Research Article Mobile Robot Path Planning Using ... · network using clonal operator, clonal...

Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2013 Article ID 416715 13 pageshttpdxdoiorg1011552013416715

Research ArticleMobile Robot Path Planning Using Polyclonal-Based ArtificialImmune Network

Lixia Deng1 Xin Ma1 Jason Gu12 and Yibin Li1

1 School of Control Science and Engineering Shandong University Jinan Shandong 250061 China2Department of Electrical and Computer Engineering Dalhousie University Halifax NS Canada B3J 2X4

Correspondence should be addressed to Xin Ma maxinsdueducn and Jason Gu jasongudalca

Received 14 June 2013 Accepted 14 August 2013

Academic Editor Fei Liu

Copyright copy 2013 Lixia Deng et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Polyclonal based artificial immune network (PC-AIN) is utilized for mobile robot path planning Artificial immune network (AIN)has been widely used in optimizing the navigation path with the strong searching ability and learning ability However artificialimmune network exists as a problem of immature convergence which some or all individuals tend to the same extreme value inthe solution space Thus polyclonal-based artificial immune network algorithm is proposed to solve the problem of immatureconvergence in complex unknown static environment Immunity polyclonal algorithm (IPCA) increases the diversity of antibodieswhich tend to the same extreme value and finally selects the antibody with highest concentration Meanwhile immunity polyclonalalgorithm effectively solves the problem of local minima caused by artificial potential field during the structure of parameter inartificial immune network Extensive experiments show that the proposed method not only solves immature convergence problemof artificial immune network but also overcomes local minima problem of artificial potential field So mobile robot can avoidobstacles escape traps and reach the goal with optimum path and faster convergence speed

1 Introduction

Robot path planning is one of the most fundamental func-tions for mobile robot There are two types of planning forautonomous mobile robot based on how much informationis known about static environment global path planningwhen the environment is clearly known and sensory-basedlocal path planning when partial or no information aboutthe environment is known in advance [1] In the global pathplanning the environment surrounding the robot and theposition of obstacles are well known in advance and therobot is required to navigate to its destination with avoidingobstacles The complete robot path in such applications canbe calculated from the prior knowledge of the coordinatesof the starting point the destination point and obstaclesOn the other hand the local motion planning dynamicallyguides the robot according to the locally sensed obstacleswhich requires less prior knowledge about the environment

Therefore the local path planning methods are more suitableand practical for mobile robot since the environment is toocomplicated to be known precisely and may also be time-varying [2] While the local path planning faces significantchallenges

This paper focuses on mobile robot path planning inunknown complex static environment Artificial immunenetwork (AIN) can optimize mobile robot path planningbut it exists as a problem of immature convergence Sopolyclonal-based artificial immune network (PC-AIN) isproposed to solve the problem Immunity polyclonal algo-rithm (IPCA) increases the diversity of antibodies whichtend to the same extreme value through clonal operatorclonal crossover operator clonal mutation operator andclonal selection operator and finally selects the antibodywith highest concentrationMeanwhile immunity polyclonalalgorithm solves the problem of local minima caused byartificial potential field during the structure of parameter in

2 Journal of Control Science and Engineering

artificial immune network Experimental results show thatthe proposedmethod effectively optimizes path planning andimproves the performance of path planning

The remainder of this paper is organized as follows Thenext section discusses related works for autonomous mobilerobot path planning in unknown complex environmentSection 3 presents the proposed mobile robot path planningalgorithm in detail Simulation results and real-time experi-ments are presented in Section 4 Finally Section 5 concludesthe paper

2 The Related Works

Local path planning in unknown complex environment is ahot research topic in recent years Artificial potential field-based path planning algorithm [3 4] utilizes the attractiveforce from goals and the repulsive force from obstacles formobile robot path planning This method is known for itsmathematical simplicity and little computation but it suffersfrom a problem of local minima Many artificial intelligenttechniques have been proposed by scholars for mobile robotpath planning such as reinforcement learning fuzzy logicand genetic algorithm Reinforcement learning algorithm [15 6] has simple and complete theory but it is mostly usedin static environment because its infinite state in complexenvironment Fuzzy logic control (FLC) [7ndash9] has the capac-ity to handle uncertain and imprecise information obtainedfrom sensors using linguistic rules The advantages of fuzzysystem are that it does not require precise analytical modelsof environment and it has better real-time performance butits computational complexity increases with the geometricprogression growth of rulesrsquo number Genetic algorithm (GA)[10 11] is a multipoint searching algorithm and it is morelikely to search the global optimal solution in static anddynamic environment However GA suffers from immatureconvergence in complex environment

Artificial immune system (AIS) is an optimization algo-rithm based on the biological immune system It has the fol-lowing features self-organization intelligence recognitionadaptation and self-learning There are lots of researchesinvestigating the interactions between various components ofthe immune system or the overall behaviors of systems basedon an immunological point of view Artificial immune systemmainly includes the following categories

Innate immune-based path planner Deepak et al [12]proposed a motion planner motivated from the biologi-cal innate immune system To actuate a suitable roboticaction one new parameter named as learning rate has beenintroduced The further movement of robot is decided byselecting of a suitable robot predefined task so the robotwill move in sequence until it reaches to its destinationRobot actions are defined as antibodies and environmentalscenarios are defined as antigens The algorithm is simpleand less numerical complex because of very few controllingparameters in this structure

Immune genetic algorithm Chen et al [13] proposeda new method of optimal path planning for mobile robotsbased on immune genetic algorithm with elitism The grid

theory is utilized to establish the free space model of themobile robot in a given environment and a sequence numberis used to identify a grid The initial chromosomes aregenerated with a string of sequence numbers Meanwhilean insertion operator and a deletion operator are defined toensure that each obtained path is continuous and collision-free

Jernersquos idiotypic immune network many researchers uti-lize the equation generated by Farmer et al based on thehypothesis proposed by Jerne (1973) for path planning (1)Immune network model Raza and Fernandez [14] used thedynamic equation of the idiotypic system to perform search-ing and rescuing operation in unstructured environmentTheenvironment is translated into antigen according to the sen-sory arrangement of every robot Antibody stimulation andsuppression are implemented to navigate robots along withthe idiotypic connections to establish interrobot communica-tions Yuan et al [15] proposed an improved artificial immunenetwork strategy based on APF method to avoid absoluterandom transition of antibody and improve the searchingefficiency of immunenetworkThe environment surroundingthe robot is defined as antigen and robot action is defined asantibody respectivelyThe planning results of APFmethod isregarded as prior knowledge and the instruction definitionof new antibody is initialized through vaccine extractionand inoculation (2) Reactive immune network Luh andLiu [16] proposed reactive immune network algorithm formobile robot path planning with data representation forantigens and steering directions for antibodies in the U-shape environment In [16] the resultant force of artificialpotential field is defined as the affinity between antigen andantibody Adaptive virtual target method is used to solve thelocal minima problem of artificial potential field method (3)Mixture of artificial immune algorithm Challoo et al [17]proposed a mixture algorithm based on immune networkand negative selectionThe introduction of negative selectionmakes the system faster to react for certain conditions whichare defined as self-conditions After computing the concen-tration of antibodies there is a reward or a penalty to trainan antibody incrementally The proposed controller providesa principled way for organizing an intelligent robotic systemMoreover implementation of this controller is done in realtime in three different scenarios Ozcelik and Sukumaran [18]used the dynamic equation of the idiotypic system as outputand the concentration of helper T cells as feedback system tocontrol the output The squashing function is performed byawarding or penalizing the antibody based on the antibodythat has the highest priority The highest priority is givento the antibody which perfectly matches to the antigen Theconcentration of helper T cells is used to compute the numberof penalties computing

But the existing artificial immune network algorithmexists as a problem of immature convergence The ability ofoptimizing navigation path is decreased with the decreasingof antibody diversity

Clonal selection algorithm [19ndash26] is a new algorithm ofartificial immune algorithm which is designed based on the

Journal of Control Science and Engineering 3

adaptive immune clonal selection principle and iswidely usedin pattern recognition control optimization multimodaland combination problem

Clonal selection Cortes and Coello [22] introduced anew multiobjective optimization approach based on theclonal selection principle They indicate that the use of anartificial immune system for multiobjective optimization is aviable alternative Huizar et al [24] used the clonal selectionalgorithm to generate optimal or nearly optimal solutionsfor solving combinatorial optimization problems Meng andQiuhong [23] proposed a new artificial immune algorithmbased on the clonal selection theory and the structure of anti-idiotype (IAAI) IAAI is improved to achieve the evolutionof the whole antibody population and the new algorithmhas strong searching capability which makes it reach betterperformance by performing global search and local search inmany directions in the solution space

Monoclonal algorithm Liu et al [25] proposed ImmuneMonoclonal Strategy Algorithm (IMSA) which realizes theglobal optimal computation as well as the local searchAccording to antibody-antigen affinity the algorithm adap-tively adjusts the clonal scale of antibody population More-over it shows that IMSAhas the strong abilities in having highconvergence speed enhancing the diversity of the populationand avoiding the immature convergence to some degreeHowever the algorithm has the problem of weakeninglocal searching ability because of that the local searchingmechanism of the algorithm itself is not perfect and theoptimization function is complicated

Polyclonal algorithm ployclonal is the foundation of thespecific immune response Different from the monoclonalstrategy which has only one or a few antigenic determinantand epitope polyclonal performance at the cellular level isthe structure of extreme diversity of TCR (T cell antigenreceptors) and BCR (B cell antigen receptor) Thereforeit can directly lead to the diversity of antibody networkmemory and specificity Shen andYuan [26] proposed a novelpolyclone particle swarm optimization algorithm (PCPSOA)for mobile robot path planning PCPSOA is characterizedby strong searching ability and quick convergence speedThe simulation results show that the path planning based onPCPSOA is feasible and effective

Immunity polyclonal algorithm is used to solve theimmature convergence problem of artificial immune networkand the local minima problem of artificial potential fieldmethod The proposed polyclonal based artificial immunealgorithm increases diversity of antibodies which tend to thesame extreme value in the solution space of artificial immunenetwork using clonal operator clonal crossover operatorclonal mutation operator and clonal selection operator

3 The Proposed Path Planning Algorithm

31 Graphical Representation of the Proposed Algorithm Inthis paper polyclonal-based artificial immune network (PC-AIN) is used for mobile robot path planning in unknownstatic environment Artificial immune network (AIN) isused to compute concentrations of antibodies Immunity

polyclonal algorithm (IPCA) is used to solve the problemsof immature convergence and local minima The graphicalrepresentation of the proposed path planning system isdepicted in Figure 1

32 Antigen and Antibody Representation Artificial immunenetwork algorithm transforms the actual state of robotand defines antibodies and antigens from the perspectiveof information processing Antigenrsquos epitope is a data setdetected by sensors and provides the information about therelationship among the current positions of robot obstaclesand goal An antigen may have several different epitopeswhich means that an antigen can be recognized by a numberof different antibodies However an antibody can bind onlyone antigenrsquos epitope In this paper a paratope with a built-in robotrsquos steering direction is regarded as antibody Theseantibodiessteering directions are induced by recognitionof the available antigensdetected information It should benoted that only the antibody with highest concentration willbe selected to act on robot according to the immune net-work hypothesis Antigen represents the local environmentsurrounding the robot and its epitope is a data set containingthe azimuth of the goal 120579119892 the distance between obstacles andthe 119895th sensor 119889119895 and the azimuth of sensor 120579119878119895

119860119892119895 equiv 120579119892 119889119895 120579119878119895 119895 = 1 2 119873119878 (1)

where 119873119878 is the number of sensors equally spaced aroundthe base plate of the mobile robot 119889min le 119889119895 le 119889maxParameters 119889min and 119889max represent the nearest and longestdistance measured by the range sensors respectively 120579119878119895 =2120587(119895 minus 1)119873119878 119895 = 1 2 119873119878

In addition the relationship between antibody and steer-ing direction is illustrated as follows

Ab119894 equiv 120579119894 =2120587

119873Ab(119894 minus 1) 119894 = 1 2 119873Ab (2)

where119873Ab is the number of antibodies and 120579119894 is the steeringangle between the moving path and the head orientation ofthemobile robot Note that 0 le 120579119894 le 2120587There is no necessaryrelationship between 119873Ab and 119873119878 since they depend on thehardware of mobile robot Nevertheless simulation resultsshow that better performance could be derived if 119873119878 equalto or larger than119873Ab In this paper119873119878 = 119873Ab = 8

33 Artificial Immune Network Immune response forms adynamic balance network through the interaction betweenantibody and antigen and the interaction between antibodiesWhen antigens invade the body it achieves a new balancethrough the regulation of the immune system Even whenno antigen intrusion it maintains the appropriate intensitythrough mutual stimulation and suppression between anti-bodies and it conforms to the idiotypic network hypothesisIn this paper this reaction mechanism is adopted Thedynamic equation proposed by Farmer et al is employed to


AntigenEpitope

Idiotope

Paratope

Artificial immune networkAntibodiesrsquo concentration space

Some or all individuals tend to the same extreme value

All individuals are different

Clonal operator

Clonal crossover operator

Clonal mutation operator

Clonal selection operator

Antibody with highest concentration

Immunity polyclonal algorithm


Robot

Antibody i + 1Antibody imiddot middot middotmiddot middot middot

middot middot middotmiddot middot middot

middot middot middot


middot middot middot middot middot middot














StimulationSuppression

Antibody i minus 1 Antibody i + 1Antibody i

Antibody i minus 1Antibody i + 1

Antibody i


Figure 1The graphic representation of the proposed path planning system Antigen represents the local environment surrounding the robotAntigenrsquos epitope represents a data set detected by sensors including the azimuth of the goal the distance between obstacles and sensor and theazimuth of sensor Antibody represents robotrsquos steering direction The interaction between antibodies is achieved by idiotope and paratopeOnly the antibody with highest concentration will be selected to act on robot

calculate the variation of antibody concentration as shown inthe following equations

119889119860 119894 (119905)

119889119905= (

119873Ab

sum119895=1

119898st119894119895119886119895 (119905) minus

119873Ab

sum119896=1

119898su119896119894119886119896 (119905) + 119898119894 minus 119896119894)

times 119886119894 (119905)

(3)

119886119894 (119905) =1

1 + exp (05 minus 119860 119894 (119905)) (4)

where 119894 119895 119896 = 0 1 119873Ab are the subscripts to distinguishthe antibody types and119873Ab is the number of antibodies 119886119894 isthe concentration of the 119894th antibody and 119889119860 119894119889119905 is the rateof change of concentration 119898st

119894119895 119898su119896119894indicate the stimulative

and suppressive affinity between the 119894th and the 119895th 119896thantibodies respectively 119898119894 denotes the affinity betweenantigen and the 119894th antibody and 119896119894 represents the naturaldeath coefficient Equation (3) is composed of four termsThe first term shows the stimulative interaction betweenantibodies while the second term depicts the suppressiveinteraction between antibodiesThe third term is the stimulus

from the antigen and the final term is the natural extinctionterm which indicates the dissipation tendency in the absenceof any interaction Equation (4) is a squashing function toensure the stability of the concentration [16]

The affinity between antigen and the 119894th antibody 119898119894is computed using artificial potential field method In theproposed immune network the resultant force of artificialpotential field is defined as119898119894 and the calculating process of119898119894 is illustrated as follows

331 Attractive Force of the 119894th AntibodySteering DirectionConsider

119865goal119894 =10 + cos (120579119894 minus 120579119892)

20 119894 = 1 2 119873Ab

(5)

where 0 le 119865goal119894 le 1 Obviously the attractive force is atits maximal level (119865goal119894 = 1) when the mobile robot goesstraightforward to the goal (120579119894 minus 120579119892 = 0) On the contrary itis minimized (119865goal119894 = 0) when the robotrsquos steering directionis the opposite of the goal (120579119894 minus 120579119892 = 120587)


332 Repulsive Force of the 119894th AntibodySteering DirectionConsider

119865obs119894 =

119873119878

sum119895=1

120572119894119895119889119895 (6)

where 120572119894119895 = exp(minus119873119878 times (1 minus 120575119894119895)) and 120575119894119895 = (1 + cos(120579119894 minus120579119878119895))2 Parameter 120572119894119895 indicates the weighting ratio for the 119895thsensor to steering angle 120579119894 while119889119895 represents the normalizeddistance between the 119895th sensor and obstacles Coefficient 120575119894119895expresses influence and importance of each sensor at differentlocations 119889119895 is fuzzified using the fuzzy set definitionsThreefuzzy if-then rules are defined to compute 119889119895

if 119889119895 is 119904 then119910 = 1198711

if119889119895 is119898 then119910 = 1198712

if119889119895 is119889 then119910 = 1198713

(7)

where 1198711 1198712 and 1198713 are defined as 025 05 and 10respectively The input variable of each rule is the detecteddistance 119889119895 of the 119895th sensor s m and d represent 119904119886119891119890119898119890119889119894119906119898 and 119889119886119899119892119890119903 respectivelyThemembership functionof s m and d are defined as (8) (9) and (10) respectively

120583119904 =

0 119889119895 le 119889119898

119889119895 minus 119889119898

119889max minus 119889119898 119889119898 lt 119889119895 le 119889max

1 119889119895 gt 119889max

(8)

120583119898 =

0 119889119895 le 119889min119889119895 minus 119889min

119889119898 minus 119889min 119889min lt 119889119895 le 119889119898

119889max minus 119889119895


0 119889119895 gt 119889max

(9)

120583119889 =

1 119889119895 le 119889min119889119898 minus 119889119895


0 119889119895 gt 119889119898

(10)

The normalized distance between 119895th sensor and obsta-cles 119889119895 is computed as (11)

119889119895 =120583119904 times 1198711 + 120583119898 times 1198712 + 120583119889 times 1198713

120583119904 + 120583119898 + 120583119889 (11)

333 Resultant Force of the 119894th AntibodySteering DirectionConsider

119898119894 = 1205961119865goal119894 + 1205962119865obs119894 119894 = 1 2 119873Ab (12)

where parameters1205961 1205962 indicate the weighting ratio betweenattractive and repulsive forces 0 le 1205961 1205962 le 1 1205961 + 1205962 = 1

The stimulative and suppressive affinity between anti-bodies are combined and the stimulative-suppressive affinitybetween antibodies119898ss

119894119897is defined as (13)

119898ss119894119897= 119898

st119894119897minus 119898

su119897119894= cos (120579119894 minus 120579119897) = cos (Δ120579119894119897)

119894 119897 = 1 2 119873Ab(13)

Obviously stimulative-suppressive effect is positive(119898ss119894119897gt 0) if 0 lt Δ120579119894119897 lt 1205872 or 31205872 lt Δ120579119894119897 lt 2120587 On the

contrary stimulative-suppressive effect is negative (119898ss119894119897lt 0)

if 1205872 lt Δ120579119894119897 lt 31205872 In addition there is no any neteffect between orthogonal antibodies (ie Δ120579119894119897 = 1205872 orΔ120579119894119897 = 31205872)

Equations (3) and (4) are discretized

119860 119894 (119899 + 1) = 119860 119894 (119899)

+ (

119873Ab

sum119895=1

119898st119894119895119886119895 (119899) minus

119873Ab

sum119896=1

119898su119896119894119886119896 (119899) + 119898119894 minus 119896119894)

times 119886119894 (119899)

119886119894 (119899 + 1) =1

1 + exp (05 minus 119860 119894 (119899 + 1))

(14)

where 119899 is the initial time at every step and 119899+1 is the currenttime at every step

34 Immunity Polyclonal Algorithm Artificial immune net-work exists as a problem of immature convergence whichsome or all individuals in the solution space tend to thesame extreme value and robot will stop moving or movewith wrong direction From the view of biology the reasonof immature convergence problem is that the antibody con-centration increases exponentially and someor all individualstend to the same extreme value so the diversity of antibodyis decreased and one antigenrsquos epitope can be recognized byseveral antibodies at the same time The phenomenon doesnot conform with the biological immune theory which oneepitope can only be identified by one antibody Specific tothe process of mobile robot path planning the normalizeddistance between sensor and obstacles reaches the maximumvalue 1 when the distance between robot and obstacles is lessthan the risk threshold and concentrations of some or allantibodies tend to the same extreme value Robot selects theantibody with highest concentration to act on at every stepbut at the above situation the moving probabilities towardcertain directions are equal and the robot has multipleoptimal solutions at this point So the robot will act wrongly

Artificial potential field method is applied to computeparameter in artificial immune network so artificial immunenetwork exists as a problem of local minima Attractive forceand repulsive force have effect on robot and there are somepoints which balance the attractive force and repulsive forceso the resultant force is zero at these points It is the causeof local minima More densely obstacles and more repulsiveforces act on robot so greater danger of local minima When


the robot traps in local minima robot will shock or stop atthis point and this phenomenon is known as ldquodead lockrdquo

When the problems of immature convergence and localminima appear in the process of mobile robot path planningrobot periodically wanders around at the point and cannotreach the goal successfully In this paper immunity polyclonalalgorithm is utilized to solve the above two problems

The essence of immunity polyclonal algorithm is creatinga new subpopulation based on the value of affinity around thecandidate solution in the generation of evolution and expand-ing the searching scope Meanwhile immunity polyclonalalgorithm implements the exchange of information betweenpopulations and increases the diversity of antibodies Inother words polyclonal transforms the problem from a lowdimensional space into a high dimensional space and thenmaps the result into the low dimensional space

The antigen of immunity polyclonal algorithm corre-sponds to the objective function of optimal problem andvarious constraints the antibody corresponds to the optimalsolution and the affinity between antigen and antibodycorresponds to the matching degree of objective functionand homographic solution In this paper the antigen corre-sponds to the local environmental information the antibodycorresponds to the individuals tending to the same extremevalue in solution space of artificial immune network and theaffinity between antigen and antibody corresponds to 119898119894 ofartificial immune network

Assuming the initial antibody population A =

1198881 1198882 119888119899 119899 is the size of initial antibody populationand 119888119894 is the concentration of 119894th antibody which is one ofindividuals tending to the same extreme value in the solutionspace of artificial immune network Polyclonal operatordivided the point 119888119894 isin A into 119902119894 same points 1198881015840

119894isin A1015840 and

then getting the new antibody population through clonaloperator clonal crossover operator clonal mutation operatorand clonal selection operator Polyclonal operator can bedescribed as follows

341 Clonal Operator Defined as

Θ (A) = [Θ (1198881) Θ (1198882) Θ (119888119899)]119879 (15)

where Θ(119888119894) = I119894 times 119888119894 119894 = 1 2 119899 and I119894 is a 119902119894-dimensionalvector

Generally

119902119894 = Int(119873 times119898(119888119894)

sum119899

119895=1119898(119888119895)

) 119894 = 1 2 119899 (16)

119873 gt 119899 is a given value related to the clonal scale andInt (119909) rounds the argument 119909 toward the least integergreater than 119909 119898(119888119894) is the affinity between antigen andantibody 119902119894 is used to reflect the clonal scale of antibodyTheprevious equation implies that every antibody will be viewedlocally and has its clonal scale different from the other onesAfter cloning the initial antibody population becomes thefollowing population

B = AA10158401A10158402 A1015840

119899 (17)

where

A1015840119894= 1198881198941 1198881198942 119888119894119902119894minus1 (18)

where 119888119894119895 = 119888119894 119895 = 1 2 119902119894 minus 1The range of clonal scale is [10 100]The bigger the clonal

scale the more time complexity of the algorithm In thispaper the affinity between antigen and every antibody issame so every antibodyrsquos clonal scale is same Clonal scaleof every antibody is119873119888 = 119873 times 119861 = 40 119861 is clonal coefficientand 0 lt 119861 lt 1 119861 = 0125119873 = 320

342 Clonal Crossover Operator Crossover selects two indi-viduals from the population by the larger probability andexchanges one or some components of two individualsCrossover guarantees the search of solution space will nottrap into immature convergence because of high fitnessindividuals and makes the search stronger

Clonal crossover operator maintains the information ofinitial population and does not act on A isin A1015840 The followingcrossover method is adopted Considering two antibodies119888119894 = 1199091 1199092 119909119873119888 and 119888119895 = 1199101 1199102 119910119873119888 the 1199041thcomponent is selected as crossover point namely

119879119862

119888(119888119894 119888119895) = 1199091 1199091199041 1199101 1199101199042

1199041 + 1199042 = 119873119888 119888119894 isin A1015840 119888119895 isin A1015840(19)

The range of crossover probability values are [05 099]In this paper the crossover probability is 119875119888 = 08

343 Clonal Mutation Operator Clonal mutation operatorchanges some genes in the group list of population and theexchange is to put negation of some genetic value that is0 rarr 1 or 1 rarr 0 The specific step is described as followsthe clonal mutation probability 119875119898 and every gene of the pathproduce a random number 119877 isin [0 1] if 119875119898 ge 119877 the geneproduces mutation (0 rarr 1 or 1 rarr 0)

The range of mutation probability values are [001 005]In this paper the mutation probability is 119875119898 = 003

344 Clonal Selection Operator For all 119894 = 1 2 119899 ifthere is a mutated antibody 119887 such that 119898(119887) = max119898(119888119894)satisfying the following

119898(119888119894) lt 119898 (119887) 119888119894 isin A1015840 (20)

then 119887 replaces 119888119894 in the antibody populationIn this paper immunity polyclonal algorithm increases

the diversity of antibodies which tend to the same extremevalue and selects the antibody with highest concentration asthe final antibodysteering direction Thus it overcomes theproblems of immature convergence and local minima

4 Simulation and Discussions

Some experiments are carried out for validating the proposedalgorithm using MATLAB 2011 (a) GUI The initial positionof robot goal and obstacles get randomly in experimental


environment Assume robot has eight uniformly distributeddistance sensors (119873119878 = 8) and eight moving directions(119873Ab = 8) including forward left right back forward leftforward right back left and back right Experimental envi-ronment is 20 times 20m obstacles are expressed with blacksquare and the size of obstacles is 1 times 1m

41 PC-AIN Comparison with AIN

411 PC-AIN Improves Immature Convergence Problem ofAIN Artificial immune network (AIN) for mobile robotpath planning exists as an immature convergence problembecause some or all individuals in the solution space tendto the same extreme value In this case the robot will stopmoving or move with wrong direction

Experimental environment sets are as follows the initialposition of robot (98) the goal position (816) and thevelocity of robot is 01ms In Figures 2(a) and 2(b) artificialimmune network is utilized for mobile robot path planningThere exists a condition that some or all individuals in thesolution space of AIN tend to the same extreme value asshown in Figure 2(a) At this point robot randomly selectsone of the directions to move because the moving proba-bilities toward several directions are equal If this conditioncannot improved effectively robotwill collidewith obstacle asshown in Figure 2(b) and path planning fails at this timeThesituation that some or all individuals in solution space tend tothe same extreme value appeared and robotrsquos path is shownin Figure 2(b) expressed by black circle and the selectedantibody at every step when some or all concentrations insolution space tend to the same extreme value is shown inFigure 2(d) expressed by red ldquolowastrdquo

Immunity polyclonal algorithm increases the diversity ofantibodies which tend to the same extreme value in the solu-tion space of AIN through clonal operator clonal crossoveroperator clonal mutation operator and clonal selectionoperator In polyclonal-based artificial immunenetwork (PC-AIN) for mobile robot path planning robot will move withthe optimal direction at every step and get optimal pathfinally Figure 2(c) shows polyclonal-based artificial immunenetwork algorithm for mobile robot path planning under theexperimental environment in Figure 2(a) The black circlerepresents the path when some or all individuals tend to thesame extreme value in solution space of AIN and the selectedantibody at every step during this path is shown in Figure 2(d)expressed by black ldquolowastrdquo From Figure 2(c) it can be seenthat polyclonal-based artificial immune network (PC-AIN)solves the problem of immature convergence with increasingdiversity of antibodies and robot successfully reaches the goalin this condition

Based on Figure 2 the selected antibody when some orall individuals tend to the same extreme value in solutionspace of AIN and PC-AIN is shown in Figure 2(d) It can beseen that artificial immune network (AIN) cannot effectivelyselect the antibody with highest concentration and robottraps into immature convergence problem when some or allindividuals tend to the same extreme value in concentrationsolution space while polyclonal-based artificial immune

Table 1 Performance comparison of AIN and PC-AIN

Algorithm PC-AIN AINRunning time(s) 637 813Steps of path planning 157 227

network (PC-AIN) successfully selects the antibodysteeringdirection with highest concentration and solves the problemof immature convergence with increasing the diversity ofantibodies and robot successfully reaches the goal

412 Performance Comparison of AIN and PC-AIN Exper-imental environment sets are as follows the initial positionof robot (5 4) the goal position (10 16) the number ofobstacles are 5 the obstacles position (9 10) (7 6) (5 8)(8 13) and (6 12) respectively The velocity is 01msAIN and PC-AIN for mobile robot path planning is in theabove environment Table 1 is the results of performancecomparison formobile robot path planning betweenAIN andPC-AIN The performance involves steps of path planningand running time from the initial position to the goalFrom the property of running time it can be seen that therunning time of PC-AIN is less than the running time of AINfor the same operating environment Meanwhile from thecomparison of steps the length of PC-AIN is shorter thanthe length of AIN AIN and PC-AIN for mobile robot pathplanning are shown in Figures 3(a) and 3(b) respectively

From the above comparison it can be seen that thepolyclonal-based artificial immune network algorithm solvesthe problem of immature convergence with increasing thediversity of antibodies which tend to the same extremevalue and it has better optimal ability than artificial immunenetwork

42 Local Minima A series of experiments are performed tocompare the behavior of the proposed algorithmwith reactiveimmune network [16] in solving the problemof localminimaExperimental environment sets are as follows robotrsquos initialposition (3 8) goalrsquos initial position (12 11) and obstaclesrsquoposition (9 10) (7 11) (5 8) and (12 8)The velocity is 01msand 119905 = 1 s

421 Reactive Immune Network Virtual target method isused to solve local minima problem in reactive immune net-work (RIN) Robot moves to the goal under the interactionfrom virtual target original goal and obstacles Revokingthe virtual target until the robot is out of the local minimaproblem and then the robot moves to the original goalunder the interaction from original goal and obstaclesWhenrobot meets local minima again it creates virtual target untilreaching the goal

In the above experimental environment reactive immunenetwork (RIN) is utilized for mobile robot path planning andthe simulation result is shown in Figure 4(a)

422 Polyclonal-Based Artificial Immune NetworkPolyclonal-based artificial immune network effectively


0 5 10 15 200

5

10

15

20

Start

End

Obstacles

X (m)

Y(m

)

(a) Some or all individuals tend to the same extreme value

Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)

(b) Robot moves wrongly with AIN

Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)

(c) PC-AIN for path planning

110 120 130 140 150 160 170 1804

45

5

55

6

65

7

75

8

Step

Sele

cted

antib

ody

PC-AINAIN

(d) The selected antibody of AIN and PC-AIN at every step

Figure 2 Mobile robot path planning with AIN and PC-AIN

solves the problem of local minima caused by artificialpotential field during the structure of parameter in artificialimmune network through ployclonal operator Under theabove environment PC-AIN solves the problem of localminima and the path planning is shown in Figure 4(b)

Figure 5 shows the comparison of steps from the initialposition to the goal with reactive immune network andpolyclonal-based artificial immune network Figure 5 showsthat path length of PC-AIN is less than the path length of RINfor mobile robot path planning when the robot traps in localminima problem under the same experimental environment

43 Robotrsquos Moving Velocity Impact on the Convergence RateRobotrsquos experimental environment is the same as Figure 3where 119905 = 1 s When the robot moves at different velocity

the convergence rate of the algorithm is different Whenthe velocity within a certain range robotrsquos convergence rateincreases with rising of the velocity While when the velocitybeyond a certain range robotrsquos convergence rate decreaseswith increasing of the velocity

As shown in Figure 6 the robot moves at differentvelocities 005ms 01ms 015ms 02ms 025ms and03ms respectively With different velocities robot hasdifferent running steps and different convergence rate Theresult shows that when the velocity is less than 025ms stepsused reaching the goal are reduced and convergence rateis increased with rising of velocity While when the robotrsquosvelocity is 025ms steps of robot for path planning aregreater than the steps with the speed of 02ms and 015msandwhen the robotrsquos velocity is 03ms steps of robot for path


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)

(a) Path planning with AIN

Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)

(b) Path planning with PC-AIN


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)

(a) Path planning with RIN

Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)


Figure 4 Mobile robot path planning with RIN and PC-AIN

planning are greater than the steps with the speed of 02msSo robotrsquos convergence rate does not increase with rising ofvelocity

Accordingly the velocity of robot is not faster or better inmobile robot path planning and the velocity has certain limi-tations Selecting a proper velocity increases the convergencerate for mobile robot path planning

44 The Interaction between Antibodies This experiment ismainly used for validating stimulative affinity and suppressiveaffinity between antibodies and expounding the antibodydoes not exist in the body independently Figure 7 shows theaffinity between antibody 1 and other antibodies

There are eight antibodies in the experiment affinitybetween antibody 1 and other antibodies expressed by red

ldquolowastrdquo in Figure 7 The other antibodies have stimulative affinityimpact on antibody 1 if the affinity is greater than zeroand the other antibodies have suppressive affinity impact onantibody 1 if the affinity is less than zero And the antibody 1has the maximum stimulative affinity impact on antibody 1The results correspond to (13) Stimulative-suppressive effectis positive if 0 lt Δ120579119894119897 lt 1205872 or 31205872 lt Δ120579119894119897 lt 2120587 andstimulative-suppressive effect is negative if 1205872 lt Δ120579119894119897 lt

31205872 The interaction between antibodies has a great impacton the immune network

45 Analysis of Time Complexity Polyclonal-based artificialimmune network optimizes the path planning and speeds upthe convergence rate Meanwhile it also solves the problemsof immature convergence and local minima but itrsquos time


0 50 100 150 2000

2

4

6

8

10

Step

Dist

ance

bet

wee

n ro

bot a

nd g

oal (

m)

PC-AINRIN

Figure 5 Path planning comparison of RIN and PC-AIN

0 50 100 150 200 250 300 350 4000

2

4

6

8

10

12

14

Step

Dist

ance

bet

wee

n ro

bot a

nd g

oal (

m)

Vel 005 msVel 01 msVel 015 ms


Figure 6 Moving velocity impact on convergence rate

complexity of each generation increases because of the useof clonal operator clonal crossover operator clonal mutationoperator and clonal selection operator

Assuming that 119899 is the size of antibody population 119873 gt

119899 is a given value related to the clonal scale and 119873119888 isevery antibodyrsquos clone scale In this paper 119873119888 = 5119899 Atevery generation of evolution the worst time complexityof clonal operator is 119874(119899119873119888) the worst time complexity ofclonal crossover operator is119874(119873) the worst time complexityof clonal mutation operator is 119874(119873) and the worst timecomplexity of clonal selection operator is 119874(119873 + 119899) So

1 2 3 4 5 6 7 8

0

05

1

Antibody

Affi

nity

of a

ntib

ody

and

antib

ody

minus05

minus1

Figure 7 Affinity variation of antibody 1 with other antibodies

x

y

2rL

R

120579

Robotdw

Y

X

Figure 8 Differential drive mobile robot

the worst time complexity of the proposed algorithm in thegeneration is computed as follows

119874 (119899119873119888) + 119874 (119873) + 119874 (119873) + 119874 (119873 + 119899)

= 119874 (119899119873119888 + 3119873 + 119899)

= 119874 (119899 sdot 5119899 +3119899 sdot 119873119888 + 119899)

= 119874 (51198992+3119899 sdot 5119899 + 119899)

= 119874 (51198992+ 15119899

2+ 119899)

= 119874 (201198992+ 119899)

(21)

So the worst time complexity of the proposed algorithmin the generation is 119874(1198992)

46 Real-Time Simulation In this experimental amigo isused to validate the proposed algorithm and programminglanguages used are MATLAB and C++ The system mainlyconsists of the following parts host computer vision systemamigo with an on-board PC and wireless EthernetThe cam-era is used to get the environmental information includingobstacles and goal in this systemMATLAB is used to execute


(a)

Start

(b)

(c) (d)

(e) (f)Target

Figure 9 Barrier wall

the path planning algorithm and C++ is used to control themotion of robotThehost computer controls the on-board PCthrough wireless Ethernet

The robot is a differential drive two-wheeled mobilerobot In Cartesian coordinates the pose velocity andangular of differential drive two-wheeledmobile robot can bedescribed as (22) [27]

[

[

119909

119910

120579

]

]

= [

[

cos 120579 0

sin 120579 0

0 1

]

]

[V120596] (22)

where V is the robot translation velocity and 120596 is the robotrotation velocity defined as (23)

120596 =V119877 minus V119871119889119908

V =V119877 + V119871

2 (23)

V119877 and V119871 are right and left wheels translation velocities ofrobot respectively and 119889119908 is the distance between twowheelscenters as shown in Figure 8

In this paper polyclonal-based artificial immune networkis used to get the pose of robot At real environment twowheels velocities are computed through robot pose

Assuming Δ119878119877 and Δ119878119871 are the displacement of right andleft wheels during Δ119905 so

Δ119909 =Δ119878119871 + Δ119878119877

2times cos 120579

Δ119910 =Δ119878119871 + Δ119878119877

2times sin 120579

Δ120579 =Δ119878119877 minus Δ119878119871

119887

(24)

Based on (24) the displacement of right and left wheels iscomputed as follows

Δ119878119877 =Δ119909

cos 120579+119889119908Δ120579

2 cos 120579 = 0

Δ119878119871 =Δ119909

cos 120579minus119889119908Δ120579

2 cos 120579 = 0

(25)


(a)

Start

(b)

(c) (d)

(e) (f)Target

Figure 10 Complex environment

or

Δ119878119877 =Δ119910

sin 120579+119889119908Δ120579

2 sin 120579 = 0

Δ119878119871 =Δ119910

sin 120579minus119889119908Δ120579

2 sin 120579 = 0

(26)

From (25) and (26) left and right wheels velocities arecomputed

The proposed algorithm is validated at the followingscenarios as shown in Figures 9 and 10 Figure 9 is a barrierwall and Figure 10 is a complex environment Robot reachesthe target successfully at the previous scenarios

5 Conclusion

This paper deals with a polyclonal-based artificial immunenetwork algorithm for mobile robot path planning inunknown static environment This algorithm overcomes theimmature convergence problem of artificial immune network

and local minima problem of artificial potential field withincreasing diversity of antibodies which tend to the sameextreme value in solution space Different simulated testscenarios are conducted to test the performance of theproposed algorithm Simulation results validate the flexibil-ity efficiency and effectiveness of the robot path planningarchitecture especially the immature convergence and localminima problem Meanwhile some real-time experimentsvalidate the implementability of the proposed algorithm

Conflict of Interests

The authors declare that they have no conflict of interests

Acknowledgments

This project was supported by the National Natural Sci-ence Foundation of China (nos 61075091 61105100 and61240052) the Natural Science Foundation of Shandong


Province China (no ZR2012FM036) and the Indepen-dent Innovation Foundation of Shandong University (nos2011JC011 and 2012JC005)

References

[1] X Ma Y Xu G-Q Sun L-X Deng and Y-B Li ldquoState-chainsequential feedback reinforcement learning for path planningof autonomous mobile robotsrdquo Journal of Zhejiang UniversityScience C vol 14 no 3 pp 167ndash178 2013

[2] R Abiyev D Ibrahim andB Erin ldquoNavigation ofmobile robotsin the presence of obstaclesrdquo Advances in Engineering Softwarevol 41 no 10-11 pp 1179ndash1186 2010

[3] Q Zhang D Chen and T Chen ldquoAn obstacle avoidancemethod of soccer robot based on evolutionary artificial poten-tial fieldrdquo Journal of Energy Procedia vol 16 pp 1792ndash1798 2012

[4] R A F Romero E PrestesM A P Idiart andG Faria ldquoLocallyoriented potential field for controllingmulti-robotsrdquoCommuni-cations in Nonlinear Science and Numerical Simulation vol 17no 12 pp 4664ndash4671 2012

[5] M A Kareem Jaradat M Al-Rousan and L Quadan ldquoRein-forcement based mobile robot navigation in dynamic environ-mentrdquo Robotics and Computer-Integrated Manufacturing vol27 no 1 pp 135ndash149 2011

[6] N Navarro-Guerrero C Weber P Schroeter and S WermterldquoReal-world reinforcement learning for autonomous humanoidrobot dockingrdquo Journal of Robotics and Autonomous Systemsvol 60 pp 1400ndash1407 2012

[7] O Motlagh S H Tang N Ismail and A R Ramli ldquoAn expertfuzzy cognitive map for reactive navigation of mobile robotsrdquoJournal of Fuzzy Sets and Systems vol 201 pp 105ndash121 2012

[8] M T Ibrahim D Hanafi and R Ghoni ldquoAutonomous naviga-tion for a dynamical hexapod robot using fuzzy logic controllerrdquoJournal of Procedia Engineering vol 38 pp 330ndash341 2012

[9] O Castillo R Martınez-Marroquın P Melin F Valdez and JSoria ldquoComparative study of bio-inspired algorithms applied tothe optimization of type-1 and type-2 fuzzy controllers for anautonomous mobile robotrdquo Journal of Information Sciences vol192 pp 19ndash38 2012

[10] A Tuncer and M Yildirim ldquoDynamic path planning of mobilerobots with improved genetic algorithmrdquo Journal of Computersand Electrical Engineering vol 38 pp 1564ndash1572 2012

[11] M Aly and A Abbas ldquoSimulation of obstacles effect on indus-trial robots working space using genetic algorithmrdquo Journal ofKing Saud UniversitymdashEngineering Sciences 2013

[12] B Deepak D R Parhi and S Kundu ldquoInnate immune basedpath planner of an autonomous mobile robotrdquo Journal ofProcedia Engineering vol 38 pp 2663ndash2671 2012

[13] X Chen G-Z Tan and B Jiang ldquoReal-time optimal path plan-ning for mobile robots based on immune genetic algorithmrdquoJournal of Central South University (Science and Technology)vol 39 no 3 pp 577ndash583 2008

[14] A Raza and B R Fernandez ldquoImmuno-inspired heterogeneousmobile robotic systemsrdquo in Proceedings of the 49th IEEEConference on Decision and Control (CDC rsquo10) pp 7178ndash7183December 2010

[15] M Yuan S-A Wang C Wu and N Chen ldquoA novel immunenetwork strategy for robot path planning in complicated envi-ronmentsrdquo Journal of Intelligent amp Robotic Systems vol 60 no1 pp 111ndash131 2010

[16] G-C Luh and W-W Liu ldquoAn immunological approach tomobile robot reactive navigationrdquo Applied Soft ComputingJournal vol 8 no 1 pp 30ndash45 2008

[17] R Challoo P Rao S Ozcelik L Challoo and S Li ldquoNavigationcontrol and path mapping of a mobile robot using artificialimmune systemsrdquo Journal of Robotics and Automation vol 1no 1 pp 1ndash25 2010

[18] S Ozcelik and S Sukumaran ldquoImplementation of an artificialimmune system on a mobile robotrdquo Journal of Procedia Com-puter Science vol 6 pp 317ndash322 2011

[19] T Bonaci P Lee L Bushnell and R Poovendran ldquoA convexoptimization approach for clone detection in wireless sensornetworksrdquo Journal of Pervasive and Mobile Computing vol 9no 4 pp 528ndash545 2013

[20] LNDeCastro andF J VonZuben ldquoLearning andoptimizationusing the clonal selection principlerdquo IEEE Transactions onEvolutionary Computation vol 6 no 3 pp 239ndash251 2002

[21] J Chen andMMahfouf ldquoA population adaptive based immunealgorithm for solving multi-objective optimization problemsrdquoin Proceedings of the International Symposium on ArtificialImmune Systems pp 280ndash293 Springer 2006

[22] N C Cortes and C A C Coello ldquoMultiobjective optimizationusing ideas from the clonal selection principlerdquo in Proceedingsof the International Symposium on Genetic and EvolutionaryComputation pp 158ndash170 2003

[23] G Meng and C Qiuhong ldquoA new immune algorithm and itsapplicationrdquo WSEAS Transactions on Computers vol 9 no 1pp 72ndash82 2010

[24] CHuizarOMontiel-Ross R Sepulveda and F J DDelgadilloldquoPath planning using clonal selection algorithmrdquo in Proceedingsof the International SymposiumonHybrid Intelligent Systems pp303ndash312 Springer 2013

[25] R-C Liu H-F Du and L-C Jiao ldquoAn immune monoclonalstrategy algorithmrdquo Acta Electronica Sinica vol 32 no 11 pp1880ndash1884 2004

[26] Y Shen and M Yuan ldquoA novel poly-clone particle swarmoptimization algorithm and its application inmobile robot pathplanningrdquo in Proceedings of the Chinese Control and DecisionConference (CCDC rsquo10) pp 2271ndash2276 May 2010

[27] S-W Yu and W-J Yan ldquoDesign of low-level motion controllerfor a two-wheel mobile mini-robotrdquo Journal of Mechanical andElectrical Engineering Magazine vol 23 no 9 pp 38ndash46 2006

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



artificial immune network Experimental results show thatthe proposedmethod effectively optimizes path planning andimproves the performance of path planning

The remainder of this paper is organized as follows Thenext section discusses related works for autonomous mobilerobot path planning in unknown complex environmentSection 3 presents the proposed mobile robot path planningalgorithm in detail Simulation results and real-time experi-ments are presented in Section 4 Finally Section 5 concludesthe paper

2 The Related Works

Local path planning in unknown complex environment is ahot research topic in recent years Artificial potential field-based path planning algorithm [3 4] utilizes the attractiveforce from goals and the repulsive force from obstacles formobile robot path planning This method is known for itsmathematical simplicity and little computation but it suffersfrom a problem of local minima Many artificial intelligenttechniques have been proposed by scholars for mobile robotpath planning such as reinforcement learning fuzzy logicand genetic algorithm Reinforcement learning algorithm [15 6] has simple and complete theory but it is mostly usedin static environment because its infinite state in complexenvironment Fuzzy logic control (FLC) [7ndash9] has the capac-ity to handle uncertain and imprecise information obtainedfrom sensors using linguistic rules The advantages of fuzzysystem are that it does not require precise analytical modelsof environment and it has better real-time performance butits computational complexity increases with the geometricprogression growth of rulesrsquo number Genetic algorithm (GA)[10 11] is a multipoint searching algorithm and it is morelikely to search the global optimal solution in static anddynamic environment However GA suffers from immatureconvergence in complex environment

Artificial immune system (AIS) is an optimization algo-rithm based on the biological immune system It has the fol-lowing features self-organization intelligence recognitionadaptation and self-learning There are lots of researchesinvestigating the interactions between various components ofthe immune system or the overall behaviors of systems basedon an immunological point of view Artificial immune systemmainly includes the following categories

Innate immune-based path planner Deepak et al [12]proposed a motion planner motivated from the biologi-cal innate immune system To actuate a suitable roboticaction one new parameter named as learning rate has beenintroduced The further movement of robot is decided byselecting of a suitable robot predefined task so the robotwill move in sequence until it reaches to its destinationRobot actions are defined as antibodies and environmentalscenarios are defined as antigens The algorithm is simpleand less numerical complex because of very few controllingparameters in this structure

Immune genetic algorithm Chen et al [13] proposeda new method of optimal path planning for mobile robotsbased on immune genetic algorithm with elitism The grid

theory is utilized to establish the free space model of themobile robot in a given environment and a sequence numberis used to identify a grid The initial chromosomes aregenerated with a string of sequence numbers Meanwhilean insertion operator and a deletion operator are defined toensure that each obtained path is continuous and collision-free

Jernersquos idiotypic immune network many researchers uti-lize the equation generated by Farmer et al based on thehypothesis proposed by Jerne (1973) for path planning (1)Immune network model Raza and Fernandez [14] used thedynamic equation of the idiotypic system to perform search-ing and rescuing operation in unstructured environmentTheenvironment is translated into antigen according to the sen-sory arrangement of every robot Antibody stimulation andsuppression are implemented to navigate robots along withthe idiotypic connections to establish interrobot communica-tions Yuan et al [15] proposed an improved artificial immunenetwork strategy based on APF method to avoid absoluterandom transition of antibody and improve the searchingefficiency of immunenetworkThe environment surroundingthe robot is defined as antigen and robot action is defined asantibody respectivelyThe planning results of APFmethod isregarded as prior knowledge and the instruction definitionof new antibody is initialized through vaccine extractionand inoculation (2) Reactive immune network Luh andLiu [16] proposed reactive immune network algorithm formobile robot path planning with data representation forantigens and steering directions for antibodies in the U-shape environment In [16] the resultant force of artificialpotential field is defined as the affinity between antigen andantibody Adaptive virtual target method is used to solve thelocal minima problem of artificial potential field method (3)Mixture of artificial immune algorithm Challoo et al [17]proposed a mixture algorithm based on immune networkand negative selectionThe introduction of negative selectionmakes the system faster to react for certain conditions whichare defined as self-conditions After computing the concen-tration of antibodies there is a reward or a penalty to trainan antibody incrementally The proposed controller providesa principled way for organizing an intelligent robotic systemMoreover implementation of this controller is done in realtime in three different scenarios Ozcelik and Sukumaran [18]used the dynamic equation of the idiotypic system as outputand the concentration of helper T cells as feedback system tocontrol the output The squashing function is performed byawarding or penalizing the antibody based on the antibodythat has the highest priority The highest priority is givento the antibody which perfectly matches to the antigen Theconcentration of helper T cells is used to compute the numberof penalties computing

But the existing artificial immune network algorithmexists as a problem of immature convergence The ability ofoptimizing navigation path is decreased with the decreasingof antibody diversity

Clonal selection algorithm [19ndash26] is a new algorithm ofartificial immune algorithm which is designed based on the











119860119892119895 equiv 120579119892 119889119895 120579119878119895 119895 = 1 2 119873119878 (1)



Ab119894 equiv 120579119894 =2120587

119873Ab(119894 minus 1) 119894 = 1 2 119873Ab (2)




AntigenEpitope

Idiotope

Paratope




Clonal operator







Robot






















Antibody i




119889119860 119894 (119905)

119889119905= (

119873Ab

sum119895=1

119898st119894119895119886119895 (119905) minus

119873Ab

sum119896=1

119898su119896119894119886119896 (119905) + 119898119894 minus 119896119894)

times 119886119894 (119905)

(3)

119886119894 (119905) =1

1 + exp (05 minus 119860 119894 (119905)) (4)







119865goal119894 =10 + cos (120579119894 minus 120579119892)

20 119894 = 1 2 119873Ab

(5)




119865obs119894 =

119873119878

sum119895=1

120572119894119895119889119895 (6)


if 119889119895 is 119904 then119910 = 1198711

if119889119895 is119898 then119910 = 1198712

if119889119895 is119889 then119910 = 1198713

(7)


120583119904 =

0 119889119895 le 119889119898

119889119895 minus 119889119898


1 119889119895 gt 119889max

(8)

120583119898 =

0 119889119895 le 119889min119889119895 minus 119889min


119889max minus 119889119895


0 119889119895 gt 119889max

(9)

120583119889 =

1 119889119895 le 119889min119889119898 minus 119889119895


0 119889119895 gt 119889119898

(10)



120583119904 + 120583119898 + 120583119889 (11)


119898119894 = 1205961119865goal119894 + 1205962119865obs119894 119894 = 1 2 119873Ab (12)



119894119897is defined as (13)

119898ss119894119897= 119898

st119894119897minus 119898

su119897119894= cos (120579119894 minus 120579119897) = cos (Δ120579119894119897)

119894 119897 = 1 2 119873Ab(13)





119860 119894 (119899 + 1) = 119860 119894 (119899)

+ (

119873Ab

sum119895=1

119898st119894119895119886119895 (119899) minus

119873Ab

sum119896=1

119898su119896119894119886119896 (119899) + 119898119894 minus 119896119894)

times 119886119894 (119899)

119886119894 (119899 + 1) =1

1 + exp (05 minus 119860 119894 (119899 + 1))

(14)











119894isin A1015840 and



Θ (A) = [Θ (1198881) Θ (1198882) Θ (119888119899)]119879 (15)


Generally

119902119894 = Int(119873 times119898(119888119894)

sum119899

119895=1119898(119888119895)

) 119894 = 1 2 119899 (16)


B = AA10158401A10158402 A1015840

119899 (17)

where

A1015840119894= 1198881198941 1198881198942 119888119894119902119894minus1 (18)





119879119862

119888(119888119894 119888119895) = 1199091 1199091199041 1199101 1199101199042

1199041 + 1199042 = 119873119888 119888119894 isin A1015840 119888119895 isin A1015840(19)





119898(119888119894) lt 119898 (119887) 119888119894 isin A1015840 (20)






















0 5 10 15 200

5

10

15

20

Start

End

Obstacles

X (m)

Y(m

)


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)


110 120 130 140 150 160 170 1804

45

5

55

6

65

7

75

8

Step

Sele

cted

antib

ody

PC-AINAIN









Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)



Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)











0 50 100 150 2000

2

4

6

8

10

Step

Dist

ance

bet

wee

n ro

bot a

nd g

oal (

m)

PC-AINRIN


0 50 100 150 200 250 300 350 4000

2

4

6

8

10

12

14

Step

Dist

ance

bet

wee

n ro

bot a

nd g

oal (

m)







1 2 3 4 5 6 7 8

0

05

1

Antibody

Affi

nity

of a

ntib

ody

and

antib

ody

minus05

minus1


x

y

2rL

R

120579

Robotdw

Y

X



119874 (119899119873119888) + 119874 (119873) + 119874 (119873) + 119874 (119873 + 119899)

= 119874 (119899119873119888 + 3119873 + 119899)

= 119874 (119899 sdot 5119899 +3119899 sdot 119873119888 + 119899)

= 119874 (51198992+3119899 sdot 5119899 + 119899)

= 119874 (51198992+ 15119899

2+ 119899)

= 119874 (201198992+ 119899)

(21)




(a)

Start

(b)

(c) (d)

(e) (f)Target




[

[

119909

119910

120579

]

]

= [

[

cos 120579 0

sin 120579 0

0 1

]

]

[V120596] (22)


120596 =V119877 minus V119871119889119908

V =V119877 + V119871

2 (23)




Δ119909 =Δ119878119871 + Δ119878119877

2times cos 120579

Δ119910 =Δ119878119871 + Δ119878119877

2times sin 120579

Δ120579 =Δ119878119877 minus Δ119878119871

119887

(24)


Δ119878119877 =Δ119909

cos 120579+119889119908Δ120579

2 cos 120579 = 0

Δ119878119871 =Δ119909

cos 120579minus119889119908Δ120579

2 cos 120579 = 0

(25)


(a)

Start

(b)

(c) (d)

(e) (f)Target


or

Δ119878119877 =Δ119910

sin 120579+119889119908Δ120579

2 sin 120579 = 0

Δ119878119871 =Δ119910

sin 120579minus119889119908Δ120579

2 sin 120579 = 0

(26)



5 Conclusion





Acknowledgments




References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















119860119892119895 equiv 120579119892 119889119895 120579119878119895 119895 = 1 2 119873119878 (1)



Ab119894 equiv 120579119894 =2120587

119873Ab(119894 minus 1) 119894 = 1 2 119873Ab (2)




AntigenEpitope

Idiotope

Paratope




Clonal operator







Robot






















Antibody i




119889119860 119894 (119905)

119889119905= (

119873Ab

sum119895=1

119898st119894119895119886119895 (119905) minus

119873Ab

sum119896=1

119898su119896119894119886119896 (119905) + 119898119894 minus 119896119894)

times 119886119894 (119905)

(3)

119886119894 (119905) =1

1 + exp (05 minus 119860 119894 (119905)) (4)







119865goal119894 =10 + cos (120579119894 minus 120579119892)

20 119894 = 1 2 119873Ab

(5)




119865obs119894 =

119873119878

sum119895=1

120572119894119895119889119895 (6)


if 119889119895 is 119904 then119910 = 1198711

if119889119895 is119898 then119910 = 1198712

if119889119895 is119889 then119910 = 1198713

(7)


120583119904 =

0 119889119895 le 119889119898

119889119895 minus 119889119898


1 119889119895 gt 119889max

(8)

120583119898 =

0 119889119895 le 119889min119889119895 minus 119889min


119889max minus 119889119895


0 119889119895 gt 119889max

(9)

120583119889 =

1 119889119895 le 119889min119889119898 minus 119889119895


0 119889119895 gt 119889119898

(10)



120583119904 + 120583119898 + 120583119889 (11)


119898119894 = 1205961119865goal119894 + 1205962119865obs119894 119894 = 1 2 119873Ab (12)



119894119897is defined as (13)

119898ss119894119897= 119898

st119894119897minus 119898

su119897119894= cos (120579119894 minus 120579119897) = cos (Δ120579119894119897)

119894 119897 = 1 2 119873Ab(13)





119860 119894 (119899 + 1) = 119860 119894 (119899)

+ (

119873Ab

sum119895=1

119898st119894119895119886119895 (119899) minus

119873Ab

sum119896=1

119898su119896119894119886119896 (119899) + 119898119894 minus 119896119894)

times 119886119894 (119899)

119886119894 (119899 + 1) =1

1 + exp (05 minus 119860 119894 (119899 + 1))

(14)











119894isin A1015840 and



Θ (A) = [Θ (1198881) Θ (1198882) Θ (119888119899)]119879 (15)


Generally

119902119894 = Int(119873 times119898(119888119894)

sum119899

119895=1119898(119888119895)

) 119894 = 1 2 119899 (16)


B = AA10158401A10158402 A1015840

119899 (17)

where

A1015840119894= 1198881198941 1198881198942 119888119894119902119894minus1 (18)





119879119862

119888(119888119894 119888119895) = 1199091 1199091199041 1199101 1199101199042

1199041 + 1199042 = 119873119888 119888119894 isin A1015840 119888119895 isin A1015840(19)





119898(119888119894) lt 119898 (119887) 119888119894 isin A1015840 (20)






















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ntib

ody

and

antib

ody

minus05

minus1


x

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2rL

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120579

Robotdw

Y

X



119874 (119899119873119888) + 119874 (119873) + 119874 (119873) + 119874 (119873 + 119899)

= 119874 (119899119873119888 + 3119873 + 119899)

= 119874 (119899 sdot 5119899 +3119899 sdot 119873119888 + 119899)

= 119874 (51198992+3119899 sdot 5119899 + 119899)

= 119874 (51198992+ 15119899

2+ 119899)

= 119874 (201198992+ 119899)

(21)




(a)

Start

(b)

(c) (d)

(e) (f)Target




[

[

119909

119910

120579

]

]

= [

[

cos 120579 0

sin 120579 0

0 1

]

]

[V120596] (22)


120596 =V119877 minus V119871119889119908

V =V119877 + V119871

2 (23)




Δ119909 =Δ119878119871 + Δ119878119877

2times cos 120579

Δ119910 =Δ119878119871 + Δ119878119877

2times sin 120579

Δ120579 =Δ119878119877 minus Δ119878119871

119887

(24)


Δ119878119877 =Δ119909

cos 120579+119889119908Δ120579

2 cos 120579 = 0

Δ119878119871 =Δ119909

cos 120579minus119889119908Δ120579

2 cos 120579 = 0

(25)


(a)

Start

(b)

(c) (d)

(e) (f)Target


or

Δ119878119877 =Δ119910

sin 120579+119889119908Δ120579

2 sin 120579 = 0

Δ119878119871 =Δ119910

sin 120579minus119889119908Δ120579

2 sin 120579 = 0

(26)



5 Conclusion





Acknowledgments




References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










AntigenEpitope

Idiotope

Paratope




Clonal operator







Robot






















Antibody i




119889119860 119894 (119905)

119889119905= (

119873Ab

sum119895=1

119898st119894119895119886119895 (119905) minus

119873Ab

sum119896=1

119898su119896119894119886119896 (119905) + 119898119894 minus 119896119894)

times 119886119894 (119905)

(3)

119886119894 (119905) =1

1 + exp (05 minus 119860 119894 (119905)) (4)







119865goal119894 =10 + cos (120579119894 minus 120579119892)

20 119894 = 1 2 119873Ab

(5)




119865obs119894 =

119873119878

sum119895=1

120572119894119895119889119895 (6)


if 119889119895 is 119904 then119910 = 1198711

if119889119895 is119898 then119910 = 1198712

if119889119895 is119889 then119910 = 1198713

(7)


120583119904 =

0 119889119895 le 119889119898

119889119895 minus 119889119898


1 119889119895 gt 119889max

(8)

120583119898 =

0 119889119895 le 119889min119889119895 minus 119889min


119889max minus 119889119895


0 119889119895 gt 119889max

(9)

120583119889 =

1 119889119895 le 119889min119889119898 minus 119889119895


0 119889119895 gt 119889119898

(10)



120583119904 + 120583119898 + 120583119889 (11)


119898119894 = 1205961119865goal119894 + 1205962119865obs119894 119894 = 1 2 119873Ab (12)



119894119897is defined as (13)

119898ss119894119897= 119898

st119894119897minus 119898

su119897119894= cos (120579119894 minus 120579119897) = cos (Δ120579119894119897)

119894 119897 = 1 2 119873Ab(13)





119860 119894 (119899 + 1) = 119860 119894 (119899)

+ (

119873Ab

sum119895=1

119898st119894119895119886119895 (119899) minus

119873Ab

sum119896=1

119898su119896119894119886119896 (119899) + 119898119894 minus 119896119894)

times 119886119894 (119899)

119886119894 (119899 + 1) =1

1 + exp (05 minus 119860 119894 (119899 + 1))

(14)











119894isin A1015840 and



Θ (A) = [Θ (1198881) Θ (1198882) Θ (119888119899)]119879 (15)


Generally

119902119894 = Int(119873 times119898(119888119894)

sum119899

119895=1119898(119888119895)

) 119894 = 1 2 119899 (16)


B = AA10158401A10158402 A1015840

119899 (17)

where

A1015840119894= 1198881198941 1198881198942 119888119894119902119894minus1 (18)





119879119862

119888(119888119894 119888119895) = 1199091 1199091199041 1199101 1199101199042

1199041 + 1199042 = 119873119888 119888119894 isin A1015840 119888119895 isin A1015840(19)





119898(119888119894) lt 119898 (119887) 119888119894 isin A1015840 (20)






















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Robotdw

Y

X



119874 (119899119873119888) + 119874 (119873) + 119874 (119873) + 119874 (119873 + 119899)

= 119874 (119899119873119888 + 3119873 + 119899)

= 119874 (119899 sdot 5119899 +3119899 sdot 119873119888 + 119899)

= 119874 (51198992+3119899 sdot 5119899 + 119899)

= 119874 (51198992+ 15119899

2+ 119899)

= 119874 (201198992+ 119899)

(21)




(a)

Start

(b)

(c) (d)

(e) (f)Target




[

[

119909

119910

120579

]

]

= [

[

cos 120579 0

sin 120579 0

0 1

]

]

[V120596] (22)


120596 =V119877 minus V119871119889119908

V =V119877 + V119871

2 (23)




Δ119909 =Δ119878119871 + Δ119878119877

2times cos 120579

Δ119910 =Δ119878119871 + Δ119878119877

2times sin 120579

Δ120579 =Δ119878119877 minus Δ119878119871

119887

(24)


Δ119878119877 =Δ119909

cos 120579+119889119908Δ120579

2 cos 120579 = 0

Δ119878119871 =Δ119909

cos 120579minus119889119908Δ120579

2 cos 120579 = 0

(25)


(a)

Start

(b)

(c) (d)

(e) (f)Target


or

Δ119878119877 =Δ119910

sin 120579+119889119908Δ120579

2 sin 120579 = 0

Δ119878119871 =Δ119910

sin 120579minus119889119908Δ120579

2 sin 120579 = 0

(26)



5 Conclusion





Acknowledgments




References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119865obs119894 =

119873119878

sum119895=1

120572119894119895119889119895 (6)


if 119889119895 is 119904 then119910 = 1198711

if119889119895 is119898 then119910 = 1198712

if119889119895 is119889 then119910 = 1198713

(7)


120583119904 =

0 119889119895 le 119889119898

119889119895 minus 119889119898


1 119889119895 gt 119889max

(8)

120583119898 =

0 119889119895 le 119889min119889119895 minus 119889min


119889max minus 119889119895


0 119889119895 gt 119889max

(9)

120583119889 =

1 119889119895 le 119889min119889119898 minus 119889119895


0 119889119895 gt 119889119898

(10)



120583119904 + 120583119898 + 120583119889 (11)


119898119894 = 1205961119865goal119894 + 1205962119865obs119894 119894 = 1 2 119873Ab (12)



119894119897is defined as (13)

119898ss119894119897= 119898

st119894119897minus 119898

su119897119894= cos (120579119894 minus 120579119897) = cos (Δ120579119894119897)

119894 119897 = 1 2 119873Ab(13)





119860 119894 (119899 + 1) = 119860 119894 (119899)

+ (

119873Ab

sum119895=1

119898st119894119895119886119895 (119899) minus

119873Ab

sum119896=1

119898su119896119894119886119896 (119899) + 119898119894 minus 119896119894)

times 119886119894 (119899)

119886119894 (119899 + 1) =1

1 + exp (05 minus 119860 119894 (119899 + 1))

(14)











119894isin A1015840 and



Θ (A) = [Θ (1198881) Θ (1198882) Θ (119888119899)]119879 (15)


Generally

119902119894 = Int(119873 times119898(119888119894)

sum119899

119895=1119898(119888119895)

) 119894 = 1 2 119899 (16)


B = AA10158401A10158402 A1015840

119899 (17)

where

A1015840119894= 1198881198941 1198881198942 119888119894119902119894minus1 (18)





119879119862

119888(119888119894 119888119895) = 1199091 1199091199041 1199101 1199101199042

1199041 + 1199042 = 119873119888 119888119894 isin A1015840 119888119895 isin A1015840(19)





119898(119888119894) lt 119898 (119887) 119888119894 isin A1015840 (20)






















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Antibody

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120579

Robotdw

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119874 (119899119873119888) + 119874 (119873) + 119874 (119873) + 119874 (119873 + 119899)

= 119874 (119899119873119888 + 3119873 + 119899)

= 119874 (119899 sdot 5119899 +3119899 sdot 119873119888 + 119899)

= 119874 (51198992+3119899 sdot 5119899 + 119899)

= 119874 (51198992+ 15119899

2+ 119899)

= 119874 (201198992+ 119899)

(21)




(a)

Start

(b)

(c) (d)

(e) (f)Target




[

[

119909

119910

120579

]

]

= [

[

cos 120579 0

sin 120579 0

0 1

]

]

[V120596] (22)


120596 =V119877 minus V119871119889119908

V =V119877 + V119871

2 (23)




Δ119909 =Δ119878119871 + Δ119878119877

2times cos 120579

Δ119910 =Δ119878119871 + Δ119878119877

2times sin 120579

Δ120579 =Δ119878119877 minus Δ119878119871

119887

(24)


Δ119878119877 =Δ119909

cos 120579+119889119908Δ120579

2 cos 120579 = 0

Δ119878119871 =Δ119909

cos 120579minus119889119908Δ120579

2 cos 120579 = 0

(25)


(a)

Start

(b)

(c) (d)

(e) (f)Target


or

Δ119878119877 =Δ119910

sin 120579+119889119908Δ120579

2 sin 120579 = 0

Δ119878119871 =Δ119910

sin 120579minus119889119908Δ120579

2 sin 120579 = 0

(26)



5 Conclusion





Acknowledgments




References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119894isin A1015840 and



Θ (A) = [Θ (1198881) Θ (1198882) Θ (119888119899)]119879 (15)


Generally

119902119894 = Int(119873 times119898(119888119894)

sum119899

119895=1119898(119888119895)

) 119894 = 1 2 119899 (16)


B = AA10158401A10158402 A1015840

119899 (17)

where

A1015840119894= 1198881198941 1198881198942 119888119894119902119894minus1 (18)





119879119862

119888(119888119894 119888119895) = 1199091 1199091199041 1199101 1199101199042

1199041 + 1199042 = 119873119888 119888119894 isin A1015840 119888119895 isin A1015840(19)





119898(119888119894) lt 119898 (119887) 119888119894 isin A1015840 (20)






















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Robotdw

Y

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119874 (119899119873119888) + 119874 (119873) + 119874 (119873) + 119874 (119873 + 119899)

= 119874 (119899119873119888 + 3119873 + 119899)

= 119874 (119899 sdot 5119899 +3119899 sdot 119873119888 + 119899)

= 119874 (51198992+3119899 sdot 5119899 + 119899)

= 119874 (51198992+ 15119899

2+ 119899)

= 119874 (201198992+ 119899)

(21)




(a)

Start

(b)

(c) (d)

(e) (f)Target




[

[

119909

119910

120579

]

]

= [

[

cos 120579 0

sin 120579 0

0 1

]

]

[V120596] (22)


120596 =V119877 minus V119871119889119908

V =V119877 + V119871

2 (23)




Δ119909 =Δ119878119871 + Δ119878119877

2times cos 120579

Δ119910 =Δ119878119871 + Δ119878119877

2times sin 120579

Δ120579 =Δ119878119877 minus Δ119878119871

119887

(24)


Δ119878119877 =Δ119909

cos 120579+119889119908Δ120579

2 cos 120579 = 0

Δ119878119871 =Δ119909

cos 120579minus119889119908Δ120579

2 cos 120579 = 0

(25)


(a)

Start

(b)

(c) (d)

(e) (f)Target


or

Δ119878119877 =Δ119910

sin 120579+119889119908Δ120579

2 sin 120579 = 0

Δ119878119871 =Δ119910

sin 120579minus119889119908Δ120579

2 sin 120579 = 0

(26)



5 Conclusion





Acknowledgments




References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























0 5 10 15 200

5

10

15

20

Start

End

Obstacles

X (m)

Y(m

)


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)


110 120 130 140 150 160 170 1804

45

5

55

6

65

7

75

8

Step

Sele

cted

antib

ody

PC-AINAIN









Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)



Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)











0 50 100 150 2000

2

4

6

8

10

Step

Dist

ance

bet

wee

n ro

bot a

nd g

oal (

m)

PC-AINRIN


0 50 100 150 200 250 300 350 4000

2

4

6

8

10

12

14

Step

Dist

ance

bet

wee

n ro

bot a

nd g

oal (

m)







1 2 3 4 5 6 7 8

0

05

1

Antibody

Affi

nity

of a

ntib

ody

and

antib

ody

minus05

minus1


x

y

2rL

R

120579

Robotdw

Y

X



119874 (119899119873119888) + 119874 (119873) + 119874 (119873) + 119874 (119873 + 119899)

= 119874 (119899119873119888 + 3119873 + 119899)

= 119874 (119899 sdot 5119899 +3119899 sdot 119873119888 + 119899)

= 119874 (51198992+3119899 sdot 5119899 + 119899)

= 119874 (51198992+ 15119899

2+ 119899)

= 119874 (201198992+ 119899)

(21)




(a)

Start

(b)

(c) (d)

(e) (f)Target




[

[

119909

119910

120579

]

]

= [

[

cos 120579 0

sin 120579 0

0 1

]

]

[V120596] (22)


120596 =V119877 minus V119871119889119908

V =V119877 + V119871

2 (23)




Δ119909 =Δ119878119871 + Δ119878119877

2times cos 120579

Δ119910 =Δ119878119871 + Δ119878119877

2times sin 120579

Δ120579 =Δ119878119877 minus Δ119878119871

119887

(24)


Δ119878119877 =Δ119909

cos 120579+119889119908Δ120579

2 cos 120579 = 0

Δ119878119871 =Δ119909

cos 120579minus119889119908Δ120579

2 cos 120579 = 0

(25)


(a)

Start

(b)

(c) (d)

(e) (f)Target


or

Δ119878119877 =Δ119910

sin 120579+119889119908Δ120579

2 sin 120579 = 0

Δ119878119871 =Δ119910

sin 120579minus119889119908Δ120579

2 sin 120579 = 0

(26)



5 Conclusion





Acknowledgments




References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)



Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)


Start

End

Obstacles

0 5 10 15 200

5

10

15

20

X (m)

Y(m

)











0 50 100 150 2000

2

4

6

8

10

Step

Dist

ance

bet

wee

n ro

bot a

nd g

oal (

m)

PC-AINRIN


0 50 100 150 200 250 300 350 4000

2

4

6

8

10

12

14

Step

Dist

ance

bet

wee

n ro

bot a

nd g

oal (

m)







1 2 3 4 5 6 7 8

0

05

1

Antibody

Affi

nity

of a

ntib

ody

and

antib

ody

minus05

minus1


x

y

2rL

R

120579

Robotdw

Y

X



119874 (119899119873119888) + 119874 (119873) + 119874 (119873) + 119874 (119873 + 119899)

= 119874 (119899119873119888 + 3119873 + 119899)

= 119874 (119899 sdot 5119899 +3119899 sdot 119873119888 + 119899)

= 119874 (51198992+3119899 sdot 5119899 + 119899)

= 119874 (51198992+ 15119899

2+ 119899)

= 119874 (201198992+ 119899)

(21)




(a)

Start

(b)

(c) (d)

(e) (f)Target




[

[

119909

119910

120579

]

]

= [

[

cos 120579 0

sin 120579 0

0 1

]

]

[V120596] (22)


120596 =V119877 minus V119871119889119908

V =V119877 + V119871

2 (23)




Δ119909 =Δ119878119871 + Δ119878119877

2times cos 120579

Δ119910 =Δ119878119871 + Δ119878119877

2times sin 120579

Δ120579 =Δ119878119877 minus Δ119878119871

119887

(24)


Δ119878119877 =Δ119909

cos 120579+119889119908Δ120579

2 cos 120579 = 0

Δ119878119871 =Δ119909

cos 120579minus119889119908Δ120579

2 cos 120579 = 0

(25)


(a)

Start

(b)

(c) (d)

(e) (f)Target


or

Δ119878119877 =Δ119910

sin 120579+119889119908Δ120579

2 sin 120579 = 0

Δ119878119871 =Δ119910

sin 120579minus119889119908Δ120579

2 sin 120579 = 0

(26)



5 Conclusion





Acknowledgments




References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 50 100 150 2000

2

4

6

8

10

Step

Dist

ance

bet

wee

n ro

bot a

nd g

oal (

m)

PC-AINRIN


0 50 100 150 200 250 300 350 4000

2

4

6

8

10

12

14

Step

Dist

ance

bet

wee

n ro

bot a

nd g

oal (

m)







1 2 3 4 5 6 7 8

0

05

1

Antibody

Affi

nity

of a

ntib

ody

and

antib

ody

minus05

minus1


x

y

2rL

R

120579

Robotdw

Y

X



119874 (119899119873119888) + 119874 (119873) + 119874 (119873) + 119874 (119873 + 119899)

= 119874 (119899119873119888 + 3119873 + 119899)

= 119874 (119899 sdot 5119899 +3119899 sdot 119873119888 + 119899)

= 119874 (51198992+3119899 sdot 5119899 + 119899)

= 119874 (51198992+ 15119899

2+ 119899)

= 119874 (201198992+ 119899)

(21)




(a)

Start

(b)

(c) (d)

(e) (f)Target




[

[

119909

119910

120579

]

]

= [

[

cos 120579 0

sin 120579 0

0 1

]

]

[V120596] (22)


120596 =V119877 minus V119871119889119908

V =V119877 + V119871

2 (23)




Δ119909 =Δ119878119871 + Δ119878119877

2times cos 120579

Δ119910 =Δ119878119871 + Δ119878119877

2times sin 120579

Δ120579 =Δ119878119877 minus Δ119878119871

119887

(24)


Δ119878119877 =Δ119909

cos 120579+119889119908Δ120579

2 cos 120579 = 0

Δ119878119871 =Δ119909

cos 120579minus119889119908Δ120579

2 cos 120579 = 0

(25)


(a)

Start

(b)

(c) (d)

(e) (f)Target


or

Δ119878119877 =Δ119910

sin 120579+119889119908Δ120579

2 sin 120579 = 0

Δ119878119871 =Δ119910

sin 120579minus119889119908Δ120579

2 sin 120579 = 0

(26)



5 Conclusion





Acknowledgments




References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

Start

(b)

(c) (d)

(e) (f)Target




[

[

119909

119910

120579

]

]

= [

[

cos 120579 0

sin 120579 0

0 1

]

]

[V120596] (22)


120596 =V119877 minus V119871119889119908

V =V119877 + V119871

2 (23)




Δ119909 =Δ119878119871 + Δ119878119877

2times cos 120579

Δ119910 =Δ119878119871 + Δ119878119877

2times sin 120579

Δ120579 =Δ119878119877 minus Δ119878119871

119887

(24)


Δ119878119877 =Δ119909

cos 120579+119889119908Δ120579

2 cos 120579 = 0

Δ119878119871 =Δ119909

cos 120579minus119889119908Δ120579

2 cos 120579 = 0

(25)


(a)

Start

(b)

(c) (d)

(e) (f)Target


or

Δ119878119877 =Δ119910

sin 120579+119889119908Δ120579

2 sin 120579 = 0

Δ119878119871 =Δ119910

sin 120579minus119889119908Δ120579

2 sin 120579 = 0

(26)



5 Conclusion





Acknowledgments




References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

Start

(b)

(c) (d)

(e) (f)Target


or

Δ119878119877 =Δ119910

sin 120579+119889119908Δ120579

2 sin 120579 = 0

Δ119878119871 =Δ119910

sin 120579minus119889119908Δ120579

2 sin 120579 = 0

(26)



5 Conclusion





Acknowledgments




References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Mobile Robot Path Planning Using ... · network using clonal operator, clonal...

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