Computers and Electrical Engineering 43 (2015) 278–291

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Computers and Electrical Engineering

journal homepage: www.elsevier .com/ locate /compeleceng

A review of metaheuristics in robotics q

http://dx.doi.org/10.1016/j.compeleceng.2015.01.0090045-7906/� 2015 Elsevier Ltd. All rights reserved.

q Reviews processed and recommended for publication to the Editor-in-Chief by Associate Editor Dr. Ankit Chaudhary.⇑ Corresponding author.

E-mail addresses: ccfong@umac.mo (S. Fong), suashdeb@gmail.com (S. Deb), dr.ankit@ieee.org (A. Chaudhary).

Simon Fong a,⇑, Suash Deb b, Ankit Chaudhary c

a Department of Computer and Information Science, University of Macau, Macaub Department of Computer Science and Engineering, Cambridge Institute of Technology, Ranchi, Indiac Department of Computer Science, Truman State University, Kirksville, MO 63501, USA

a r t i c l e i n f o

Article history:Received 14 March 2014Received in revised form 2 January 2015Accepted 13 January 2015Available online 13 March 2015

Keywords:Collaborative roboticsMetaheuristicsRoboticsSwarm intelligenceSurvey

a b s t r a c t

Metaheuristics have a substantial history in fine-tuning machine learning algorithms. Theygained tremendous popularity in many application domains. Robotics on the other hand isa wide research discipline that embraces artificial intelligence in a complex individually-thinking robot and distributed robots. Recently, metaheuristics made a significant impacton the application areas of collaborating robotics. This new trend of collaborating robotics,offers the possibility of enhanced task performance, high reliability, low unit complexityand decreased cost over traditional robotic systems. Collaborating robots however aremore than just networks of independent agents; they are potentially reconfigurable net-works of communicating agents capable of coordinated sensing and interaction with theenvironment. On the conceptual level, these bots can be empowered by the logics of meta-heuristic algorithms which share the same functionalities and capabilities. This paperreviews the recent advances of metaheuristic algorithms on robotics applications. A taxon-omy is provided as a reference for robotics designers.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Robotics has long been a multi-discipline that combines mechanical science and machine learning in computer science,for designing robots that would be able to navigate, perceive and manipulate objects in the surrounding in the physicalworld. Apart from those who are dedicated into specific and monotonous tasks (like those in the factory assembly line),robots often would have to embrace a high uncertainty associated with their physical surroundings. Therefore, the tasksto perform and the approaches to tackle the tasks are highly diversified. There exist enormously large combinational optionsin how a robot can interact with its environment, with of course the aim of accomplishing the tasks eventually and minimiz-ing costs or risks. In some extreme examples, some robots are designed to perform housework at home which is full of fur-niture obstacles, to search for military targets behind the enemy line, and to explore even unknown terrain by unsupervisedlearning and to collect extra-terrestrial samples on the surface of remote planet. They will have to cope with uncertaintyautonomously and make sound decision in response to the real-world situations, while keeping the original aim in alignmentto their actions and reactions.

Out of many complex tasks which a robot would possibly have to perform, exploration and navigation are essential abili-ties for designs of mobile robot. Based on the vision they perceive in real-time, and the amount of control of the gears for

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moving, they are tasked to make decision on the spot in finding a collision-free path from the start position to the destinationwhere obstacles may be encountered along the way. Path planning is a key problem here that is comprised of challenges innavigation and exploration, for staying on course on a reasonably collision-free path and steering away from obstacles or atotally new terrain.

To overcome the challenges of path planning which is central to the design of mobile robotics, optimization techniqueshave been popularly applied. The techniques essentially attempt to find a solution that optimizes the gain of some goals, atthe same time search for a set of the most suitable actions (or reactions) subject to certain constraints. Optimization tech-niques have a long track record in successfully solving hard-optimization problems in industrial applications such asresource allocation, job scheduling, network routing, and path planning for unmanned-aerial vehicles or similar mobilerobots etc. In path planning which is known as a difficult task for mobile robots, for instance, an optimal route is to be chosendynamically from the current position to the finish point out of large possible combinations of route segments. A mobilerobot usually will have to find the shortest path or one that optimizes the value of the objectives.

In nature, some computing techniques such as genetic algorithm (GA), Particle Swarm Optimization (PSO) and Ant ColonyOptimization (ACO), just to name a few, would demonstrate their suitability in finding the optimal solution in optimizationproblems similar to path planning in mobile robotics. The underlying principle of these nature-inspired optimization tech-niques is to tap on the power of swarming behaviour of individual search agents, for collectively finding a desired solutionout of many possibilities, given some environmental variables or constraints. Take ACO as an example, a colony of ants scoutthe search space in swarm in order to find the best food source. Each individual ant performs relatively simple functions suchas sensing for food, roaming around every corner with an inclination of following the scent of pheromone paths left by itsfellow ants, and leaving pheromone trails behind during its course of search. Together the swarm of ants that work as a col-ony can effectively achieve the goal in a distributed manner. However, individually each ant is programmed with only simplelogics, such as sensing and responding to their environment. This would be an ideal feature in implementing simple mobilerobots in large quantity that collaboratively function together as a group.

The nature-inspired optimization techniques are generally known as meta-heuristic algorithms, in an abstract sense.Meta-heuristics are high-level strategies that guide the search agents to progressively improve the overall solution. The solu-tion is therefore optimized by checking across some random elements and possibilities, in the hope of finding a better qualitysolution, while the candidate solution is inherited from one stochastic iteration to the next. Meta-heuristics may not yield anabsolute best solution unlike deterministic methods. But quite often they produce sufficiently good solution in most caseswithin a reasonable amount of time. Readers are referred to a recently published handbook in metaheuristics for the basis ofthe technical details and the mathematical fundamentals of these optimization methods [1].

The objective of this paper is to provide a comprehensive review over metaheuristic approaches to mobile robotics, espe-cially on how they swarm collectively for a common goal. Starting with an introduction to robotic swarm, previous and cur-rent works dedicated to the advances of swarming robots are presented in Section 2. A taxonomy is provided in Section 3 as areference guide for robotics designers. Section 4 presents a detailed review with respective to the proposed taxonomy oversome representative metaheuristics on robotics, from the classical works to the most recent ones, along with a discussion oftheir application areas. Section 5 concludes this paper.

2. Swarm robots

The term swarm robot is first coined by Goss et al. [2] where the robots do collectively work together. Each individual oneof the swarm robots has omni-sensing abilities being able to mark trails on par with ants’ pheromone. There are several fea-tures that can be observed from their swarming behaviour, as follow. (1) Their swarming process is based on their abilities inwhat they can sense locally and individually. (2) In most situations, swarm robots are capable of maintaining a duplex com-munication channel to a base station, thereby facilitating uploads of local information sensed by each robot and downloadsof commands from a centralized decision maker. (3) Multiple robot groups can communicate one group with another, inorder to allow other robot groups to exploit these connections and navigate along the visited trails. (4) As an essential qualityto swarm robotics, swarm robots are scalable to become large groups of robots without the need of a complex control strat-egy [3]. For instance, the swarming robots by the SWARM-BOTS project [4] have simple acting, sensing and computationalcapabilities. Therefore when scaled up as a large working group, they can collectively overcome the limitations of an individ-ual, solving problems that single s-bot cannot cope with.

Taking these characteristics into consideration, the behaviours of swarming robots can be clearly distinguished fromother exploration strategies [5,6] which concentrate on seeking for a global solution by all their forces. Swarming robotsare agents that together exhibit some emergent behaviour that is not known to the individual agent. The emergent beha-viour could be self-assembly but it may not always be the case. They however would have to collectively solve problemsthat cannot be easily solved by a single robot. Swarm robots require two tiers of movement coordination, one for guidingtheir individual search at their local proximity and the other one for their group movement over the search space. By thesetwo-tier movements, the swarm robots can achieve smart tasks that would be otherwise impossible for a single robot toaccomplish.

The two-tier search strategy is generally comprised of detailed local search that works in details of the perceivedenvironments, and abstract global search that optimizes the overall gain. Coincidentally a number of contemporary

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metaheuristic algorithms [1] are born with this unique two-tier search feature [7]. Certain similarities can be observedbetween the search behaviours of metaheuristics in a mathematical hyperspace and the spatial search strategies by swarmrobotics. Fig. 1 illustrates conceptually how the two-tier movements which can be programmed by metaheuristics are incor-porated into a robot.

3. Taxonomy of metaheuristics on robotics

In this paper we argue that robotics could be classified into several conceptual layers, from the most primitive self-motorcontrol, individual robot functioning, multiple robot movements to collaborative swarming robots. The conceptual architec-ture is shown in Fig. 2.

Conceptually the robotic technologies are layered ranging from basic motor skills to complex form-shifting and swarmingcapabilities. In each layer, there are three major management functions involved – control plane, user plan and coordinationplane. Control plan specifies mainly the information and variables that are used for internal operations such as inter-com-munication amongst processes inside a robotic machine. In the user plane, input parameters are to be specified by the usersfor configuring how they want the robots to operate. Specifically, in the coordination plane, synchronization functions arerequired to keep the local search strategies and global exploration strategies working well together. This is important, notonly for the sake of keeping a proper coordination, often a perfect balance between local search (aka intensification) and glo-bal exploration (aka diversification) yields maximum optimization results [7]. More discussion follows in the sections below,on reviewing recent papers in the literature that fit into the four layers in the taxonomy model.

Fig. 1. Two-tier search strategy for swarm robotics and metaheuristics in navigation.

Fig. 2. A conceptual architecture of robotics taxonomy with respective to optimization.

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3.1. Motor layer

This layer refers to mechanics that are confined to a self-motor robot and automation of different joints in an individualrobot. Most of the research works especially those in the relatively older times are devoted to optimizing the movements ofparts in a robotic machine. As the name suggests the works that belong to this layer are responsible for the robots’ motionfrom their mechanical motors.

Technically this is considered to be a motion planning problem in a two or three-dimensional working space. Given manydegrees of freedom, the decision in the motion planning problem is almost intractable, with a certain number of physicalconstraints. Assume that there exists some parameter space (or configuration space) for programming the robot; each pointin the space maps to some position of the robot movement in the physical space. The challenge is to decide an optimal obsta-cle-free path from the starting position to the goal position; usually that costs least amount of time or moves. The config-uration space is often discretized so that provides the basis for the finding a feasible set of motions from a NP-hard problem.

In the early 80s and 90s, in lieu of brute-force method [8] researchers proposed probabilistic approach in tackling thismotion planning problem. They include for example, randomized path planner (RPP) [9,10], rapidly-exploring random tree(RRT) [11] and probabilistic roadmap planners (PRP) [12]. These methods in general search for sub-goals by random chances.Another group of researchers in recent years capitalized on metaheuristics in improving the search. Shunji Umetani et al.tested two heuristic algorithms as metaheuristic approach, called the simulated annealing (SA) and the iterated local search(ILS) for improving the performance of motion planning. A new method called bi-directional local search (bid-LS) based onthe previous two was proposed. Shunji Umetani et al. compared the efficiency of these metaheuristics through com-putational experiments on an instance of an articulated robot with six degrees of freedom. An example of such robot as arobot arm that precisely inserts a piece of lead into the tip of a pencil is shown in Fig. 3. In their paper [13] it was com-putationally proved that bid-LS quickly found a collision-free path in the experiments.

Subsequently, Bergamaschi et al. extended the work by incorporating more metaheuristic algorithms, such as sequentialquadratic programming (SQP), genetic algorithms (GA), differential evolution (DE), and Particle Swarm Optimization (PSO).In their paper [14], the design of manipulators with three-revolute joints is reformulated as a simplified optimization prob-lem - the voids, singularities and the discontinuous generation of the envelope of the configuration space are eliminated so toreduce the complexity of the mathematical model of the 3D configuration space. The space is more compact now but theobjective function would encounter more local maxima and the performance is extremely nonlinear, imposing greaterdifficulties for the metaheuristic methods. By the findings of the experiment, the optimal configuration volumes (so calledmotion paths) as computed by the GA, DE and PSO are about the same. Nevertheless, when it comes to speed, DE was thefastest amongst the four. The authors proved that the metaheuristics are able to produce good solution although the searchspace has many local optima. The limitation of this work however is the scenario of robot arm with only three degrees offreedom [65]. It is unknown and challenging though for fellow researchers to try, if it were extended to a higher degree mak-ing more local optima and extremely non-linear search space.

For robots that are supposed to move with unconstrained degree of freedom (e.g. humanoid robots), in recent years,researchers improvised robot controllers by adding learning capability so that robots learn motor primitives by interactingwith humans [15]. Research efforts of various kinds are continuing to generate motor primitives that make the robots behavenaturally like humans. One example [16,17] is producing motor primitives that follow certain smoothest or shortest paths byusing GA. Through evolving generations of mutation, the unqualified motor primitives which do not smoothly constitute to ahuman-like movement are eliminated. New options of motor primitives are explored too. Results by researchers are shownto be superior to the traditional demonstration-based learning [15] for producing quality human-like movements for robotmotors.

Fig. 3. Precise motion by a robot arm with six degrees of freedom.

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3.2. Individual robot Layer

At this level, a robot is assumed to have equipped motor skills that are fine-tuned so that it is well-skilled to performessential moving tasks. In robotics control and automation, navigation which embraces localization, sensing and responsesto the environmental obstacles is an important topic. In particular, research on robot navigation often condenses to robotpath problem where a robot navigates alone. Robot Path Planning Problem has attracted a lot of attention from the researchcommunity over the last two decades. This problem ponders on how to plan a collision-free path from a start position to arequired goal position amidst a number of obstacles for a mobile robot. Path planning has been tackled by optimizationmethods which target at finding the best path with certain constraints. The optimization objectives may cover one or com-binations of the following: travelling distance, travelling time, and resource consumption. However, the travelling distance isthe most common objective, usually the shorter the better. In addition, the optimization is sometimes needed to achievecollisions avoidance, stop-over minimization and path smoothness. Linear programming and operation research [18] havebeen used favourably for solving such optimization problems.

Hussein et al. recently proposed a metaheuristic optimization-based approach [19] to solve path planning problemmobile robot. In their paper the two domains of trajectory-based and population-based metaheuristic optimization havebeen comparatively studied. Taking a ground truth reference from a time-consuming deterministic search by Breadth-first,metaheuristics such as Tabu search (TS), Simulated annealing (SA) and GA are compared by the quality of the path generated.The authors showed that via the simulation study SA outperformed the other algorithms with regards of run time, and TSoffered the best path.

The central role of metaheuristics in an individual robot is searching for the most suitable behaviour and/or the most fea-sible path in case of navigation when the optimal solution is unknown. Assume there is no need to insist on a deterministicmethod nor it is possible to glimpse a full picture of possibilities. Brute-force search is therefore inappropriate when thesearch space is too vast, and processing every possible move is too time-consuming. Relying only on little heuristic informa-tion that is accumulated from previous generation from time to time, metaheuristic works on a candidate solution by eval-uating how fit it is respective to the ultimate objective. As an example found in [20] the optimal set of robot behaviours is yetto be found in simulating a soccer goalie robot. Any possible combination of behaviour set can be tested in turn and a qualityscore is assigned to it. Since it was not known in advance what the optimal behaviour set should be, the search is delegatedto a metaheuristic algorithm to proceed on finding an optimal goal given some predefined rules and definitions on what agood behaviour set should be.

The easiest approach is Random Search – just try shuffling the parameters values in a behaviour set randomly, keep ontrying for as long as you can afford, and return the best one so far before exit. A better alternative called Hill-Climbing, wouldinitiate the behaviour parameter values set at random. Then a small yet random modification is attempted in each round ofiteration. Every time when it is found that the new version is better than the old best one, discard the old one and replace thecurrent best solution with the newest version. This process, again, can repeat as long as the user’s allowed time can beafforded. Hill-climbing forms the basis of a metaheuristic algorithm. A heuristic belief about the possible space of candidatesolutions is exploited. The underlying designs of all metaheuristics are nearly the same that tap on the features of com-binations of random search and hill-climbing. A classic example as shown in Fig. 4 is Elvis robot where genetic algorithm(GA) was used to find the optimal behaviour set, through a combination of random search (exploring new options) and hillclimbing (modifying the existing solution).

Extending from the basis of GA and Elvis robot, Blum and Roli [53] generalized the fundamental elements that constituteto metaheuristics as follow:

� A guide is needed to empower the search process.� Search space is scrutinized and local optima are avoided in order to find an approximate optimal solution which may

never be proven as a ground truth; therefore they are non-deterministic.� The metaheuristic search consists of heuristic mechanisms ranging from simple local search to complex memetic learning

algorithms.� Variants of metaheuristics emerged with additional mechanisms designed for avoiding being trapped in local solution

areas.� The applications of metaheuristics are not problem-specific. However, in the context of robotics, they are mainly used for

path finding, navigation, and behaviour optimization where the possibilities are vast, so is the search space.� Domain-specific knowledge is used in the upper level strategy, often in the format of rules and constraints, as well as how

to migrate away from the local optima for farther exploration.

Some exotic metaheuristics emerged lately such as glow-worm algorithm [21] in detecting multiple source locationsin robotics. A novel version of GA called Petri-GA that employs Petri-net in the navigational controller together with GAis proposed [22]. It works by iteratively referring the observed geometry of the environment over a priori map of posi-tion locations, in order to estimate an appropriate heading angle of the moving robots to locate targets. It is demon-strated that the Petri-GA method can better avoid collisions and achieve a near optimal robot path in complexenvironments.

Fig. 4. Elvis the robot which coordinate its arm movement with its camera vision.

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3.3. Multiple robots layer

This layer concerns mainly at the multi-robot control. A popular example of everyday applications making use of multiplerobots includes intelligent carts in large airports powered by robots draw themselves automatically together at designatedcollection points. This is done technologically using mobile software agents to locate other robots where they are scattered inan open area such as an airport hall. The robots operate autonomously. From the view of optimization, the objective is todefine the moving patterns of these mobile robot carts in such a way that is shortest, easiest and do not impose obstaclesto travellers. Typically PSO-based clustering algorithm is used in this scenario where the ant agents would collectively findthe best paths together, from where they are to the designated target locations. In general, the objective function considersabout how the resources must be utilized efficiently while the overall benefit should be maximized by a distributed multi-robot team. Similarly the applications can be extended to battlefield, reconnaissance mission trip or terrain explorer, just toquote some examples. Usually two levels of optimization are enforced: reaching the targets and limited rescue time is of theutmost importance, while for planetary exploration fuel efficiency is being imposed along the way by path planning [23–25].

This concept of multi-robot control has evolved to a popular computer science domain called multi-agent (MA) optimiza-tion. By the Handbook of metaheuristics [26], MAs are generally known as ‘genetic hybrids’ that are programmed across thetwo related fields of machine learning and robotics. A popular machine learning scheme is artificial neural network (ANN)where MAs (and their robotic hardware syndicates) are trained by using ANN [27–29]. In particular, some are trained to dopattern recognition or matching [30] while some are trained for more specific pattern classification [31,32] distinguishingbetween different types. Some MAs are to be trained to analyse time-series data [33]. A popular mechanism found in thismulti-robot layer is manipulator motion planning [34], which is usually coupled with time optimal control [35]. Fig. 5 showsan example of how multiple robots (robot arms) behave autonomously while their motions are to be synchronized with theother robots and the sequence of the job tasks. Optimal motions and precise timings are in effect simultaneously.

MAs are believed to have a promising future, backed by several factors. Firstly they demonstrate a remarkable trackrecord of efficient implementations making them suitable for practical problems. Secondly they show that theoretical algo-rithms such as metaheuristics do have successful attempts in fusing with daily applications. In particular, population-basedmeta-heuristic optimization has found its merits in approximating feasible solutions in solving complex optimization prob-lems – MAs and these population-based metaheuristics do just fit like hand into glove, combining the physical hardware inrobotics and theoretical logics from the algorithms. The other term that closely resembles population-based metaheuristicsis Swarm Intelligence (SI) which both is based on the collective behaviour of a group of mobile agents. The SI here is some-what different from the swarming behaviour at the swarm-bots layer. In this layer, MAs move or navigate in two-tier strate-gies; swarm-bots which are to be discussed in the next section evolve from MAs, they integrate as a whole system in additionto the distributed navigation patterns.

The collective behaviour of MAs inherently is founded on the basis of autocatalytic behaviour in some self-organizing sys-tem [36]. SI is usually made up of a population of primitive agents interacting with one another locally as a swarm as well astheir environment. The SI in the sense of collective movements is referred to the distributed group navigations. Originally SIis inspired from the nature where the movements of animal herding, ant colony mobilization, bird flocking, fish schoolingetc. In the context of robotics, SI refers to design of complex adaptive systems that are found in the behaviour of MAs.

The essential feature in this layer is the Collective Robotic Search (CRS) which is tapped on the collective powers of MAslooking for a target in a scattered and distributed fashion. Usually CRS finds its practical applications in some high risk

Fig. 5. Multi-robots function as a team in car manufacturing.

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environment where a gang of unmanned mobile robots in lieu of humans are searching for a target. The operational assump-tion is the MA which manifests as a mobile robot could be randomly added to a bounded search space, and they could besomehow transported at high speed through the search space with a new position computed for each robot per iteration.The coordinates of a candidate target can be known and the quality of the target is calculated by an appropriate fitness func-tion in each robot. The fitness value could be estimated by measuring the Euclidean distance of the individual robots relativeto the target in the case of searching for a prime target, in comparison to the status of their current position, like remainingfuel level, favourability of the terrain etc. Constraint functions could be obstacles around the robot and the boundary of thesearch space.

3.4. Swarm-bots layer

From the multi-robot layer, technologies on collaborating Robotics has evolved to ‘swarm bots’ using nature-inspiredmeta-heuristics, in their structural forms in addition to their navigation patterns, collectively and collaboratively. Theseswarm bots (SB) are sometimes known as collaborating-bots which take dynamic shape of robots being able to self-organizeand self-assemble in different situations solving different problems depending on the ever-changing environment. These SBskilfully borrow the concept of swarm intelligence in their form of swarming, and implement the behaviours and shapes byflexibly reconfiguring themselves in real-time. They transform and aggregate their structure dynamically when the needs ofmatching the environmental variations arise.

These SBs are usually made of a large quantity of tiny and identical bot. Each of these bots work individually, they aresimple in hardware design which enables manufacturing them in bulk in relatively low costs. Their modular structureenables them to individually form long chains or a complex structure whenever it is needed. They use simple magnetic con-nection contacts allowing them to gather and plug onto one another at some specific points. According to the inventors,1 thedesign is founded on a lattice robot which is a robot made up of small and identical components being combined to form a com-plex robot.

The SB which is an epic in collective robotics taps on the power of the swarm. Recently they attract a lot of interest inresearch and implementation: to just name a few, teams of robots2 that play soccer cooperatively, some work at the airportapron that unloads cargos from planes, some work as surveillance patrolling over vast areas in the best distributed manner.Some swarm bots are unique in a sense that they do cluster objects and they do self-assemble and perhaps one day will par-ticipate in battlefields. Depending on the environments, sometimes they assembly to bridge a gap, and sometimes they swarmto transport a prey. Some examples3 are shown in pictures in Fig. 6 of these simple and self-assembly swarm bots and how theyform a chain in an attempt of accomplishing complex tasks, like crossing a gap. The original concept of Swarm Bots was coinedabout a decade ago, by academic researchers [58,59] as an experimental prototype of self-adaptive and self-configurable smallrobots. Working prototypes are implemented lately in 2014, such as the first 1000-robot flash mob that has assembled atHarvard University [60].

4. Metaheuristics applied to robotics: advances from the past decade

4.1. The classical metaheuristics for robotics

In this section we review several popular metaheuristics that have been successfully applied to optimise different aspectsof robotics, such as motion path planning and selection of optimal parameter values etc. Out of the popular metaheuristics,Particle Swarm Optimization (PSO) has a long history of serving as an optimization algorithm fine-tuning operations inrobotics [37]. The potential solution candidates in PSO are coded in ‘particles’ that roam around the problem space by

1 http://science.howstuffworks.com/real-transformer1.htm.2 http://www.robocup.org.3 http://www.swarm-bots.org.

Fig. 6. Swarm bots in action (Photo courtesy of swarm-bots.org).

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obeying some basic rule. The particles carry their own fitness values relative to their positions and their own velocities thatgovern their flight directions. After the particles have been randomly assigned with solutions (positions) at the first round,they aim at looking for optima by repeatedly updating their positions in the subsequent iterations. The new position of eachparticle is updated according to two computed ‘best’ values. The first is the best self-fitness of the particle that has attainedso far, called Self-Best. The other is the group best value that is achieved by any particle amongst the whole group in theneighbourhood so far, called Group-Best. The velocity and position of each particle is updated according to the following sim-ple equations at the end of each iteration:

vcþ1 ¼ coef tvc þ l1 � rand1 � ðSelfBestc � poscÞ þ l2 � rand2 � ðGroupBestc � poscÞ

poscþ1 ¼ posc þ vcþ1

where vc is the current velocity of the cth particle; coeft is the inertia coefficient at tth iteration that is used to slow the par-ticle velocity over time for convergence; two random numbers 2[0,1] are rand1 and rand2; learning factors l1 and l2; and thecurrent position in the search space, posc for the cth particle. With only four additions or subtractions and four multiplica-tions, PSO has the computational advantage that makes it as a favourable metaheuristics in robotics. It is relatively easilyscalable in terms of computation by assuming each robot in multiple robots or each bot in swarm bots as a PSO particle.PSO runs the above equations and each robot updates its own fitness, Self-Best, in relation to the wellness of its positionin the search space, and they also broadcast amongst themselves in the swarm for updating the Group-Best variable.

By this simple principle, PSO has made an underlying metaheuristics that guides the search patterns for multiple robots,and Table 1 lists a number of recent research along this direction. The list is not meant to be exhaustive but showcases therecent efforts made in applying PSO as a simple metaheuristics in guiding the robots for specific purposes. The robots appli-cations in these cases fit either in the Multiple Robots Layer or Swarm-bots Layers in our taxonomy.

4.2. Newly emerging models

In the early 2000, researchers Hayes et al., [38] suggested that beacon localization can be realized by autonomous mobilerobots. Later on, the search techniques were extended [39] to track odour sources with the incorporation of the biologicalprinciples found in PSO in sniffing out the singularity in the data patterns. In the latter years 2006 and 2007, other research-ers such as Pugh et al. [40,41] followed the research direction in improving the search algorithm based on PSO making thesearch works in noisy environments while enabling the mobile robots with unsupervised learning ability. In particular therobot controller is optimized in functioning by using PSO with the aim of avoiding obstacles and staying on course in trackingthe source. The other group of researchers Jatmiko et al. further improvised the search algorithm to adapt to changes in thesearch space [42,43]; real-life situations like wind changes and turbulence that constantly affect the conditions of the searchspace. In 2010, researchers Hereford & Siebold argued that the so-called PSO-based search by the previous researchers wasonly partially built under the control of PSO swarming behaviour; e.g. PSO was rather used to evolve the robot controller forbetter manoeuvre by optimizing the parameters in localization. In their work [44] a new version called pePSO is said to bedirectly embedded into each mobile robot, and they thereafter swarm together in exact manners as PSO search undertakes.

Hereford & Siebold combined pePSO in their proposed trophallaxis-based algorithm (TBA). Under the concept of TBA, therobots do not need to exchange information remotely; information is only exchanged when they happen to be in contactalong their flights. They swarm and move like how PSO does; the inertia is mimicked by how the robots stay stationaryfor a brief length of time proportional to the fitness value being measured in their positions. Thus, robots that are stationedin positions of high fitness tend to remain there and draw others to come, eventually lead to convergence. pePSO + TBA issaid to have advantages such as free from the inter-communication needs, free from message exchange in finding the globalbest fitness, the bots do not have to know their position. It is relatively simple because the robots by pePSO would just moverandomly during the search, pause, evaluate the fitness of the current solution, and waits. When the search ends the robotswould cluster around an optimal location that could be easily spotted. The robot’s localization controller is therefore much

Table 1Recent research in robotics based on PSO and variants in the last decade.

Year Refs. Metaheuristic Taxonomy Application Comments

2004 Doctoret al. [37]

PSO Multiplerobots

Collective roboticsearch

The possibilities of utilizing PSO for multiple robotsearches were discussed. The aim was at optimizing theparameters of the search PSO. Scalability of expanding thestandard PSO to many robots was not considered

2006 Schmickl &Crailsheim[45]

Honey bees Swarm-bots

Localization An alternative communication means amongst swarm bots

2006 Pugh &Martinoli[40]

PSO Multiplerobots

Multi-robot learning The search techniques are based on the biologicalprinciples that single out the normal pattern for detecting‘‘surges’’. PSO algorithm is not directly used for controllingtheir movements

2006 Jatmikoet al. [42]

PSO Multiplerobots

Odour search andlocalization

As above

2007 Pugh &Martinoli[41]

PSO Multiplerobots

Collective roboticsearch

As above

2007 Jatmikoet al. [43]

PSO Multiplerobots

Odour search andlocalization; obstacleavoidance

As above

2008 Schmickl &Crailsheim[46]

Honey bees Swarm-bots

Localization An alternative communication means amongst swarm bots

2008 Akat andGazi [57]

PSO Multiplerobots

Dynamicneighbourhoodlocalization

Proposed dynamic and asynchronous updates ofneighbourhoods amongst robot swarm under PSO

2008 Pugh &Martinoli[48]

Noise-resistant PSO(inspired by chemotaxisbehaviour in bacteria)

Multiplerobots

Collective roboticsearch, multi-targetslocalization

Proposed a modified version of PSO for adapting freeparameters in the multi-robot search algorithm in wherethe robots are engaged in the localization of several targets

2010 Hereford &Siebold[44]

PSO Swarm-bots

Collective roboticsearch

PSO is directly embedded into the movement of eachindividual robots, guiding them move as a swarm of bots

2011 Gong et al.[61]

Multi-objective PSO Multiplerobots

Robot path planning Proposed a multi-objective PSO for global path planningthat avoids dangers and obstacles in robotics

2011 Valdezet al. [62]

Hybrid PSO + GA Individualrobots

Fuzzy logic controlleroptimization

Proposed a new version of fuzzy logic that integrates thePSO and GA results to benchmark fitness functions

2011 Couceiroet al. [52]

PSO with sub-grouping Multiplerobots

Collective roboticsearch

Proposed an extension to PSO where the whole swarm ispartitioned into sub-groups for facilitating parallelsearches

2012 Martinez-Soto et al.[49]

Hybrid PSO + GA Individualrobots

Fuzzy logic controlleroptimization

Proposed hybrid PSO + GA for obtaining the bestparameters of the membership functions of the trajectorytracking robot control

2012 Abidinet al. [5]

Fruit Fly Swarm-bots

Drosobot swarming forlocalization andcollaborative search

Simulation and pre-deployment prototype of water bots

2013 Zheng &Tan [63]

GES Multiplerobots

Collective roboticsearch

Proposed a new version of PSO that is specifically suitablefor parallel group search; the swarm is exploded into sub-group, thereafter they search independently and convergeon the final optima

2013 Shaukatet al. [64]

Fish-larva Multiplerobots

Coral reef search usingacoustic cues by AUV

Proposed a Fish-larva target-driven algorithm forsearching an underwater acoustic source usingAutonomous Underwater Vehicle

2014 Siddiqui &Khatibi[50]

PSO Individualrobots

Visual tracking Useful component in robotics

286 S. Fong et al. / Computers and Electrical Engineering 43 (2015) 278–291

simpler, which needs to only encode the logics of PSO that involves only several addition and multiplication operations. It isclaimed to be easy in programming such digital logic in the microcontroller hardware.

The TBA concept by Hereford and Siebold can be found from the trophallactic model proposed by Schmickl andCrailsheim, which was originally inspired by honey bees’ communication method. In their papers [45,46] the TBA modelwhich dictates how a swarm of robots transfer dirt from a source location to a dump site. The robots upload informationwhich is stored in the robot internally as ‘nectar’ from the source. When the robots navigate away, the stored nectar inthe robots reduce in amount. It would be known therefore how close the source is by the level of nectar remaining. By thisway, the robots would be able to climb uphill in the gradient by querying the nectar store level of the other local neighbourrobots. The TBA method is improved with the function of recharging the nectar by [47].

S. Fong et al. / Computers and Electrical Engineering 43 (2015) 278–291 287

In the same year 2008, Pugh and Martinoli proposed a similar concept to Hereford and Siebold’s that maps the virtual PSOparticle to each individual swarm bot. A one-to-one parallel mapping between particles and robots is established. Theauthors claimed that the method [48] needs no external supervisor to oversee the optimization process. As the robots assearch agents evaluate the fitness in parallel the speed is greatly improved, and it shortens the total learning time.Furthermore the fitness evaluation method in the PSO was said to have improved, more resistant to noise. The algorithmwas inspired by the chemotaxis behaviour of E. coli bacteria which influences the swimming pattern (tumble or keepstraight) by rotating the flagella for each robot, as a search strategy for localizing targets in an unknown space.

Improving PSO algorithm for achieving better robotic search strategy seems becoming a trend. In 2012, Martinez-Sotoet al. proposed a hybrid PSO + GA method [49] for designing an optimal fuzzy logic controller for each search robot. The opti-mal parameter of the fuzzy membership functions allows autonomous mobile robots to have better trajectory tracking con-trol. The authors compared the new hybrid method with GA and PSO being used separately. They found that the score of t-Student test on the hybrid PSO + GA is higher than the traditional methods, that means there is sufficient statistical evidenceto support the claim of improvement with a 95% of confidence. Performance wise, the mobile robots with their fuzzy logiccontroller optimized by hybrid PSO + GA has an error rate of 0.136014, where the same by GA and PSO are 0.154186 and0.16132 respectively. The theoretical basis for hybridizing PSO and GA is rather simple: the results by PSO and GA aremerged periodically. In every four cycles, the best solution found by either PSO or GA is mixed into the solution populationof the worst method of the two. As a result, the best parameters of the fuzzy membership functions are found, and it provesto be more robust than using the GA or PSO alone.

Another important work in 2014, by Siddiqui and Khatibi [50] is visual tracking using PSO. The author studied a novelapproach in solving visual tracking problem which is common in robotics by tracking a projection of the plane. A non-linearimage alignment is adopted and correct parameters of the transformation are recovered by optimizing the similaritybetween the planar regions using PSO.

Similar to PSO, a group of researchers lately proposed Fruit Fly algorithm [51] that was used to simulate the swarmingbehaviour of water bots called drosobots. In their work a framework was established that allows water robots communicateamongst themselves in order to reach a desired destination. The searching is optimized by Fruit Fly which works very similarto PSO. Though remained unverified in extensive experimentation, the Fruit Fly search strategy was said to be better thanthose inspired by bees and ants, which makes it suitable for efficient and wireless sensor network environment. The errorrate was found to be appropriate for using Fruit Fly to optimize a regression neural network model, resulting in good con-vergence. Wireless communication, low-cost microcontroller and GPS steering form both physical and mechanical setupswere built in addition to the search strategy control method.

Lately in 2013, research Zheng and Tan proposed an interesting and novel group search strategy specialized in enablingparallel group search based on individual PSO swarming movement. It is called Group Explosion Strategy (GES) for allowingsearching for multiple targets in constrained environments via a collection of simple robots. GES is inspired by natural explo-sion phenomenon where the full gang of robots are ‘‘blown’’ into small groups to be scattered over the search space.Thereafter the search agents in different groups search in different areas of the search space for multiple targets indepen-dently and self-adaptively. A similar work is by Couceiro et al. [52] which proposed an extended version of PSO which dividesthe whole swarm into appropriate sub-groups dynamically during the search process. GES is featured by its advantages ofspeedy convergence that depends on both the intra- and inters- groups searching patterns while multiple targets are beingsearched in parallel. Importantly the authors validated GES by comparing vis-à-vis to PSO which is its predecessor searchmethod. GES is superior to PSO in regards of efficiency in energy consumption, success in finding multiple targets bycooperating robots in different exploded groups. Good stability in achieving the same in obstructive environments wasobserved too. This shows a success example in innovating new metaheuristics for robotics originated from classical PSO.

4.3. Prospects of metaheuristics for robotics

Regarding the future prospect of metaheuristics algorithms being applied to robotics, Fig. 7 shows that both trends ofresearch in the areas of robotics and optimizations4 are moving steadily. A stable momentum of research efforts are observedfor both areas, which are inputted as search keywords in Google search engine in the past 10 years. In particular, one can noticethat the two trends are coinciding pretty much in the past ten months. The future prediction on the two trends continues toshow the intervention. That is a possible indication that these two research areas continue to complement each other like fittingglove to a hand. It was also noted that both trends in ten years ago experienced a slow decline, the two trends intersected inapproximately year 2008; the optimization trend has since slightly overtaken the hype of robotics, and the two eventuallymerged in late 2013 onwards. This suggests a situation that the robotics research has matured and now experiencing a steadytrend. Optimization, on the other hand is experiencing a similar steady trend of interest over time; qualitatively by reviewingthe research articles as in Table 1, new hybrid solutions are being proposed increasingly with novel extension from classicalmetaheuristics like PSO and GA. The prospect of the two areas as well as their synergy looks strong. Another interestingside-note is that the research outputs of from both academic conferences and journals, provide ample opportunities for fusing

4 The search term optimization is used as it embraces relevant terms under metaheuristics, such as bio-inspired optimization, nature-inspired optimizationtheories, stochastic optimization, and swarm optimization etc.

Fig. 7. Google trends on the keywords of robotics and optimization.

288 S. Fong et al. / Computers and Electrical Engineering 43 (2015) 278–291

the two fields of robotics and optimization together. Citations of the two fields over the past five years (that was all the dataavailable since 2009) from Google Scholars are charted in Figs. 8 and 9 respectively, using the search terms robotics andoptimization. The charts are represented in box-plots with an average value of citations over the years; the citations are in termsof the maximum h5-indexed citations extracted from the top 10 most popular research conferences/journals, as search resultsreturned from Google Scholars using the respective search keywords. The box-plots in Fig. 8 show that the citations in the fieldof robotics are relatively steady over the years, while the citations in the field of optimization fluctuate. They are both in slowdecline which coincides with the results returned from Google Trend. While the minimum citations for robotics (the lowerwhisker) remain at about the pace over the years, the maximum citations of both robotics and optimization seem to be corre-lated in time. That is when the two research momentums combined and being cited. A good research synergy is implied whenthese two fields are studied together, by either applying metaheuristics in solving a robotics problem or validating new meta-heuristics through a robotics case study.

Another research synergy that may have been over-looked by a relatively few published works is the hybridization ofmetaheuristics which applies to robotics. While there are many applications of metaheuristics in engineering design andprocess design optimization, there are likewise potential fusion of metaheuristics algorithms, having one to complementanother. Some researchers have demonstrated the efficacy of such hybrid metaheuristics for robotic applications, such ashybridizing a new ACO-GA algorithm to solve the global robot path planning problem called SmartPath [54]; integratingACO with Simulated annealing [55], again for finding the global robot path; and combining the message passing and searchbehaviours of ACO/PSO as a new control algorithm for distributed swarm robots [56]. These emerging publications suggest agood niche research endeavour in evolving new metaheuristics for robotics.

82.6 76.8 85.5 76.554

10

20

40

80

160

320

640

2009 2010 2011 2012 2013

Fig. 8. Citation chart of top-10 journals found on Google Scholars by the search term ‘‘Robotics’’.

75.8 93.7

56 54.941.5

6

12

24

48

96

192

384

768

2009 2010 2011 2012 2013

Fig. 9. Citation chart of top-10 journals found on Google Scholars by the search term ‘‘Optimization’’.

S. Fong et al. / Computers and Electrical Engineering 43 (2015) 278–291 289

5. Conclusion

In this survey paper, a comprehensive review over metaheuristics approaches to mobile robotics, especially on how theyswarm collectively for a common goal is provided. Modern optimization techniques such as metaheuristics have revealedtheir power lately in robotics and automation. These powerful techniques are inspired by nature and it facilitates stochasticoperation that does progressively and iteratively finding a candidate solution by dealing with random elements, they step-by-step lead to a new, possibly better solution in terms of a given measure of fitness, and evolves into an ultimate solutioneventually.

Specifically, this paper takes a hierarchical perspective reviewing from fundamental mechanisms and moves up to morerecent but novel level of swarm bots which is still considered in infancy stage. It is pointed out how they contribute thepower of these computational techniques to building robotics at different levels of sophistication, with different applications.As a useful reference guide to robotics researchers, a taxonomy of how metaheuristics have been shown useful to differentlevel of optimization in robotics, as well as a detailed review with respective to the taxonomy over some representativemetaheuristics on robotics, from the classic methods to the leading edge researches, are provided.

Acknowledgments

The authors are thankful for the financial support from the Research Grant ‘‘Adaptive OVFDT with Incremental Pruningand ROC Corrective Learning for Data Stream Mining,’’ Grant no. MYRG073(Y3-L2)-FST12-FCC, offered by the University ofMacau, Fundação para a Ciência e a Tecnologia, and RDAO.

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Simon Fong graduated from La Trobe University, Australia, with a 1st Class Honours BEng. Computer Systems degree and a PhD. Computer Science degreein 1993 and 1998 respectively. Simon is now an Associate Professor of the Computer and Information Science Department, University of Macau. He haspublished over 230 peer-reviewed conference and journal papers, mainly in Data-mining and Metaheuristics.

Suash Deb specializes in Soft Computing, Nanocomputing, Artificial Intelligence, Bioinformatics, and Machine Learning. He received BE in MechanicalEngineering from Jadavpur University, Kolkata, M.Tech. in Computer Science from University of Calcutta and UNDP fellowship in Computer Science fromStanford University, USA. A Senior Member of IEEE, Suash is an elected President of the International Neural Network Society (INNS) – India.

Ankit Chaudhary is Assistant Professor at Dept. of Computer Science, Truman State University USA. He received his BS, MS and PhD, in Computer Science &Engineering. His research interests include Vision based applications, Intelligent Systems and Graph Algorithms. He has authored fifty publications, onebook and served as guest editor for CAEE, Elsevier, as well as editors of other international journals.