial interspersed of robots in search space,
                                                                     differences in sampling frequency of sensors independently
The standard neighbourhood structure in PSO requires                 carried by individual robots and communication delays
particles to share swarm information with others anywhere            make it practical to control swarm robots in asynchronous
in search space. Robots often have strict limitations on their       fashion. As a consequence, we try to move the parallel
maximum communication range, power consuming and so                  asynchronous properties of PSO to control swarm robots
on. In this context, it makes more sense to pre-define a             after tailoring or modifying.
neighbourhood structure based on their mutual positional
relationship in the search space, where vicinal robots belong
to the same neighbourhood and corresponding interactions             3.1   Simplifying target signals detection
are conformed to itself neighbourhood. Upon that we will             Imagine that a single victim is situated in a large-scale area.
give a concept of time-varying character swarm in the next           The extent of this 2-D surface enclosed within a boundary is
section to facilitate decision-making on the best-found              150 x 150 unit (see Table 2). A swarm of homogeneous
positions. Now, we define at first a robot’s neighbourhood           robots are deployed into this area to search for the victim,
as all other robots within some fixed geometrical distance           moving about according to the swarm intelligent principles.
(see Figure 4, this distance may be the maximum                      Each robot is equipped with an appropriate electronic sensor,
communication range R). Because robots are constantly in             assuming it cannot always read the correct intensity value
motion for search, this means that the neighbourhood                 everywhere and sensor errors are considered as a kind of
structure is dynamic at different time moments. This is the          random noise. Compared with the scale of the search area,
reason why we call the character swarm ‘time-varying’ in             communication range of robots is related narrow. We also
the next section.                                                    assume that no robot in target searching has capability of
                                                                     global communication. Based on the assumptions, parallel
                                                                     asynchronous communication strategy is designed and
                                                                     control algorithm is developed as well as simulation
                                                                     experiments are conducted to evaluate effects. To compare
                                                                     the results, we initialize a target at a fixed scope in the
                                                                     environment. In addition, the environment is ‘static’, there
                                                                     is no obstacle in the environment, and the intensity of
                                                                     signals at each point depends on the distance from the target.
                                                                     The farther is away from the target, the lower the intensity
                                                                     of the signal. In order to simplify simulation, we use the
                                                                     following mathematical model to generate the intensity of
                                                                     each position in which each robot is situated in the
   Figure 4 Neighborhood structure of swarm robotic system           environment (Pugh and Martinoli, 2007).
            ⎧0,            d >r                                   on signals being complemented in their on-board processors
I (d ) =    ⎨ 2                                            (13)   rather than in processing centre. And the limitations to
            ⎩ P /d + η (), d ≤ r                                  hardware and power supply make it impossible that robots
                                                                  interact successfully beyond communication range of robot.
where P is signal power, d is the distance from robot to
                                                                  Apparently, the swarm that each robot dwells in differs from
target, r is the radius of detection of sensor and η() is a
                                                                  others, since every robot selects itself and all other robots
sampling of additive Gaussian noise, which satisfying
                                                                  within certain distance (usually communication range here)
distance inverse square law within the reaction range of the
                                                                  in the search space as its evolving swarm.
sensor. Therefore, if the distance from target to robot is
                                                                    Accordingly, we present a concept of time-varying
greater than the sensor reaction range then I (d) = 0.
                                                                  character swarm for signals comparison and decision-
                                                                  making on the best-found positions. Take the position of
3.2       Modelling swarm robotic system                          one robot at time k as the centre, the communication range
                                                                  as radius to construct a limited circle neighbourhood. The
Upon mapping PSO to swarm robotic systems (Xue and                set of those robots covered by this neighbourhood is named
Zeng, 2008a), the swarm robotic system can be modeled             as the character swarm of this robot at time k. This results in
with extended particle swarm optimization approach (Pugh          a variable of number of neighbours, as a robot may be close
and Martinoli, 2007; Xue and Zeng, 2008b):                        to very few or very many other robots at different times. As
v k +1 = wk v k + c1r1 (p k − x k ) + c2 r2 (p k − x k )
  i                     i           i       i   g    i
                                                           (14)   a consequence, the size of character swarm depends on the
                                                                  communication range of robots and the relationship of
 v k +Δk = v k + ( v k +1 − v k ) Δk
      i             i           i       i
                                                           (15)   relative positions at time k. This implies the property of
            i                                                     time-varying in character swarm of our swarm system.
where x k +1 is the expected velocity vector of robot i at time
k+1. ∆k is a factor to decrease the step taken when robots
move about in the search space. By the way, we add the ∆k         3.4 Moving parallel asynchronous characteristics to
factor in order to make individual robots have a ‘smoother’       swarm robots control
displacement, and therefore a more refined search may be          Assume each robot is equipped with different types of
desirable. More importantly, this factor reflects the             sensors, including sound, odor and radio frequency sensors.
kinematics properties of real robot because robot may have        The fusion of detected heterogeneous signals can be used to
to take several time steps to move to an evolution position
                                                                  make decision on the best-found position (Xue and Zeng,
from the previous evolution one. In addition, the parameter
                                                                  2008c). But we simplify the fusion with (13). The control
∆k is somehow different from the others, as it is not related
                                                                  over robots should be done in a fine-grained way, as
to the physical nature of the problem. However, we can also
understand it in this fashion: robot in real world has inertia    individual robots detect target signals independently at the
due to its mass (Xue and Zeng, 2008b).                            same time and fuse them as fitness evaluate to determine the
   In fact, the moving speed of robot has to be limited to the    best-found position by intensity (concentration) comparison
locomotion capacity of robot, i.e., the kinematics and            (Xue and Zeng, 2008b). Due to heterogeneous hardware
dynamics constraints of robot must be satisfied. The              caused by parameter distribution of sensors and actuators,
following is simplifying process based on this principle.         difference of detecting and fusing time required among
Where, vmax stands for the maximum velocity of robot.             different positions because of multi-sources heterogeneous
                                                                  signals diffusing, part of swarm robots having completed
             ⎧ v max , v ik +Δk > v max                           signals detection and fusing have to wait for update at a
             ⎪                                                    synchronous point. The reason is that the update depends on
v ik +Δk   = ⎨0        , v ik +Δk < 0                      (16)
                                                                  the slowest robot (Schutte et al, 2004). As shown in Figure
             ⎪ i
             ⎩ v k +Δk , 0 ≤ v k +Δk ≤ v max
                                                                  5, to get an insight into the mechanism, we select randomly
                                                                  processes of four robots from the related swarm and make
Upon that each robot moves toward the current expected            use of their behaviors to illuminate (Kolda and Torczon,
evolutionary position for a little distance every time step       2003). Of all line-types in Figure 5, horizontal real line
according to the above speed limitations.                         represents detecting & fusing time and horizontal grey line
                                                                  represents wait-for-processing time. By this means,
x k + Δk = x k + Δkv k + Δk
 i              i           i
                                                           (17)   velocities and positions of all robots are updated at the same
Formulas (14) - (17) constitute our mathematical swarm            time point until evaluate task having fully completed. The
robotic system model.                                             update occurs at synchronous time k = 2, 5, 8 respectively.
                                                                    As mentioned above, update of velocity vector of particle
                                                                  is the key in particle swarm optimization algorithm. To
3.3       Time-varying character swarm                            update the velocity of particle in an asynchronous way, the
Cooperative control over swarm robots can be carried out          velocity and individual history cognition should be updated
after system modeling. But such control algorithm works on        directly after the completion of single particle. While the
the base of signals detection and fusion. While the relative      best-found position can be pg and should keep it until the
independency of individual robots demands the evaluation          next iteration occurs. As for the swarm robotic system, the
                                                                  built-in each robot in parallel, which fusion of signals is
                                                                  immediately compared with the best-found of robot itself
                                                                  and swarm. The individual information is updated every
                                                                  time step, while the shared information within swarm is
                                                                  updated in an asynchronous way according to the following
                                                                  communication strategy.

                                                                  3.5   Asynchronous communication strategy

                                                                  The difference between synchronous and asynchronous
    Figure 5 Part of robots wait for synchronous update
                                                                  control pattern lines in their update types (Zhao et al, 2005).
key to asynchronous implementation of control algorithm is        Differing from the ideal particles in PSO, robot possesses
to partition the individual update behavior from the group        mass in real world that causes it to have inertia when moves
update behavior to take the different property into account.      about in the search environment. Therefore, as for same an
These update behaviors include updating the individual            evolution position of certain particle, it is unlimited to reach
information and the shared information. Similarly, as for the     at any speed in PSO case, while robot may arrive at the
asynchronous particle swarm optimization, the update              same position in several time steps due to constraint of
action starts after fitness evaluating, while the update of       kinematics and dynamics as the evolution position is only
shared information starts in the last at each iteration (Venter   expected (Pugh and Martinoli, 2007). These factors should
and Sobieszczanki-Sobieksi, 2006). For the case of target         be taken consideration when we design the asynchronous
search with swarm robots, detection and fusion of target          communication or interaction strategies.
signals depends only on their own on-board processor rather          According to this control principle, update of the shared
than so called ‘processing centre’. The processors work           information cannot be carried out in the current iteration
independently and in parallel between one another. The            before the previous evolution position having not reached.
individual robot updates its velocity, position and history       That is to say, robots communicate when they arrive at the
cognition as soon as completing the detection and fusion of       decided expected or desired evolution positions regardless
target signals and making decision on the best-found              of the iteration history and the requirement for next iteration.
positions by comparison with the best of its character swarm      Robot does not communicate with each other between two
(Zhao et al, 2005). But the update of the shared information      continuous evolution expected positions every time step,
of swarm should start in accordance with asynchronous             which makes robot moving continuously, saving power and
control strategy. Before describing our asynchronous              decreasing communication time-consuming.
strategy and corresponding control algorithm, we present
                                                                  3.5.1 Monitor
several notions about the communication policy in advance
to understand better.                                             Each robot detects and fuses the multi-source heterogeneous
                                                                  target signals and updates its cognition every time step. Also,
3.4.1 Real & expected velocity
                                                                  robot tries to find a better position than the best-found
As for PSO, velocity vector of particle is the key to this        positions within its character swarm. At the same time,
algorithm. In order to update the velocity asynchronously,        robot listens in the change of the shared information of its
position of particle must be updated and history experience       swarm. And this robot computes its next expected position
about the best-found of itself and of its swarm must be           and starts new round of control as soon as having known the
remembered. As for asynchronous control over target search        update of shared information by certain neighbour. By this
with swarm robots, however, the first key is to make a            way, we consider two sub-processes of communication as
difference between individual information and the shared          monitor and broadcast to describe interactions among robots
information update. The second is that the update behavior        clearly.
of individual robot has to confine to its real capability,
                                                                  3.5.2 Broadcast
which involves real velocity and expected velocity. The
former has practical sense, depending on real design and          After the current expected position is decided, each robot
implementation of robot, but the latter has an algorithmic        moves toward its destination. The process may consume
sense only. Individual information includes the best history      some time steps, which depends on its locomotion ability
and expected velocity and position, while the shared              with kinematics and dynamics constraints because it can
information includes the best-found position of swarm and         only move a limited distance in one time step. But this robot
the corresponding signal intensity.                               will compute the next expected evolution position, update
                                                                  the shard information of swarm and broadcast this message
3.4.2 Individual & shared inf. update
                                                                  all over the character swarm at once. Those neighbours
As for asynchronous PSO, update of individual information         listening in the change of the shared information will
occurs as soon as completing fitness evaluate. But as for         terminate the current process that moving toward the current
asynchronous control of swarm robots search, target signals       expected position and turn out compute the next expected
are detected and fused independently by on-board processor        position and move toward the new destination.
3.5.3 A better position be or not be found                           INITIALIZE CONSTANTS;
                                                                                       i          i
In the process of moving toward the current evolution                INITIALIZE VEL. v k & POS. x k ;
expected position, each robot detects and fuses the target           INITIALIZE TGT. POS.;
signals to decide the best-found position and updates its            INITIALIZE INDIVIDUAL COGNITION
own cognition every time step. Therewith, they listen in the             COMPUTE SIG. INTENSITY I k ;
change of the shared information. The robot will compute
                                                                           I max ← I k ; //remember best-found sig.
                                                                            i                  i
new expected evolution position, broadcast this message all
                                                                          p k ← x k ; //remember best-found pos.
                                                                            i              i
over the character swarm, and move toward the new
expected position at once as soon as its finding excels the
                                                                     INITIALIZE SHARED INF.
best-found, regardless of not reaching the current expected
                                                                         I max ← I k ; //best-found sig.
                                                                           g       i
position. That is to say, knowing update of the shared
information will trigger new round of control process                     p k ← x k ; //best-found pos.
                                                                            g              i

whichever its state, in spite of such trigger caused by itself
                                                                          CONFIRM INDEX OF BEST INDIVIDUAL;
or by its certain neighbour.                                     While (1)
   To visualize the relationship of terms about several              k ← k +1;
expected positions, we can reveal them with Figure 6.               INTERACTIONS AMONG SWARM
Where, numbered circles stand for the expected positions.                 CONFIRM NEIGHBORHOOD;
The real and grey lines represent passing path of robot and               For j=1; j< num. of neighbours; j++
planned but not passing path, respectively. Suppose robot i                                 j
                                                                              COMPUTE I k ;
is at certain point on the real line segment that joins the
                                                                                 I max ← max( I k , I k ) ;
                                                                                   g                                               i                   j
previous expected position and the current expected point.
According to the strategy, robot i moves toward the current
                                                                                 p k ← x k , arg max{I ( x k ), m ∈ (i , j ) } ;
                                                                                   g                           m                                                       m

expected position along planned straight line from the                                                                         m
previous expected. It turns out the next expected position as        COMPUTE EXPECTED VEL. & POS.
soon as having found a better position or known the change
                                                                           v k +1 ← wk v k + c1 r1 (p k − x k ) + c2 r2 (p k − x k ) ;
                                                                            i                              i                               i                       i               g   i

of the shared information updated by some neighbor at the
                                                                           x k +1 ← x k + v k +1 ;
                                                                            i                  i                   i
trigger point. While the real line segment that joins early
expected position and the previous expected would be
                                                                           wk ← c3 wk ; // 0 < c3 < 1
considered that robot i neither finds a better position nor
                                                                          compute ρ expec = || x k − x k +1 || ;
                                                                                                                                       i                       i
knows change of the shared information. Therefore, this
robot decides its current expected position when it arrives at       COMPUTE REAL VEL.
the previous expected position by communicating with its
                                                                           v k + Δk ← v k + ( v k +1 − v k ) / T ;
                                                                            i                      i                       i                       i
neighbors and computing with corresponding conditions. In
addition, robot may move from an expected position toward                 CONSTRAINTS PROCESS;
the successive expected one for several time steps, which            n ← 0 ; // counter of time step
depends on the locomotion capability.                                do //move toward current expected pos.
                                                                          n ← n +1;
                                                                           x k + n×Δk ← x k + n × Δkv k + Δk ;
                                                                            i                          i                                       i
                                Trigger Point
                         2                          3
                                                                          COMPUTE ρ now = || x k + n×Δk − x k +1 || ;
                                                                                                                                                           i               i

                                                                          COMPUTE SIG. INTENSITY I k + n×Δk ;
                                                                          LISTEN UPDATE OF SHARED INF.;
        1                                           4
                                                                          If I k + n×Δk > I max then; //capture better finding
                                                                               i            g

                                                                                 I max ← I k + n×Δk ; //update cognition value
                                                                                   i                               i
       1. Early expected pos. 2. Previous expected pos.
       3. Current expected pos. 4. Next expected pos.
                                                                                 x k +1 ← x k + n×Δk ; //update cognition pos.
                                                                                   i                               i

   Figure 6 Sequential expected evolution positions of Robot i
                                                                                  I max ← I k + n×Δk ; //update shared inf.
                                                                                       g                               i

                                                                                 x k +1 ← x k + n×Δk ;
                                                                                   g                               i
3.6   Algorithm description
                                                                               BROADCAST ALL OVER THE SWARM;
Based on the above, an asynchronous control algorithm for                      break;
target searching with mobile swarm robots is proposed. This              If shared inf. updated by neighbour then;
distributed algorithm can be carried out on each individual                    COMPUTE NEXT EXPECTED POS.
robot in parallel. Without loss of generality, we can describe       while ρ now > 0.1 × ρ expec ; //reach expected pos.
the algorithm run on robot i as follows:
                                                                 If succeed in search break;
INITIALIZE                                                       OUTPUT RESULTS
    k ← 0 ; //counter of time step
4     SIMULATION AND DISCUSSION                                    communication cycle be T and time step be t, then we can
                                                                   set T = nt (n = 1, 2, 3,…). Besides, different robots can be
The performed simulation experiments depend on the multi-          allowed to have different sampling frequencies or time steps.
thread technology. In simulation, the main thread initiates        On the other hand, the best-found signals value and position
all control algorithmic constants, velocities and positions of     of character swarm should be remembered before the next
individual robots as well as the shared information within         iteration starts.
character swarm. Then each robot is derived to independent         4.1.2 Asynchronous communication strategy based on
thread object respectively. These thread objects hold a            absolute evolution position principle
referral to same a shared information object (Luo and Zhong,
2005). When the swarm robots start to search for a static          According to this control principle, the shared information
potential target in parallel, each individual detects and fuses    is not updated before having reached the current evolution
independently target signals at the same time as fitness           position, regardless of any better signals reading appearing
evaluate in PSO (Xue and Zeng, 2008b). Comparing the               in the process of moving toward the current evolution
signals value with the best-found within its character swarm       position. That is to say, robots only communicate when they
at time k, robot makes decision on the best value and best-        arrive at the decided expected evolution positions rightly,
found position it intends to move toward in the successive         regardless of signals reading. In a sense, this asynchronous
time steps. If the current finding (fusion of target signals) by   communication strategy can be called ‘static’ expected
robot has advantage over the best of itself, then the velocity     position-based and the presented strategy in the above
and position of robot are updated immediately at any time          section can be ‘dynamic’ position-based. Though it is
step. But the shared information is not updated according to       impossible for each robot reaching respective current
the aforementioned asynchronous control principle until the        expected position at the same time step, all members
finding of some robot is superior to the best-found of swarm.      communicate synchronously. The main difference between
At the same time, each robot listens in the change of shared       this strategy and the topic of this paper is whether robot may
information. It is being ready to compute next expected            act under different conditions before having arrived at the
position and start new round of control at any time. In the        current expected position. No communication between two
process of target search, the main thread is also responsive       ideal evolution positions makes robot moving continuously,
for the iteration-counting and judgement of terminate              saving power and decreasing required time for search.
criteria. Hence, the experiment will be terminated as soon as      However, this control strategy may cause missing best-
the search turns out to be successful or the pre-established       found position having better signals reading than previous
searching time elapsed. Because the simulation involves            best positions in the process of moving toward the current
updating operation to the same shared information object,          evolution position.
we have to take synchronous visit among different threads          4.1.3 Synchronous communication strategy
into account carefully (Luo and Zhong, 2005).
                                                                   To compare the running properties of algorithm, we directly
                                                                   cite the results of synchronous version of swarm robots
4.1   Simulation
                                                                   search. In this case, all individual robots detect and fuse
We can programme and simulate algorithm presented in the           target signals independently on each on-board processor in
previous section to validate the parallel asynchronous             parallel and interact with neighbours to make decision on
communication strategy. During the runs, trajectories of all       the best-found position and the evolution position. When
robots are recorded in formatted data files. And the common        iteration occurs every time step, each robot computes its
configuration of parameters used in experiments is shown in        expected position, updates its history cognition (signals
Table 2. Note that these parameters here have mathematical         intensity and best-found position) and updates the shared
meaning rather than physical significance. Aiming at test of       information (signals value, best-found position and index of
our parallel asynchronous communication strategy and               the individual having the best signal) within swarm in which
corresponding control algorithm, we compare them with the          it is situated (Xue and Zeng, 2008b).
following three communication strategies:                              We perform the experiments of four strategies for 50 runs
                                                                   repeatedly and respectively to research success rate of
4.1.1 Asynchronous communication strategy based on                 searching and efficiency with statistics. Here, we define the
fixed communication cycle principle                                success of searching as the best position of swarm is away
As for this asynchronous pattern, communication cycle is           from target coming in the range of vision sensor (suppose
named as number of evolution iterations. Similar to the            each robot is also equipped with vision sensor, but keep
coarse-grained parallel particle swarm optimization, we can        switched off in the course of nature-inspired search)
make robot i interact every n time steps to decide the best-       (Kowadlo et al, 2006). That is to say, if one or more robots
found position within its character swarm (Wang et al, 2007;       are close to the target enough, the run is considered to be
Huang and Fan, 2006; Zhao et al, 2005), regardless of              successful. Further, success rate is defined as successful
whenever updating of the shared information. To improve            running-times to total search times. In addition, we define
systematic running efficiency, a communication cycle can           search efficiency factor as reciprocal of the mean evolution
be assigned to several fixed multiple of time steps. Let           generations required in one successful search. In fact, the
metric of concerning efficiency is elapsed time, which                           Table 4 Required iterations for strategy II
indicates the iterations in simulation indirectly. In a sense,                                         Success         Required
                                                                       Comm. Cycle       Trial Runs
this metric makes the mathematic meaning conform to                                                    Rate (%)        Iterations
physical significance of problem. In summary, the former                    1                50          100             193.58
metric is to examine convergence of algorithm and the latter                3                50          100             206.12
                                                                            5                50          100             204.42
is to examine the speed of target search. Based on the
                                                                            10               50          100             182.92
presented asynchronous communication strategy and                           20               50           98             188.24
corresponding algorithm as well as simulation settings, we                  30               50          100             194.00
can show the results in next sub-section.                                   40               50          100             184.76
                Table 2 Simulation experiment settings                  4) The ‘dynamic’ position-based asynchronous strategy
  Symbol                  Meaning                    Value           presented in this paper possesses the most efficient running
 E               Search Space                  150 x 150 unit        effect among three asynchronous communication strategies,
 R               Max Comm. Range               50 unit               see Figure 8.
 r               Detect Radius                 50 unit
 N               Num. of Robots                9
 vmax            Max Vel.                      2 unit/s              4.3   Discussions
 t               Time Step                     100 ms
                                                                     The analysis of interest is finding control strategy which is
                                                                     consistently more efficient.
4.2     Results                                                        1) As for the relationship between communication cycle
                                                                     and efficiency. The more frequent the velocity adjusts, the
To make the comparison clear and facilitate our analysis, we
                                                                     more time-consuming is required, the more inefficient the
can assign Roman numerals I, II, III and IV respectively to
                                                                     search algorithm runs because more communicating times is
the above mentioned communication strategy, see Table 3.
                                                                     required when smaller cycle is assigned in target searching.
Further, the concerned statistics can be found there. Table 3
                                                                       2) As for the modification to evolution position-based
shows the trial times, success rate of trials and required
                                                                     principle (including ‘static’ and ‘dynamic’). Robots may not
mean generations for one successful search, depending on
                                                                     arrive at some decisive evolution positions accurately. Then
our asynchronous communication strategy and its counter-
                                                                     we modify the position-arriving principle to the position-
parts. In particular, the simulations going with varying
                                                                     approaching principle, i.e., we decide the update time step
values of some parameters result in a relational graph
                                                                     depending on the degree of approach to the current
between communication and search efficiency. As shown in
                                                                     evolution position from the previous one (e.g. 90 to 110
Figure 7, the search efficiency varies when communication
                                                                     percent of distance between two adjacent evolution expected
principle is adopted in search mission. The collected data
demonstrate that all control algorithms can approach to very
                                                                       3) As for adjacent evolution expected positions. Consider
high success rate. But the search efficiency differs from            an arbitrary individual robot, the distance between adjacent
with each other.                                                     evolutional expected positions is related to the inertia of
  1) The communication cycle-based asynchronous control              robot itself. Such distance increases as the inertia decreases
algorithm runs more efficiently than the ‘static’ evolution          in the course of search.
position-based one. But the value of communication-cycle T             4) As communication cycle and time step or sampling
must be set appropriately.                                           period. Here, a communication cycle may consist of several
  2) As for the communication cycle-based asynchronous               sampling periods. Therefore, each-iteration-update approach
control principle, the required communication times and the          is not taken in asynchronous control. Clearly, the best value
time-consuming for a successful target search increases as           should be remembered in those steps that update does not
communication cycle decreases.                                       occurs.
   3) As for the synchronous strategy, the corresponding
algorithm runs efficiently. But it is impractical for control
over swarm robots in the real world because there is no such
synchronization mechanism to ensure interactions.
        Table 3 Results of running parallel control algorithms
                                    Success      Efficiency Factor
 Comm. Strategy        Trial Runs
                                    Rate (%)          (x 10-3)
            I             50          100              12.31
           II             50          100              4.794
          III             50          100              5.780
          IV             50 x 7       99.9             5.170
  I : synchronous comm. strategy
  II : ‘static’ position-based asynchronous comm. strategy
  III: ‘dynamic’ position-based asynchronous comm. strategy
  IV: fixed comm. cycle-based asynchronous comm. strategy                  Figure 7 Iterations-comm. cycle of strategy IV
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