Research ArticleResearch of Pose Control Algorithm of CoalMine Rescue Snake Robot

Yun Bai 1 and YuanBin Hou2

1Engineering Training Center Xirsquoan University of Science amp Technology Xirsquoan 710054 China2College of Electrical and Control Engineering Xirsquoan University of Science amp Technology Xirsquoan 710054 China

Correspondence should be addressed to Yun Bai 494361962qqcom

Received 10 November 2017 Revised 17 January 2018 Accepted 24 January 2018 Published 22 February 2018

Academic Editor Luis Gracia

Copyright copy 2018 Yun Bai and YuanBin Hou This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Aiming at how to achieve optimal control of joint pitch angles in the process of the robot surmounting obstacle taking the developedcoal mine rescue snake robot as an experimental platform a pose control algorithm based on particle swarm optimization weightcoefficient of extreme learning machine (PSOELM) is proposed In order to obtain the optimized hidden layer matrix of theextreme learning machine (ELM) particle swarm optimization (PSO) is applied to optimize the weight coefficient of hidden layermatrixThe simulation and experiment results prove that compared with the ELM algorithm the smaller mean square error (MSE)between the joint pitch angles of robot and the expected values is acquired by the PSOELM which overcomes the shortcoming thattraditional extreme learning machine cannot reach the best performance because of the random selection of the parameters of thehidden layer nodes PSOELM is superior to ELM algorithm in control accuracy fast searching for the optimal and stability Optimalcontrol of robotrsquos joint pitch angles is achievedThe algorithm is applied to the surmounting obstacle control of the developed snakerobot and it lays the foundation for further implement of the coal mine rescue

1 Introduction

The snake robot has the characteristics of good stabilitymultiple degrees of freedom multimovement gaits smallcross-section and so forth The snake robot can walk on therugged grounds can move through caves and has strongobstacle surmounting abilities Therefore compared withthe traditional mobile robot driven by wheels or caterpillartracks faced with the complex environment after a coal minedisaster the snake robot can quickly and reliably respond torescue work The robot can replace the rescue personnel toenter the site as a first responder The site information can becollected and scientific basis for a rapid rescue is providedHence developing a coal mine rescue snake robot has a veryimportant practical significance At the same time multipledegrees of freedom and flexibility in the movement of thesnake robot has brought opportunities and challenges forthe research of its pose control To allow the snake robot tomove as flexibly as biological snakes there are a variety ofmethods for pose control such as the discrete curve method

dynamics and kinematics model generation method neuralnetworkmodel generationmethod (eg CPG central patterngenerator) [1] and so on

Discrete Curve Method This method refers to that a curvewhich is defined according to biological snake gait is fittedby the body of snake robot thus each joint rotating angle ofthe robot is obtained also known as the ldquoinverse kinematicsmethodrdquo According to the serpenoid curve of serpentinelocomotion proposed by Hirose [2] Wang et al [3] usedthe specific parameters including the wave propagation rateand the number to disperse the serpenoid curve and thegoverning equations of serpentine locomotionwere obtainedYe et al [4] proposed a simple snake curve for rotational andlateral motion and thus made the motion control equationof snake robot simpler Hatton and Choset [5] used a backcurve (backbone curve) to extract the waveform of thesnake robot and to fit the waveform by using the simulatedannealing algorithm hence multiple gaits for the snakerobot were acquired Xie et al [6] developed a prototypical

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 4751245 9 pageshttpsdoiorg10115520184751245

2 Mathematical Problems in Engineering

underwater snake robot The snakersquos body is composed of16 light waterproof small servomotors and the serpentinelocomotion control of robot was realized by using the snakecurve The discrete curve method has the advantages ofsimple implementation and easy control The disadvantage isthat the jumping of joint angular velocity and torque can leadto the servomotors locking phenomenon and the damage ofservomotors

Dynamic and Kinematic Model Generation Method Aim-ing at the snake robot with linkage type equipped withthree driven wheels Ostrowski and Burdick [7] establisheda dynamic model of serpentine locomotion by using theLagrange method and analyzed the controllability of thesnake robot Liljeback et al [8] established a dynamic modelof the snake robot by making use of the relationship betweencontact force and relative angle thereby achieving controlof obstacle-aided snake robot locomotion Chen et al [9]established a space kinematic model (spatial linkage model)and two kinds of three-dimensional motion of snake robotside winding and lateral rolling were implemented Wei andSun [10] established a kinematic model of snake robot basedon orthogonal joints achieving control of the bridge cableclimbing gait Guo et al [11] put forward a velocity trackingcontrol algorithm avoiding the singular posture based onthe dynamic and control unified model The algorithm wasapplied to motion control of a snake robot with passivewheels Cheng et al [12] presented the method of surmount-ing obstacle for snake robot with 16 P-R-T unitmodules basedon the kinematic model The advantage of the dynamic andthe kinematic model generation method is that complex andaccurate gait control can be realizedThe disadvantage is thatthe modeling process is difficult and the controller mustperform a large amount of calculation and the adaptabilityto unknown environments is poor

Neural Network Model (CPG) Generation Method The CPGmethod has been widely used in the control of snake robotsCrespi and Ijspeert [13] made use of the CPG model andaccomplished optimal control of the swimming and crawlingof a snake robot Lu et al [14] proposed a cyclic inhibitoryCPG controller and serpentine locomotion of a snake robotwas successfully implemented Aiming to resolve the problemof low efficiency and instability of parameter tuning in thecyclic inhibitoryCPG controlmodel Lian et al [15] presenteda parameter optimization method of CPG model based ongenetic algorithms and the method was effectively applied tothe gait control of a snake robot Gao et al [16] established aCPG motion control network by using Hopf oscillators andapplied the network to the serpentine locomotion of a snakerobot which improved the environmental adaptability of therobot CPG control has the advantage of easy integration ofenvironmental information so that the snake robot has theability to adapt to the environment The disadvantage is thatthe control parameters in CPG model need to be furtheroptimized

Based on the present methods for pose control of thesnake robot combined with the advantages of particle swarm

Figure 1 The orthogonal joint connection diagram

optimization (PSO) algorithm and extreme learningmachine(ELM) a pose control algorithm based on particle swarmoptimization weight coefficient of extreme learning machine(PSOELM) is put forward Taking the developed coal minerescue snake robot as an experimental platform and in orderto achieve optimal control of robotrsquos joint pitch angles thePSOELM algorithm is applied to the robotrsquos surmountingobstacle behavior

2 Design of the Coal MineRescue Snake Robot

21 Design of Mechanical Structure The mechanical body ofthe coal mine rescue snake robot adopts orthogonal jointconnection which has four orthogonal joints as is shown inFigure 1 The total length of the snake robot is 1m and it iscomposed of the head the body and the tail Consideringthe rugged tunnel environment after the coal mine disasterthe robot is driven by the self-made blades wheels Comparedwith snake robot driven by wheels or caterpillar tracksthis robot has better obstacle surmounting capabilities Themechanical structure of the robot is shown in Figure 2

The robotrsquos characteristics are as follows(1) Unit module idea is adopted the head of snake robot

(6) is composed of a night vision device and sensor groupinstalled in the front end of the unit module (1)

(2) The body of snake robot (29) is composed of five unitmodules (1 2 3 4 and 5) five connecting plates (12 13 14 15and 16) four orthogonal joints (8 9 10 and 11) and two speedservomotors (27 and 28) Among them each orthogonal jointconsists of a horizontal and a vertical direction servomotor

(3)Thefive unitmodules are respectively installed on thefive connecting plates and are connected successively throughthe four orthogonal joints to form the body of the snakerobot In which the unit modules (2 3 and 4) have the samestructure each having two direction servomotors two directcurrent speed reduction motors and two blades wheels theunit modules (1 5) are identical in structure each having onedirection servomotors two direct current speed reductionmotors and two blades wheels

(4)The tail of snake robot (7) consists ofmaster controllerpower source obstacle avoidance module and communica-tion module installed in the back end of the unit module (5)

Mathematical Problems in Engineering 3

12345

28

27

6

17

18

19

20

21

22

25

26 24

23

12

11 10 89

13141516

7

29

Figure 2 Mechanical structure of the blades wheels snake robot

Snake head

Snake tail

Snake body

Blades wheels

Figure 3 The snake robot entering the simulated coal mine tunnel

(5) The blades wheels (17 18 19 20 21 22 23 24 25and 26) as moving mechanism installed on both sides of thesnake robot

(6) The speed servomotor (28) is used to control therotation of the blades wheels (17 19 21 23 and 25) on the leftside of the snake robot The speed servomotor (27) is used tocontrol the rotation of the blades wheels (18 20 22 24 and26) on the right side of the snake robot

The snake robot enters the simulated coal mine tunnelwhich is semioval tunnel as shown in Figure 3

22 Design of the Control System The control system asshown in Figure 4 is made up of the power source envi-ronmental detection system pose control system mastercontroller mobile mechanism obstacle avoidance modulecommunication module and host computer system

Among them the power source includes E1 and E2 ofwhich E1 is a 126v Li-PO rechargeable battery with chargingcurrent of 1300mAh E1 supplies power to servomotors anddirect current speed reduction motors E2 is 45v mercury-free alkaline battery and supplies power to the obstacleavoidance module

The environmental detection system consists of a nightvision device and sensor group The night vision device canbe set to night mode and general mode The sensor group iscomposed of two ultrasonic sensors and an infrared sensorTaking into account the special environment of coal minetunnel the night vision device is installed on the top ofhead and the overall environment information of simulatedcoal mine tunnel can be obtained by the night vision deviceTwo ultrasonic sensors are installed on the left and rightsides of the head and the infrared sensor is installed in themiddle The distance information between the snake robotand obstacles can be obtained by using ultrasonic sensorsand infrared sensor and the infrared sensor can effectively

moduleCommunication

Master controller

Obstacle avoidance module

Power source

system

Environmental detection

systemPose control

Host computer system

Mobile mechanism

Figure 4 Control system of the snake robot

compensate for the fade zone existing in ultrasonic sensorranging

The pose control system is mainly composed of fourhorizontal and four vertical direction servomotorsThe hori-zontal direction servomotors control serpentine and straightposture of the snake robotThe vertical direction servomotorscontrol concertina and head rising posture The M-24 digitalservomotor is selected When used as the joint motor itcan rotate 0sim300 degrees and provide up to 16 kgsdotcm oftorque which is 2 times that of the general digital servomotorEach servomotor has an individual ID Each servomotor canbe independently controlled and thus the control of snakerobotrsquos gait and pose is acquired

The master controller uses the Vensmile W10 Mini PCwhich has the Atom Z3735F Bay Trail processor 2 GBmemory and 64GB storage space

The mobile mechanism is made up of two speed ser-vomotors ten direct current speed reduction motors andten blades wheels By controlling the speed servomotorsthe direct current speed reduction motors are driven tomotivate the blades wheels to rotate and then the purposeof controlling the speed of the snake robot is realized

The obstacle avoidance module uses Arduino Uno R3control board and its main control chip is ATMEGA328P-PU of Atmel Company

The communication system uses a self-organized LAN(local area network) to complete data and video imagetransmission function

The host computer system includes a monitoring screenof the snake robotrsquos locomotion and the real-time displayscreen of the environment of the simulated coal mine tunnel

4 Mathematical Problems in Engineering

Initialization

Start

aheadStraight

Avoid obstacleMove ahead

Whether

in front

there are obstacles

End

PSOELMOptimizing by

PSOELMOptimizing by

PSOELMOptimizing by

Yes

Yes

Yes

Yes

No

No

No

No

Execute R-1

Execute R-2

Execute R-3

ℎ lt 5

ℎ lt 8

ℎ lt 12

Figure 5 Flowchart of the pose control algorithm

And intelligent identification and location of cracks on thetunnel could also be achieved

3 Pose Control AlgorithmBased on the PSOELM

Pose control algorithm based on particle swarm optimizationweight coefficient of extreme learning machine (PSOELM)is proposed and the algorithm is applied to the robotrsquossurmounting obstacle behavior The obstacles are dividedinto cuboids cubes or cylinders The flowchart of the posecontrol algorithm is shown in Figure 5 in which R-1 R-2 and R-3 refer to the first three rules in the expert rulesof robotrsquos pose control The algorithm is composed of three

steps firstly the expert rules of robotrsquos pose control areobtained secondly the control model based on extremelearning machine (ELM) is established thirdly the particleswarm optimization algorithm is used to optimize the hiddenlayer matrix weight coefficient of extreme learning machineso as to obtain the optimized hidden layer matrix and theoptimal control of joint pitch angles of the snake robot isachieved

31 The First Step Expert Rules of Pose Control (1) Whenthe sensors detect the height of obstacle is low (ℎ lt 5 cm)the first joint is raised to 45 degrees and the second joint israised to 15 degrees by UK1 and UK3 and then UK5 andUK7 cause the third and fourth joints to synchronously moveahead Here UK1 UK3 UK5 and UK7 respectively referto the output variables of master controller controlling fourvertical direction servomotors

(2) When the sensors detect the height of obstacle ishigher (5 cm lt ℎ lt 8 cm) the first joint is raised to 45 degreesand the second joint is raised to 35 degrees by UK1 and UK3and then UK5 and UK7 cause the third and fourth joints tosynchronously move ahead

(3) When the sensors detect the height of obstacle ishigher (8 cm lt ℎ lt 12 cm) the first joint is raised to 45degrees and the second joint is raised to 45 degrees and thethird joint is raised to 25 degrees by UK1 UK3 and UK5 andthen UK7 lets the fourth joint move ahead

(4) When the sensors detect the height of obstacle ishighest (ℎ gt 12 cm) the robot chooses the obstacle avoidanceaction to bypass the obstacle

(5)While surmounting the obstacle the robot must bendat the joint (waist) When the head joint of the snake is pastthe apex of the obstacle it must tilt downwards such that thejoint contacts the ground and the angle of the joint in thevertical direction is 0 degrees Such as the first joint inclinesdownward to minus45 degrees and at the same time the jointis associated with the first joint rises When the first jointis on the ground and the joint angle changes to 0 degreesthe actions of surmounting the obstacle are completed Insummary the whole process of surmounting an obstacleincludes the six related actions which are raising the headmoving forward bowing head bowing the body raising thetail and making straightening out

32 The Second Step The Control Model Based on ExtremeLearning Machine (ELM) Snake robotrsquos locomotion of sur-mounting obstacle refer to that in the orthogonal joint theangle of joint in the horizontal direction (namely left andright) keeps 0 degrees while the angle of joint in the verticaldirection (namely up and down) changes according to thecosine curve Here according to the equation of serpenoidcurve curvature of Hirose 120579119894 is defined as the angle betweenthe 119894th joint and the horizontal direction (namely the pitchangle) and expressed as follows

120579119894 = 1198860 cos(119894119871119896119899 ) (1)

where 1198860 is the initial angle of serpenoid curve 119896 is the scalefactor of robotrsquos pitch angle 119871 is the total length of snake

Mathematical Problems in Engineering 5

robot 119899 is the number of unit modules 119899 minus 1 is the numberof joints 119894 represents 119894th joint 119894 = 1 2 119899 minus 1

120593119894 is defined as the relative rotation angle between the119894th joint and the (119894 minus 1)th joint The relative rotation anglefunction of the 119894th joint in dynamic condition can be obtainedas follows

120593119894 (119905) = minus21198860 sin (1198961119897) sin (120596119905 + 1198961 (119904 minus 2 (119894 minus 1) 119897)) (2)

where 1198860 is the initial angle of serpenoid curve 1198961 is the scalefactor of jointrsquos relative rotation angle 119904 is the total lengthof serpenoid curve 2119897 is the length of unit module of snakerobot 119894 represents 119894th joint 119894 = 1 2 119899 minus 1 Here 1198961 =2120587(119904 + 119888) 119888 is the adjustment parameter

Amodel of extreme learningmachine (ELM) algorithm isa feed-forward neural network with single hidden layer Thebasic idea is that all the hidden node parameters (includingthe weight between the hidden layer and the input layer andthe bias of the hidden layer nodes) are randomly generatedand are independent of the objective functions and thetraining sample and do not need iterative adjustment Onlythe number of hidden layer nodes needs to be set and thenthe weight between the hidden layer and the output layeris analyzed and calculated The optimal weight coefficientis obtained by using the particle swarm optimization (PSO)algorithm and the final network output acquired is the opti-mal solution If the pitch angle is optimized the algorithm isused to optimize formula (1) If the relative rotation angle isoptimized the algorithm is used to optimize formula (2)Thefollowing is mainly aimed at the optimization of pitch anglein the second step

The systemmodel is the 3-6-1 type networkThe networkinput is three kinds of random permitted solution 120579119894 =[1205791198941 1205791198942 1205791198943]119879 (119894 = 1 2 3) which indicates the first three jointangles of snake robot when the obstacle is three differentheights The hidden layer nodes are 6 The output node ofnetwork is 1 which corresponds to the actual angles of thefirst three joints of the snake robot when surmounting theobstacle The angles specified by each expert rule in thefirst step are used as the expected angles The error betweenthe actual angles and the expected angles of the joints isminimized by the extreme learning algorithm that is theerror between the network output (actual angles) and theexpected output (expected angles) is minimized and Δ120579119894 rarr 0is accomplished

The extreme learning algorithm is equivalent to solvingthe objective function 119871

min 119871

= 12100381710038171003817100381712057310038171003817100381710038172 + 12119862

3

sum119894=1

1003817100381710038171003817Δ12057911989410038171003817100381710038172

minus3

sum119894=1

6

sum119895=1

120582119894 (ℎ (120579119894) 120573119895 minus 119910119894 minus Δ120579119894)

(3)

where 120579119894 = [1205791198941 1205791198942 1205791198943]119879 (119894 = 1 2 3) are input neurons forextreme learning machine 119884 = [1199101 1199102 1199103]119879 is expectedoutput for extreme learning machine 120573 is weight between

hidden layer and output layer Δ120579119894 is pitch angle errorof snake robot of network training 119862 is correspondingpenalty factor of Δ120579119894 120582119894 is Lagrange multiplier ℎ(120579119894) =[119866(1198861 1198871 120579119894) 119866(1198862 1198872 120579119894) 119866(119886119871 119887119871 120579119894)] is the output vec-tor of hidden layer about 120579119894 where119866(119886119895 119887119895 120579119894) is the output ofthe 119895th hidden node through the activation function 119886119895 is theweight between the 119895th hidden layer node and the networkinput 119887119895 is the bias of the 119895th hidden layer node Here thehyperbolic function is chosen as the activation function theinput of the 119895th hidden node of the network is gained as thefollowing formula

119902119895 =6

sum119895=1

119886119895120579119894 + 119887119895 (4)

So the output vector of the 119895th hidden node about 120579119894 is asfollows

ℎ119895 (120579119894) = 1 minus 119890minus1199011199021198951 + 119890minus119901119902119895 (5)

where 119901 is the optimal weight coefficientCalculate the partial derivative for each variable of the

objective function 119871120597119871120597120573119895 = 0 997888rarr

120573119895 =3

sum119894=1

120582119894ℎ (120579119894)119879 997888rarr

120573 = 119867119879120582120597119871

120597 (Δ120579119894) = 0 997888rarr120582119894 = 119862 (Δ120579119894)120597119871120597120582119894 = 0 997888rarr

ℎ (120579119894) 120573 minus 119910119879119894 + (Δ120579119894)119879 = 0

(6)

where119867 is a 3 times 6-dimensional hidden layer output matrix

119867 = [ℎ (1205791) ℎ (1205792) ℎ (1205793)]119879 (7)

because

119884 = [1199101 1199102 1199103]119879 (8)

From formula (3) we obtain 120597119871(120597120573119895 120597(Δ120579119894) 120597120582119894) gt 0So according to the principle of least squares the followingformula can be derived

( 119868119862 + 119867119867119879)120582 = 119884 (9)

Then the weight 120573 can be deduced as shown in thefollowing formula

120573 = 119867119879120582 = 119867119879 ( 119868119862 + 119867119867119879)minus1 119884 (10)

6 Mathematical Problems in Engineering

(a) (b)

Figure 6 (a) Action 1 of surmounting the obstacle (b) Action 2 of surmounting the obstacle

Therefore the output formula (11) of the extreme learningmachine is obtained

119891 (120579119894) = ℎ (120579119894) 120573 =6

sum119895=1

ℎ119895 (120579119894)119867119879 ( 1119862 + 119867119867119879)minus1 119884 (11)

33 The Third Step Particle Swarm Optimization WeightCoefficient 119901 In formula (11) in order to solve the optimalweight coefficient 119901 of hidden layer matrix the particleswarm optimization algorithm is used In the process ofsolving the particle is updated by tracking the two optimalvaluesThe first one is the optimal solution which is searchedby the particle itself and the other is the optimal solutionsearched by the whole swarm so far The formula used is asfollows

V119894 (119905 + 1) = 120596V119894 (119905) + 11988811199031 (119909119901best119894 minus 119909119894 (119905))+ 11988821199032 (119909119892best119894 minus 119909119894 (119905))

119909119894 (119905 + 1) = 119909119894 (119905) + V119894 (119905 + 1) (12)

where 119894 represents a particle 119909119894 indicates the position ofthe particle at 119905 moment (corresponding to the optimalweight coefficient 119901 of output matrix of the hidden layer at119905moment) V119894 indicates the velocity of particles at 119905moment119909119901best119894 represents the best position of the particle so far 119909119892best119894represents the best position searched by the whole swarmso far 0 lt 120596 lt 1 is inertial coefficient 1198881 and 1198882 arelearning factors 1199031 and 1199032 are the randomnumbers uniformlydistributed on interval (0 1) After calculating V119894(119905 + 1) theposition 119909119894(119905 + 1) of the particle 119894 at next moment can becalculatedThat is position 119909119894 is changed bymodifying speedV119894 to make Δ119901119894 rarr 0 achieving optimal weight coefficient 119901

In this system the weight coefficient of hidden layermatrix is optimized by the particle swarm optimizationalgorithm It makes that the error between the actual outputof extreme learning machine 119891(120579) and the expected output119884 is minimized that is Δ120579119894 rarr 0 The optimal pitch angle ofeach joint is obtained

4 Simulation Experiment and Result Analysis

Combined with the snake robotrsquos behavior of surmountingobstacle which are shown in Figures 6(a) and 6(b) the 15

training samples and 5 test samples were randomly selectedInput variables are pitch angles of the first three jointswhen the obstacle is three different heights that is 120579119894 =[1205791198941 1205791198942 1205791198943]119879 119894 = 1 2 3 and input layer nodes are 3 Outputvariables are the actual pitch angles of the first three jointsthat is 119891(120579) = [119891(1205791) 119891(1205792) 119891(1205793)]119879 and the output nodeis 1 The computer simulation is carried out in MATLAB

The effects of the ELM and POSELM control modelsare evaluated by comparing the following 4 indicators Theperformance and generalization ability of the model areevaluated by calculating MSE (mean square error) and deter-minant coefficient 1198772 The computation speed is evaluated bycomparing the runtime of models The stability of the modelis evaluated by analyzing the effect of the number of hiddenlayer nodes on MRE (mean relative error)

(1) MSE (Mean Square Error) and Determinant Coefficient 1198772Here

MSE = 1119899119899

sum119894=1

(119891 (120579119894) minus 119910119894)2

1198772

= (119899sum119899119894=1 119891 (120579119894) 119910119894 minus sum119899119894=1 119891 (120579119894)sum119899119894=1 119910119894)2(119899sum119899119894=1 119891 (120579119894)2 minus (sum119899119894=1 119891 (120579119894))2) (119899sum119899119894=1 1199101198942 minus (sum119899119894=1 119910119894)2)

(13)

In formula (13) 119899 represents the number of samples119891(120579119894) is the output of the optimal control model and 119910119894 isthe expected output The smaller the MSE the better theperformance of themodelThe value of1198772 is in the interval of[0 1]The closer to 1 the better the performance of themodel

PSOELM and ELM are used respectively to control thejoint pitch angles of snake robot and the simulation resultsare shown in Figure 7 The 119909-axis represents the first threejoints of snake robot and the 119910-axis indicates the joint pitchangle During surmounting the obstacle when the obstacleheight ℎ lt 5 cm pitch angles of the first three joints arerespectively controlled by the PSOELM and ELM and theresults are respectively given as shown in Figures 7(a) and7(b) Determinant coefficient 1198772 is 1 and mean square errorof pitch angles respectively reaches 64198 times 10ndash35 and 10272times 10minus32 when the obstacle height 5 cm lt ℎ lt 8 cm pitch

Mathematical Problems in Engineering 7

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

Expected outputPSOELM output

(mse = 64198e minus 35 R2 = 1)

(a)

Expected outputELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 32 R2 = 1)

(b)

Expected outputPSOELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 41087e minus 33 R2 = 1)

(c)

Expected outputELM output

(mse = 13132e minus 32 R2 = 1)

1 2 3Joint number

0807060504030201

0

Pitc

h an

gle (

rad)

minus01

(d)

Expected outputPSOELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 33 R2 = 1)

(e)

Expected outputELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 12326e minus 32 R2 = 1)

(f)

Figure 7 (a) Pitch angles optimized by the PSOELM (ℎ lt 5 cm) (b) Pitch angles controlled by the ELM (ℎ lt 5 cm) (c) Pitch angles optimizedby the PSOELM (5 cm lt ℎ lt 8 cm) (d) Pitch angles controlled by the ELM (5 cm lt ℎ lt 8 cm) (e) Pitch angles optimized by the PSOELM(8 cm lt ℎ lt 12 cm) (f) Pitch angles controlled by the ELM (8 cm lt ℎ lt 12 cm)

8 Mathematical Problems in Engineering

Table 1 MSE comparison between PSOELM and ELM

Algorithm types MSE of pitch angle(ℎ lt 5 cm)

MSE of pitch angle(5 cm lt ℎ lt 8 cm)

MSE of pitch angle(8 cm lt ℎ lt 12 cm)

PSOELM 64198 times 10minus35 41087 times 10minus33 10272 times 10minus33

ELM 10272 times 10minus32 13132 times 10minus32 12326 times 10minus32

018

016

014

012

01

008

006

004

0021 2 3 4 5 6 7 8 9 10

Model number

Runt

ime (

s)

POSELMELM

Figure 8 Comparison of the runtime of the 10 models (POSELMversus ELM)

angles of the first three joints are respectively controlled bythe PSOELMand ELM and the results are respectively givenas shown in Figures 7(c) and 7(d) Determinant coefficient1198772 is 1 and mean square error of pitch angles respectivelyreaches 41087 times 10ndash33 and 13132 times 10minus32 when the obstacleheight 8 cm lt ℎ lt 12 cm pitch angles of the first three jointsare respectively controlled by the PSOELM and ELM andthe results are respectively given as shown in Figures 7(e)and 7(f) Determinant coefficient 1198772 is 1 and mean squareerror of pitch angles respectively reaches 10272 times 10ndash33 and12326 times 10minus32 MSE based on PSOELM and ELM is shown inTable 1 It can be seen from Figure 7 and Table 1 comparedwith ELM the smaller mean square error and better controlaccuracy and generalization ability are acquired by PSOELMOptimal control of joint pitch angles can be realized

(2) The Model Runtime Since the training set and the testset are generated randomly each runtime of the model isdifferentThe above-mentioned 10 identical ELMmodels and10 identical POSELMmodels are respectively selected to testtheir computation speedThemaximumnumber of iterationsis 3 As shown in Figure 8 the average runtime of the 10 ELMmodels and the 10 POSELM models is respectively 00426 Sand 00535 S So the runtime of the ELM and POSELMmodels is roughly the same and it is all around 50ms It canbe seen that the POSELMmodel continues the characteristicsof the fast learning of the ELMmodel

j

times10minus5

PSOELMELM

6571

5459

4347

3235

2123

10112 64 8 10 12 14 16

MRE

Figure 9 Hidden layer nodes andmean relative error (MRE) curves(POSELM versus ELM)

(3) The Stability of the Model The effect of the numberof hidden layer nodes on MRE is analyzed to evaluate thestability of the model The relationship curves between thehidden layer node 119895 and MRE are shown in Figure 9 Asobtained from Figure 9 the ELMmodel shows great volatilitywith the change of 119895 which is caused by random selectionof input weight and hidden layer node bias In the POSELMmodel the fluctuation of MRE is smaller with the change of119895 and the smaller hidden layer nodes can ensure that MRE isthe smallestWhen 119895 is 6 MRE is the smallest which is 13673times 10minus16 The POSELM model has the characteristic of fastsearching for the optimal and stability and it has significantadvantages in the control of the joint pitch angles of the snakerobot

5 Conclusion

A coal mine rescue snake robot is developed and takingthe robot as an experimental platform aiming at the robotrsquosobstacle surmounting behavior a pose control algorithmbased on particle swarm optimization weight coefficient ofextreme learningmachine (PSOELM) is studied in this paperThe following conclusions are drawn

(1) The mechanical structure and control system ofthe coal mine rescue snake robot are designed and maderespectively The mechanical part is consisted of five unitmodules five connecting plates four orthogonal joints andtwo speed servomotors The robot has better capability to

Mathematical Problems in Engineering 9

surmount the obstacle because of using the self-made bladeswheels The control system is made up of the power sourceenvironmental detection system pose control system mastercontroller mobile mechanism obstacle avoidance modulecommunication module and host computer system Thesnake robot can walk on the rugged grounds By controllingthe direction servomotors serpentine straight concertinaand head rising posture of the snake robot can be acquiredand the speed of the snake robot can be changed by control-ling the speed servomotors

(2) The pose control algorithm based on PSOELM isproposed and discussed compared with simulation resultsof the algorithm based on ELM the PSOELM algorithmhas the following advantages the smaller mean square errorand better control accuracy and generalization ability areacquired the characteristics of fast learning of ELM arecontinued having the characteristic of fast searching for theoptimal and better stability so optimal control of robotrsquos jointpitch angles is achieved by the PSOELM algorithm

(3)ThePSOELMalgorithm is applied to the surmountingobstacle control of the developed snake robot and it lays thefoundation for further implement of the coal mine rescue

Disclosure

The coal mine rescue snake robot developed won specialaward in 2016 Chinese Education Robot Contest

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research has been supported by Foundation of Scienceand Technology Innovation Project of China Coal Technol-ogy Engineering Group (no KJ3013-XBMJ-03) and cultivat-ing fund of Xirsquoan University of Science And Technology (no2013024)

References

[1] A Crespi A Badertscher A Guignard and A J IjspeertldquoAmphiBot I An amphibious snake-like robotrdquo Robotics andAutonomous Systems vol 50 no 4 pp 163ndash175 2005

[2] S Hirose Biologically Inspired Robots (Snake-like Locomotorsand Manipulators) Oxford University Press Oxford UK 1993

[3] Y C Wang L Chen S G Ma et al ldquoStudies on lateral roilinglocomotion of a snake robotrdquo in Proceedings of the IntemationalConference on Robotics and Automation IEEE pp 5070ndash5074Piscataway NJ USA 2004

[4] C Ye S Ma B Li and Y Wang ldquoTurning and side motionof snake-like robotrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation (ICRA rsquo04) pp 5075ndash5080 IEEE May 2004

[5] R L Hatton and H Choset ldquoGenerating gaits for snakerobots Annealed chain fitting and keyframe wave extractionrdquoAutonomous Robots vol 28 no 3 pp 271ndash281 2010

[6] Y Xie U Zhenli and X Huigang ldquoResearch on underwa-ter snake-like robots mechanism design and their serpentineswimming performancerdquo Chinese High Technology Letters vol26 no 6 pp 599ndash605 2016

[7] J Ostrowski and J Burdick ldquoThe geometricmechanics of undu-latory robotic locomotionrdquo International Journal of RoboticsResearch vol 17 no 7 pp 683ndash701 1998

[8] P Liljeback K Y Pettersen and K Stavdahl ldquoModelling andcontrol of obstacle-aided snake robot locomotion based onjam resolutionrdquo in Proceedings of the 2009 IEEE InternationalConference on Robotics and Automation ICRA rsquo09 pp 3807ndash3814 Japan May 2009

[9] L Chen Y-C Wang S-G Ma and B Li ldquoStudy of laterallocomotion of snake robotrdquo JiqirenRobot vol 25 no 3 p 2462003

[10] W Wei and C Sun ldquoResearch on Gait Generation and Controlof Snake-like Robot for Bridge Cable Climbing [J]rdquo ChinaMechanicalengineering vol 23 no 10 pp 1230ndash1235 2012

[11] X Guo S-GMa B Li M-HWang and Y-CWang ldquoVelocitytracking control of a snake-like robot with a dynamics andcontrol unified modelrdquo Zidonghua XuebaoActa AutomaticaSinica vol 41 no 11 pp 1847ndash1856 2015

[12] Q Cheng G Wu S Li et al ldquoStatic mechanism of a climbingsnake robot navigating obstaclerdquoMachinery DesignampManufac-ture vol 3 pp 37ndash40 2016

[13] A Crespi and A J Ijspeert ldquoOnline optimization of swimmingand crawling in an amphibious snake robotrdquo IEEE Transactionson Robotics vol 24 no 1 pp 75ndash87 2008

[14] Z Lu S Ma B Li and Y Wang ldquoSnake-like robot con-troller with cyclic inhibitory CPG modelrdquo Jixie GongchengXuebaoChinese Journal of Mechanical Engineering vol 42 no5 pp 137ndash143 2006

[15] X Lian Guo W X Lian et al ldquoCPG model parametersoptimization based on genetic algorithm for snake-like robotrdquoComputure Engineeing And Design vol 36 pp 1859ndash1864 2015

[16] Q Gao Z-L Wang W-J Hu and L-Y Zhao ldquoResearch onrealization and environmental adaptability of serpentine loco-motion for a snake robotrdquoDalian Ligong Daxue XuebaoJournalof Dalian University of Technology vol 55 no 2 pp 203ndash2082015

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Mathematical Problems in Engineering 3

12345

28

27

6

17

18

19

20

21

22

25

26 24

23

12

11 10 89

13141516

7

29

Figure 2 Mechanical structure of the blades wheels snake robot

Snake head

Snake tail

Snake body

Blades wheels

Figure 3 The snake robot entering the simulated coal mine tunnel

(5) The blades wheels (17 18 19 20 21 22 23 24 25and 26) as moving mechanism installed on both sides of thesnake robot

(6) The speed servomotor (28) is used to control therotation of the blades wheels (17 19 21 23 and 25) on the leftside of the snake robot The speed servomotor (27) is used tocontrol the rotation of the blades wheels (18 20 22 24 and26) on the right side of the snake robot

The snake robot enters the simulated coal mine tunnelwhich is semioval tunnel as shown in Figure 3

22 Design of the Control System The control system asshown in Figure 4 is made up of the power source envi-ronmental detection system pose control system mastercontroller mobile mechanism obstacle avoidance modulecommunication module and host computer system

Among them the power source includes E1 and E2 ofwhich E1 is a 126v Li-PO rechargeable battery with chargingcurrent of 1300mAh E1 supplies power to servomotors anddirect current speed reduction motors E2 is 45v mercury-free alkaline battery and supplies power to the obstacleavoidance module

The environmental detection system consists of a nightvision device and sensor group The night vision device canbe set to night mode and general mode The sensor group iscomposed of two ultrasonic sensors and an infrared sensorTaking into account the special environment of coal minetunnel the night vision device is installed on the top ofhead and the overall environment information of simulatedcoal mine tunnel can be obtained by the night vision deviceTwo ultrasonic sensors are installed on the left and rightsides of the head and the infrared sensor is installed in themiddle The distance information between the snake robotand obstacles can be obtained by using ultrasonic sensorsand infrared sensor and the infrared sensor can effectively

moduleCommunication

Master controller

Obstacle avoidance module

Power source

system

Environmental detection

systemPose control

Host computer system

Mobile mechanism

Figure 4 Control system of the snake robot

compensate for the fade zone existing in ultrasonic sensorranging

The pose control system is mainly composed of fourhorizontal and four vertical direction servomotorsThe hori-zontal direction servomotors control serpentine and straightposture of the snake robotThe vertical direction servomotorscontrol concertina and head rising posture The M-24 digitalservomotor is selected When used as the joint motor itcan rotate 0sim300 degrees and provide up to 16 kgsdotcm oftorque which is 2 times that of the general digital servomotorEach servomotor has an individual ID Each servomotor canbe independently controlled and thus the control of snakerobotrsquos gait and pose is acquired

The master controller uses the Vensmile W10 Mini PCwhich has the Atom Z3735F Bay Trail processor 2 GBmemory and 64GB storage space

The mobile mechanism is made up of two speed ser-vomotors ten direct current speed reduction motors andten blades wheels By controlling the speed servomotorsthe direct current speed reduction motors are driven tomotivate the blades wheels to rotate and then the purposeof controlling the speed of the snake robot is realized

The obstacle avoidance module uses Arduino Uno R3control board and its main control chip is ATMEGA328P-PU of Atmel Company

The communication system uses a self-organized LAN(local area network) to complete data and video imagetransmission function

The host computer system includes a monitoring screenof the snake robotrsquos locomotion and the real-time displayscreen of the environment of the simulated coal mine tunnel

4 Mathematical Problems in Engineering

Initialization

Start

aheadStraight

Avoid obstacleMove ahead

Whether

in front

there are obstacles

End

PSOELMOptimizing by

PSOELMOptimizing by

PSOELMOptimizing by

Yes

Yes

Yes

Yes

No

No

No

No

Execute R-1

Execute R-2

Execute R-3

ℎ lt 5

ℎ lt 8

ℎ lt 12

Figure 5 Flowchart of the pose control algorithm

And intelligent identification and location of cracks on thetunnel could also be achieved

3 Pose Control AlgorithmBased on the PSOELM

Pose control algorithm based on particle swarm optimizationweight coefficient of extreme learning machine (PSOELM)is proposed and the algorithm is applied to the robotrsquossurmounting obstacle behavior The obstacles are dividedinto cuboids cubes or cylinders The flowchart of the posecontrol algorithm is shown in Figure 5 in which R-1 R-2 and R-3 refer to the first three rules in the expert rulesof robotrsquos pose control The algorithm is composed of three

steps firstly the expert rules of robotrsquos pose control areobtained secondly the control model based on extremelearning machine (ELM) is established thirdly the particleswarm optimization algorithm is used to optimize the hiddenlayer matrix weight coefficient of extreme learning machineso as to obtain the optimized hidden layer matrix and theoptimal control of joint pitch angles of the snake robot isachieved

31 The First Step Expert Rules of Pose Control (1) Whenthe sensors detect the height of obstacle is low (ℎ lt 5 cm)the first joint is raised to 45 degrees and the second joint israised to 15 degrees by UK1 and UK3 and then UK5 andUK7 cause the third and fourth joints to synchronously moveahead Here UK1 UK3 UK5 and UK7 respectively referto the output variables of master controller controlling fourvertical direction servomotors

(2) When the sensors detect the height of obstacle ishigher (5 cm lt ℎ lt 8 cm) the first joint is raised to 45 degreesand the second joint is raised to 35 degrees by UK1 and UK3and then UK5 and UK7 cause the third and fourth joints tosynchronously move ahead

(3) When the sensors detect the height of obstacle ishigher (8 cm lt ℎ lt 12 cm) the first joint is raised to 45degrees and the second joint is raised to 45 degrees and thethird joint is raised to 25 degrees by UK1 UK3 and UK5 andthen UK7 lets the fourth joint move ahead

(4) When the sensors detect the height of obstacle ishighest (ℎ gt 12 cm) the robot chooses the obstacle avoidanceaction to bypass the obstacle

(5)While surmounting the obstacle the robot must bendat the joint (waist) When the head joint of the snake is pastthe apex of the obstacle it must tilt downwards such that thejoint contacts the ground and the angle of the joint in thevertical direction is 0 degrees Such as the first joint inclinesdownward to minus45 degrees and at the same time the jointis associated with the first joint rises When the first jointis on the ground and the joint angle changes to 0 degreesthe actions of surmounting the obstacle are completed Insummary the whole process of surmounting an obstacleincludes the six related actions which are raising the headmoving forward bowing head bowing the body raising thetail and making straightening out

32 The Second Step The Control Model Based on ExtremeLearning Machine (ELM) Snake robotrsquos locomotion of sur-mounting obstacle refer to that in the orthogonal joint theangle of joint in the horizontal direction (namely left andright) keeps 0 degrees while the angle of joint in the verticaldirection (namely up and down) changes according to thecosine curve Here according to the equation of serpenoidcurve curvature of Hirose 120579119894 is defined as the angle betweenthe 119894th joint and the horizontal direction (namely the pitchangle) and expressed as follows

120579119894 = 1198860 cos(119894119871119896119899 ) (1)

where 1198860 is the initial angle of serpenoid curve 119896 is the scalefactor of robotrsquos pitch angle 119871 is the total length of snake

Mathematical Problems in Engineering 5

robot 119899 is the number of unit modules 119899 minus 1 is the numberof joints 119894 represents 119894th joint 119894 = 1 2 119899 minus 1

120593119894 is defined as the relative rotation angle between the119894th joint and the (119894 minus 1)th joint The relative rotation anglefunction of the 119894th joint in dynamic condition can be obtainedas follows

120593119894 (119905) = minus21198860 sin (1198961119897) sin (120596119905 + 1198961 (119904 minus 2 (119894 minus 1) 119897)) (2)

where 1198860 is the initial angle of serpenoid curve 1198961 is the scalefactor of jointrsquos relative rotation angle 119904 is the total lengthof serpenoid curve 2119897 is the length of unit module of snakerobot 119894 represents 119894th joint 119894 = 1 2 119899 minus 1 Here 1198961 =2120587(119904 + 119888) 119888 is the adjustment parameter

Amodel of extreme learningmachine (ELM) algorithm isa feed-forward neural network with single hidden layer Thebasic idea is that all the hidden node parameters (includingthe weight between the hidden layer and the input layer andthe bias of the hidden layer nodes) are randomly generatedand are independent of the objective functions and thetraining sample and do not need iterative adjustment Onlythe number of hidden layer nodes needs to be set and thenthe weight between the hidden layer and the output layeris analyzed and calculated The optimal weight coefficientis obtained by using the particle swarm optimization (PSO)algorithm and the final network output acquired is the opti-mal solution If the pitch angle is optimized the algorithm isused to optimize formula (1) If the relative rotation angle isoptimized the algorithm is used to optimize formula (2)Thefollowing is mainly aimed at the optimization of pitch anglein the second step

The systemmodel is the 3-6-1 type networkThe networkinput is three kinds of random permitted solution 120579119894 =[1205791198941 1205791198942 1205791198943]119879 (119894 = 1 2 3) which indicates the first three jointangles of snake robot when the obstacle is three differentheights The hidden layer nodes are 6 The output node ofnetwork is 1 which corresponds to the actual angles of thefirst three joints of the snake robot when surmounting theobstacle The angles specified by each expert rule in thefirst step are used as the expected angles The error betweenthe actual angles and the expected angles of the joints isminimized by the extreme learning algorithm that is theerror between the network output (actual angles) and theexpected output (expected angles) is minimized and Δ120579119894 rarr 0is accomplished

The extreme learning algorithm is equivalent to solvingthe objective function 119871

min 119871

= 12100381710038171003817100381712057310038171003817100381710038172 + 12119862

3

sum119894=1

1003817100381710038171003817Δ12057911989410038171003817100381710038172

minus3

sum119894=1

6

sum119895=1

120582119894 (ℎ (120579119894) 120573119895 minus 119910119894 minus Δ120579119894)

(3)

where 120579119894 = [1205791198941 1205791198942 1205791198943]119879 (119894 = 1 2 3) are input neurons forextreme learning machine 119884 = [1199101 1199102 1199103]119879 is expectedoutput for extreme learning machine 120573 is weight between

hidden layer and output layer Δ120579119894 is pitch angle errorof snake robot of network training 119862 is correspondingpenalty factor of Δ120579119894 120582119894 is Lagrange multiplier ℎ(120579119894) =[119866(1198861 1198871 120579119894) 119866(1198862 1198872 120579119894) 119866(119886119871 119887119871 120579119894)] is the output vec-tor of hidden layer about 120579119894 where119866(119886119895 119887119895 120579119894) is the output ofthe 119895th hidden node through the activation function 119886119895 is theweight between the 119895th hidden layer node and the networkinput 119887119895 is the bias of the 119895th hidden layer node Here thehyperbolic function is chosen as the activation function theinput of the 119895th hidden node of the network is gained as thefollowing formula

119902119895 =6

sum119895=1

119886119895120579119894 + 119887119895 (4)

So the output vector of the 119895th hidden node about 120579119894 is asfollows

ℎ119895 (120579119894) = 1 minus 119890minus1199011199021198951 + 119890minus119901119902119895 (5)

where 119901 is the optimal weight coefficientCalculate the partial derivative for each variable of the

objective function 119871120597119871120597120573119895 = 0 997888rarr

120573119895 =3

sum119894=1

120582119894ℎ (120579119894)119879 997888rarr

120573 = 119867119879120582120597119871

120597 (Δ120579119894) = 0 997888rarr120582119894 = 119862 (Δ120579119894)120597119871120597120582119894 = 0 997888rarr

ℎ (120579119894) 120573 minus 119910119879119894 + (Δ120579119894)119879 = 0

(6)

where119867 is a 3 times 6-dimensional hidden layer output matrix

119867 = [ℎ (1205791) ℎ (1205792) ℎ (1205793)]119879 (7)

because

119884 = [1199101 1199102 1199103]119879 (8)

From formula (3) we obtain 120597119871(120597120573119895 120597(Δ120579119894) 120597120582119894) gt 0So according to the principle of least squares the followingformula can be derived

( 119868119862 + 119867119867119879)120582 = 119884 (9)

Then the weight 120573 can be deduced as shown in thefollowing formula

120573 = 119867119879120582 = 119867119879 ( 119868119862 + 119867119867119879)minus1 119884 (10)

6 Mathematical Problems in Engineering

(a) (b)

Figure 6 (a) Action 1 of surmounting the obstacle (b) Action 2 of surmounting the obstacle

Therefore the output formula (11) of the extreme learningmachine is obtained

119891 (120579119894) = ℎ (120579119894) 120573 =6

sum119895=1

ℎ119895 (120579119894)119867119879 ( 1119862 + 119867119867119879)minus1 119884 (11)

33 The Third Step Particle Swarm Optimization WeightCoefficient 119901 In formula (11) in order to solve the optimalweight coefficient 119901 of hidden layer matrix the particleswarm optimization algorithm is used In the process ofsolving the particle is updated by tracking the two optimalvaluesThe first one is the optimal solution which is searchedby the particle itself and the other is the optimal solutionsearched by the whole swarm so far The formula used is asfollows

V119894 (119905 + 1) = 120596V119894 (119905) + 11988811199031 (119909119901best119894 minus 119909119894 (119905))+ 11988821199032 (119909119892best119894 minus 119909119894 (119905))

119909119894 (119905 + 1) = 119909119894 (119905) + V119894 (119905 + 1) (12)

where 119894 represents a particle 119909119894 indicates the position ofthe particle at 119905 moment (corresponding to the optimalweight coefficient 119901 of output matrix of the hidden layer at119905moment) V119894 indicates the velocity of particles at 119905moment119909119901best119894 represents the best position of the particle so far 119909119892best119894represents the best position searched by the whole swarmso far 0 lt 120596 lt 1 is inertial coefficient 1198881 and 1198882 arelearning factors 1199031 and 1199032 are the randomnumbers uniformlydistributed on interval (0 1) After calculating V119894(119905 + 1) theposition 119909119894(119905 + 1) of the particle 119894 at next moment can becalculatedThat is position 119909119894 is changed bymodifying speedV119894 to make Δ119901119894 rarr 0 achieving optimal weight coefficient 119901

In this system the weight coefficient of hidden layermatrix is optimized by the particle swarm optimizationalgorithm It makes that the error between the actual outputof extreme learning machine 119891(120579) and the expected output119884 is minimized that is Δ120579119894 rarr 0 The optimal pitch angle ofeach joint is obtained

4 Simulation Experiment and Result Analysis

Combined with the snake robotrsquos behavior of surmountingobstacle which are shown in Figures 6(a) and 6(b) the 15

training samples and 5 test samples were randomly selectedInput variables are pitch angles of the first three jointswhen the obstacle is three different heights that is 120579119894 =[1205791198941 1205791198942 1205791198943]119879 119894 = 1 2 3 and input layer nodes are 3 Outputvariables are the actual pitch angles of the first three jointsthat is 119891(120579) = [119891(1205791) 119891(1205792) 119891(1205793)]119879 and the output nodeis 1 The computer simulation is carried out in MATLAB

The effects of the ELM and POSELM control modelsare evaluated by comparing the following 4 indicators Theperformance and generalization ability of the model areevaluated by calculating MSE (mean square error) and deter-minant coefficient 1198772 The computation speed is evaluated bycomparing the runtime of models The stability of the modelis evaluated by analyzing the effect of the number of hiddenlayer nodes on MRE (mean relative error)

(1) MSE (Mean Square Error) and Determinant Coefficient 1198772Here

MSE = 1119899119899

sum119894=1

(119891 (120579119894) minus 119910119894)2

1198772

= (119899sum119899119894=1 119891 (120579119894) 119910119894 minus sum119899119894=1 119891 (120579119894)sum119899119894=1 119910119894)2(119899sum119899119894=1 119891 (120579119894)2 minus (sum119899119894=1 119891 (120579119894))2) (119899sum119899119894=1 1199101198942 minus (sum119899119894=1 119910119894)2)

(13)

In formula (13) 119899 represents the number of samples119891(120579119894) is the output of the optimal control model and 119910119894 isthe expected output The smaller the MSE the better theperformance of themodelThe value of1198772 is in the interval of[0 1]The closer to 1 the better the performance of themodel

PSOELM and ELM are used respectively to control thejoint pitch angles of snake robot and the simulation resultsare shown in Figure 7 The 119909-axis represents the first threejoints of snake robot and the 119910-axis indicates the joint pitchangle During surmounting the obstacle when the obstacleheight ℎ lt 5 cm pitch angles of the first three joints arerespectively controlled by the PSOELM and ELM and theresults are respectively given as shown in Figures 7(a) and7(b) Determinant coefficient 1198772 is 1 and mean square errorof pitch angles respectively reaches 64198 times 10ndash35 and 10272times 10minus32 when the obstacle height 5 cm lt ℎ lt 8 cm pitch

Mathematical Problems in Engineering 7

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

Expected outputPSOELM output

(mse = 64198e minus 35 R2 = 1)

(a)

Expected outputELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 32 R2 = 1)

(b)

Expected outputPSOELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 41087e minus 33 R2 = 1)

(c)

Expected outputELM output

(mse = 13132e minus 32 R2 = 1)

1 2 3Joint number

0807060504030201

0

Pitc

h an

gle (

rad)

minus01

(d)

Expected outputPSOELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 33 R2 = 1)

(e)

Expected outputELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 12326e minus 32 R2 = 1)

(f)

Figure 7 (a) Pitch angles optimized by the PSOELM (ℎ lt 5 cm) (b) Pitch angles controlled by the ELM (ℎ lt 5 cm) (c) Pitch angles optimizedby the PSOELM (5 cm lt ℎ lt 8 cm) (d) Pitch angles controlled by the ELM (5 cm lt ℎ lt 8 cm) (e) Pitch angles optimized by the PSOELM(8 cm lt ℎ lt 12 cm) (f) Pitch angles controlled by the ELM (8 cm lt ℎ lt 12 cm)

8 Mathematical Problems in Engineering

Table 1 MSE comparison between PSOELM and ELM

Algorithm types MSE of pitch angle(ℎ lt 5 cm)

MSE of pitch angle(5 cm lt ℎ lt 8 cm)

MSE of pitch angle(8 cm lt ℎ lt 12 cm)

PSOELM 64198 times 10minus35 41087 times 10minus33 10272 times 10minus33

ELM 10272 times 10minus32 13132 times 10minus32 12326 times 10minus32

018

016

014

012

01

008

006

004

0021 2 3 4 5 6 7 8 9 10

Model number

Runt

ime (

s)

POSELMELM

Figure 8 Comparison of the runtime of the 10 models (POSELMversus ELM)

angles of the first three joints are respectively controlled bythe PSOELMand ELM and the results are respectively givenas shown in Figures 7(c) and 7(d) Determinant coefficient1198772 is 1 and mean square error of pitch angles respectivelyreaches 41087 times 10ndash33 and 13132 times 10minus32 when the obstacleheight 8 cm lt ℎ lt 12 cm pitch angles of the first three jointsare respectively controlled by the PSOELM and ELM andthe results are respectively given as shown in Figures 7(e)and 7(f) Determinant coefficient 1198772 is 1 and mean squareerror of pitch angles respectively reaches 10272 times 10ndash33 and12326 times 10minus32 MSE based on PSOELM and ELM is shown inTable 1 It can be seen from Figure 7 and Table 1 comparedwith ELM the smaller mean square error and better controlaccuracy and generalization ability are acquired by PSOELMOptimal control of joint pitch angles can be realized

(2) The Model Runtime Since the training set and the testset are generated randomly each runtime of the model isdifferentThe above-mentioned 10 identical ELMmodels and10 identical POSELMmodels are respectively selected to testtheir computation speedThemaximumnumber of iterationsis 3 As shown in Figure 8 the average runtime of the 10 ELMmodels and the 10 POSELM models is respectively 00426 Sand 00535 S So the runtime of the ELM and POSELMmodels is roughly the same and it is all around 50ms It canbe seen that the POSELMmodel continues the characteristicsof the fast learning of the ELMmodel

j

times10minus5

PSOELMELM

6571

5459

4347

3235

2123

10112 64 8 10 12 14 16

MRE

Figure 9 Hidden layer nodes andmean relative error (MRE) curves(POSELM versus ELM)

(3) The Stability of the Model The effect of the numberof hidden layer nodes on MRE is analyzed to evaluate thestability of the model The relationship curves between thehidden layer node 119895 and MRE are shown in Figure 9 Asobtained from Figure 9 the ELMmodel shows great volatilitywith the change of 119895 which is caused by random selectionof input weight and hidden layer node bias In the POSELMmodel the fluctuation of MRE is smaller with the change of119895 and the smaller hidden layer nodes can ensure that MRE isthe smallestWhen 119895 is 6 MRE is the smallest which is 13673times 10minus16 The POSELM model has the characteristic of fastsearching for the optimal and stability and it has significantadvantages in the control of the joint pitch angles of the snakerobot

5 Conclusion

A coal mine rescue snake robot is developed and takingthe robot as an experimental platform aiming at the robotrsquosobstacle surmounting behavior a pose control algorithmbased on particle swarm optimization weight coefficient ofextreme learningmachine (PSOELM) is studied in this paperThe following conclusions are drawn

(1) The mechanical structure and control system ofthe coal mine rescue snake robot are designed and maderespectively The mechanical part is consisted of five unitmodules five connecting plates four orthogonal joints andtwo speed servomotors The robot has better capability to

Mathematical Problems in Engineering 9

surmount the obstacle because of using the self-made bladeswheels The control system is made up of the power sourceenvironmental detection system pose control system mastercontroller mobile mechanism obstacle avoidance modulecommunication module and host computer system Thesnake robot can walk on the rugged grounds By controllingthe direction servomotors serpentine straight concertinaand head rising posture of the snake robot can be acquiredand the speed of the snake robot can be changed by control-ling the speed servomotors

(2) The pose control algorithm based on PSOELM isproposed and discussed compared with simulation resultsof the algorithm based on ELM the PSOELM algorithmhas the following advantages the smaller mean square errorand better control accuracy and generalization ability areacquired the characteristics of fast learning of ELM arecontinued having the characteristic of fast searching for theoptimal and better stability so optimal control of robotrsquos jointpitch angles is achieved by the PSOELM algorithm

(3)ThePSOELMalgorithm is applied to the surmountingobstacle control of the developed snake robot and it lays thefoundation for further implement of the coal mine rescue

Disclosure

The coal mine rescue snake robot developed won specialaward in 2016 Chinese Education Robot Contest

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research has been supported by Foundation of Scienceand Technology Innovation Project of China Coal Technol-ogy Engineering Group (no KJ3013-XBMJ-03) and cultivat-ing fund of Xirsquoan University of Science And Technology (no2013024)

References

[1] A Crespi A Badertscher A Guignard and A J IjspeertldquoAmphiBot I An amphibious snake-like robotrdquo Robotics andAutonomous Systems vol 50 no 4 pp 163ndash175 2005

[2] S Hirose Biologically Inspired Robots (Snake-like Locomotorsand Manipulators) Oxford University Press Oxford UK 1993

[3] Y C Wang L Chen S G Ma et al ldquoStudies on lateral roilinglocomotion of a snake robotrdquo in Proceedings of the IntemationalConference on Robotics and Automation IEEE pp 5070ndash5074Piscataway NJ USA 2004

[4] C Ye S Ma B Li and Y Wang ldquoTurning and side motionof snake-like robotrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation (ICRA rsquo04) pp 5075ndash5080 IEEE May 2004

[5] R L Hatton and H Choset ldquoGenerating gaits for snakerobots Annealed chain fitting and keyframe wave extractionrdquoAutonomous Robots vol 28 no 3 pp 271ndash281 2010

[6] Y Xie U Zhenli and X Huigang ldquoResearch on underwa-ter snake-like robots mechanism design and their serpentineswimming performancerdquo Chinese High Technology Letters vol26 no 6 pp 599ndash605 2016

[7] J Ostrowski and J Burdick ldquoThe geometricmechanics of undu-latory robotic locomotionrdquo International Journal of RoboticsResearch vol 17 no 7 pp 683ndash701 1998

[8] P Liljeback K Y Pettersen and K Stavdahl ldquoModelling andcontrol of obstacle-aided snake robot locomotion based onjam resolutionrdquo in Proceedings of the 2009 IEEE InternationalConference on Robotics and Automation ICRA rsquo09 pp 3807ndash3814 Japan May 2009

[9] L Chen Y-C Wang S-G Ma and B Li ldquoStudy of laterallocomotion of snake robotrdquo JiqirenRobot vol 25 no 3 p 2462003

[10] W Wei and C Sun ldquoResearch on Gait Generation and Controlof Snake-like Robot for Bridge Cable Climbing [J]rdquo ChinaMechanicalengineering vol 23 no 10 pp 1230ndash1235 2012

[11] X Guo S-GMa B Li M-HWang and Y-CWang ldquoVelocitytracking control of a snake-like robot with a dynamics andcontrol unified modelrdquo Zidonghua XuebaoActa AutomaticaSinica vol 41 no 11 pp 1847ndash1856 2015

[12] Q Cheng G Wu S Li et al ldquoStatic mechanism of a climbingsnake robot navigating obstaclerdquoMachinery DesignampManufac-ture vol 3 pp 37ndash40 2016

[13] A Crespi and A J Ijspeert ldquoOnline optimization of swimmingand crawling in an amphibious snake robotrdquo IEEE Transactionson Robotics vol 24 no 1 pp 75ndash87 2008

[14] Z Lu S Ma B Li and Y Wang ldquoSnake-like robot con-troller with cyclic inhibitory CPG modelrdquo Jixie GongchengXuebaoChinese Journal of Mechanical Engineering vol 42 no5 pp 137ndash143 2006

[15] X Lian Guo W X Lian et al ldquoCPG model parametersoptimization based on genetic algorithm for snake-like robotrdquoComputure Engineeing And Design vol 36 pp 1859ndash1864 2015

[16] Q Gao Z-L Wang W-J Hu and L-Y Zhao ldquoResearch onrealization and environmental adaptability of serpentine loco-motion for a snake robotrdquoDalian Ligong Daxue XuebaoJournalof Dalian University of Technology vol 55 no 2 pp 203ndash2082015

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Mathematical Problems in Engineering

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4 Mathematical Problems in Engineering

Initialization

Start

aheadStraight

Avoid obstacleMove ahead

Whether

in front

there are obstacles

End

PSOELMOptimizing by

PSOELMOptimizing by

PSOELMOptimizing by

Yes

Yes

Yes

Yes

No

No

No

No

Execute R-1

Execute R-2

Execute R-3

ℎ lt 5

ℎ lt 8

ℎ lt 12

Figure 5 Flowchart of the pose control algorithm

And intelligent identification and location of cracks on thetunnel could also be achieved

3 Pose Control AlgorithmBased on the PSOELM

Pose control algorithm based on particle swarm optimizationweight coefficient of extreme learning machine (PSOELM)is proposed and the algorithm is applied to the robotrsquossurmounting obstacle behavior The obstacles are dividedinto cuboids cubes or cylinders The flowchart of the posecontrol algorithm is shown in Figure 5 in which R-1 R-2 and R-3 refer to the first three rules in the expert rulesof robotrsquos pose control The algorithm is composed of three

steps firstly the expert rules of robotrsquos pose control areobtained secondly the control model based on extremelearning machine (ELM) is established thirdly the particleswarm optimization algorithm is used to optimize the hiddenlayer matrix weight coefficient of extreme learning machineso as to obtain the optimized hidden layer matrix and theoptimal control of joint pitch angles of the snake robot isachieved

31 The First Step Expert Rules of Pose Control (1) Whenthe sensors detect the height of obstacle is low (ℎ lt 5 cm)the first joint is raised to 45 degrees and the second joint israised to 15 degrees by UK1 and UK3 and then UK5 andUK7 cause the third and fourth joints to synchronously moveahead Here UK1 UK3 UK5 and UK7 respectively referto the output variables of master controller controlling fourvertical direction servomotors

(2) When the sensors detect the height of obstacle ishigher (5 cm lt ℎ lt 8 cm) the first joint is raised to 45 degreesand the second joint is raised to 35 degrees by UK1 and UK3and then UK5 and UK7 cause the third and fourth joints tosynchronously move ahead

(3) When the sensors detect the height of obstacle ishigher (8 cm lt ℎ lt 12 cm) the first joint is raised to 45degrees and the second joint is raised to 45 degrees and thethird joint is raised to 25 degrees by UK1 UK3 and UK5 andthen UK7 lets the fourth joint move ahead

(4) When the sensors detect the height of obstacle ishighest (ℎ gt 12 cm) the robot chooses the obstacle avoidanceaction to bypass the obstacle

(5)While surmounting the obstacle the robot must bendat the joint (waist) When the head joint of the snake is pastthe apex of the obstacle it must tilt downwards such that thejoint contacts the ground and the angle of the joint in thevertical direction is 0 degrees Such as the first joint inclinesdownward to minus45 degrees and at the same time the jointis associated with the first joint rises When the first jointis on the ground and the joint angle changes to 0 degreesthe actions of surmounting the obstacle are completed Insummary the whole process of surmounting an obstacleincludes the six related actions which are raising the headmoving forward bowing head bowing the body raising thetail and making straightening out

32 The Second Step The Control Model Based on ExtremeLearning Machine (ELM) Snake robotrsquos locomotion of sur-mounting obstacle refer to that in the orthogonal joint theangle of joint in the horizontal direction (namely left andright) keeps 0 degrees while the angle of joint in the verticaldirection (namely up and down) changes according to thecosine curve Here according to the equation of serpenoidcurve curvature of Hirose 120579119894 is defined as the angle betweenthe 119894th joint and the horizontal direction (namely the pitchangle) and expressed as follows

120579119894 = 1198860 cos(119894119871119896119899 ) (1)

where 1198860 is the initial angle of serpenoid curve 119896 is the scalefactor of robotrsquos pitch angle 119871 is the total length of snake

Mathematical Problems in Engineering 5

robot 119899 is the number of unit modules 119899 minus 1 is the numberof joints 119894 represents 119894th joint 119894 = 1 2 119899 minus 1

120593119894 is defined as the relative rotation angle between the119894th joint and the (119894 minus 1)th joint The relative rotation anglefunction of the 119894th joint in dynamic condition can be obtainedas follows

120593119894 (119905) = minus21198860 sin (1198961119897) sin (120596119905 + 1198961 (119904 minus 2 (119894 minus 1) 119897)) (2)

where 1198860 is the initial angle of serpenoid curve 1198961 is the scalefactor of jointrsquos relative rotation angle 119904 is the total lengthof serpenoid curve 2119897 is the length of unit module of snakerobot 119894 represents 119894th joint 119894 = 1 2 119899 minus 1 Here 1198961 =2120587(119904 + 119888) 119888 is the adjustment parameter

Amodel of extreme learningmachine (ELM) algorithm isa feed-forward neural network with single hidden layer Thebasic idea is that all the hidden node parameters (includingthe weight between the hidden layer and the input layer andthe bias of the hidden layer nodes) are randomly generatedand are independent of the objective functions and thetraining sample and do not need iterative adjustment Onlythe number of hidden layer nodes needs to be set and thenthe weight between the hidden layer and the output layeris analyzed and calculated The optimal weight coefficientis obtained by using the particle swarm optimization (PSO)algorithm and the final network output acquired is the opti-mal solution If the pitch angle is optimized the algorithm isused to optimize formula (1) If the relative rotation angle isoptimized the algorithm is used to optimize formula (2)Thefollowing is mainly aimed at the optimization of pitch anglein the second step

The systemmodel is the 3-6-1 type networkThe networkinput is three kinds of random permitted solution 120579119894 =[1205791198941 1205791198942 1205791198943]119879 (119894 = 1 2 3) which indicates the first three jointangles of snake robot when the obstacle is three differentheights The hidden layer nodes are 6 The output node ofnetwork is 1 which corresponds to the actual angles of thefirst three joints of the snake robot when surmounting theobstacle The angles specified by each expert rule in thefirst step are used as the expected angles The error betweenthe actual angles and the expected angles of the joints isminimized by the extreme learning algorithm that is theerror between the network output (actual angles) and theexpected output (expected angles) is minimized and Δ120579119894 rarr 0is accomplished

The extreme learning algorithm is equivalent to solvingthe objective function 119871

min 119871

= 12100381710038171003817100381712057310038171003817100381710038172 + 12119862

3

sum119894=1

1003817100381710038171003817Δ12057911989410038171003817100381710038172

minus3

sum119894=1

6

sum119895=1

120582119894 (ℎ (120579119894) 120573119895 minus 119910119894 minus Δ120579119894)

(3)

where 120579119894 = [1205791198941 1205791198942 1205791198943]119879 (119894 = 1 2 3) are input neurons forextreme learning machine 119884 = [1199101 1199102 1199103]119879 is expectedoutput for extreme learning machine 120573 is weight between

hidden layer and output layer Δ120579119894 is pitch angle errorof snake robot of network training 119862 is correspondingpenalty factor of Δ120579119894 120582119894 is Lagrange multiplier ℎ(120579119894) =[119866(1198861 1198871 120579119894) 119866(1198862 1198872 120579119894) 119866(119886119871 119887119871 120579119894)] is the output vec-tor of hidden layer about 120579119894 where119866(119886119895 119887119895 120579119894) is the output ofthe 119895th hidden node through the activation function 119886119895 is theweight between the 119895th hidden layer node and the networkinput 119887119895 is the bias of the 119895th hidden layer node Here thehyperbolic function is chosen as the activation function theinput of the 119895th hidden node of the network is gained as thefollowing formula

119902119895 =6

sum119895=1

119886119895120579119894 + 119887119895 (4)

So the output vector of the 119895th hidden node about 120579119894 is asfollows

ℎ119895 (120579119894) = 1 minus 119890minus1199011199021198951 + 119890minus119901119902119895 (5)

where 119901 is the optimal weight coefficientCalculate the partial derivative for each variable of the

objective function 119871120597119871120597120573119895 = 0 997888rarr

120573119895 =3

sum119894=1

120582119894ℎ (120579119894)119879 997888rarr

120573 = 119867119879120582120597119871

120597 (Δ120579119894) = 0 997888rarr120582119894 = 119862 (Δ120579119894)120597119871120597120582119894 = 0 997888rarr

ℎ (120579119894) 120573 minus 119910119879119894 + (Δ120579119894)119879 = 0

(6)

where119867 is a 3 times 6-dimensional hidden layer output matrix

119867 = [ℎ (1205791) ℎ (1205792) ℎ (1205793)]119879 (7)

because

119884 = [1199101 1199102 1199103]119879 (8)

From formula (3) we obtain 120597119871(120597120573119895 120597(Δ120579119894) 120597120582119894) gt 0So according to the principle of least squares the followingformula can be derived

( 119868119862 + 119867119867119879)120582 = 119884 (9)

Then the weight 120573 can be deduced as shown in thefollowing formula

120573 = 119867119879120582 = 119867119879 ( 119868119862 + 119867119867119879)minus1 119884 (10)

6 Mathematical Problems in Engineering

(a) (b)

Figure 6 (a) Action 1 of surmounting the obstacle (b) Action 2 of surmounting the obstacle

Therefore the output formula (11) of the extreme learningmachine is obtained

119891 (120579119894) = ℎ (120579119894) 120573 =6

sum119895=1

ℎ119895 (120579119894)119867119879 ( 1119862 + 119867119867119879)minus1 119884 (11)

33 The Third Step Particle Swarm Optimization WeightCoefficient 119901 In formula (11) in order to solve the optimalweight coefficient 119901 of hidden layer matrix the particleswarm optimization algorithm is used In the process ofsolving the particle is updated by tracking the two optimalvaluesThe first one is the optimal solution which is searchedby the particle itself and the other is the optimal solutionsearched by the whole swarm so far The formula used is asfollows

V119894 (119905 + 1) = 120596V119894 (119905) + 11988811199031 (119909119901best119894 minus 119909119894 (119905))+ 11988821199032 (119909119892best119894 minus 119909119894 (119905))

119909119894 (119905 + 1) = 119909119894 (119905) + V119894 (119905 + 1) (12)

where 119894 represents a particle 119909119894 indicates the position ofthe particle at 119905 moment (corresponding to the optimalweight coefficient 119901 of output matrix of the hidden layer at119905moment) V119894 indicates the velocity of particles at 119905moment119909119901best119894 represents the best position of the particle so far 119909119892best119894represents the best position searched by the whole swarmso far 0 lt 120596 lt 1 is inertial coefficient 1198881 and 1198882 arelearning factors 1199031 and 1199032 are the randomnumbers uniformlydistributed on interval (0 1) After calculating V119894(119905 + 1) theposition 119909119894(119905 + 1) of the particle 119894 at next moment can becalculatedThat is position 119909119894 is changed bymodifying speedV119894 to make Δ119901119894 rarr 0 achieving optimal weight coefficient 119901

In this system the weight coefficient of hidden layermatrix is optimized by the particle swarm optimizationalgorithm It makes that the error between the actual outputof extreme learning machine 119891(120579) and the expected output119884 is minimized that is Δ120579119894 rarr 0 The optimal pitch angle ofeach joint is obtained

4 Simulation Experiment and Result Analysis

Combined with the snake robotrsquos behavior of surmountingobstacle which are shown in Figures 6(a) and 6(b) the 15

training samples and 5 test samples were randomly selectedInput variables are pitch angles of the first three jointswhen the obstacle is three different heights that is 120579119894 =[1205791198941 1205791198942 1205791198943]119879 119894 = 1 2 3 and input layer nodes are 3 Outputvariables are the actual pitch angles of the first three jointsthat is 119891(120579) = [119891(1205791) 119891(1205792) 119891(1205793)]119879 and the output nodeis 1 The computer simulation is carried out in MATLAB

The effects of the ELM and POSELM control modelsare evaluated by comparing the following 4 indicators Theperformance and generalization ability of the model areevaluated by calculating MSE (mean square error) and deter-minant coefficient 1198772 The computation speed is evaluated bycomparing the runtime of models The stability of the modelis evaluated by analyzing the effect of the number of hiddenlayer nodes on MRE (mean relative error)

(1) MSE (Mean Square Error) and Determinant Coefficient 1198772Here

MSE = 1119899119899

sum119894=1

(119891 (120579119894) minus 119910119894)2

1198772

= (119899sum119899119894=1 119891 (120579119894) 119910119894 minus sum119899119894=1 119891 (120579119894)sum119899119894=1 119910119894)2(119899sum119899119894=1 119891 (120579119894)2 minus (sum119899119894=1 119891 (120579119894))2) (119899sum119899119894=1 1199101198942 minus (sum119899119894=1 119910119894)2)

(13)

In formula (13) 119899 represents the number of samples119891(120579119894) is the output of the optimal control model and 119910119894 isthe expected output The smaller the MSE the better theperformance of themodelThe value of1198772 is in the interval of[0 1]The closer to 1 the better the performance of themodel

PSOELM and ELM are used respectively to control thejoint pitch angles of snake robot and the simulation resultsare shown in Figure 7 The 119909-axis represents the first threejoints of snake robot and the 119910-axis indicates the joint pitchangle During surmounting the obstacle when the obstacleheight ℎ lt 5 cm pitch angles of the first three joints arerespectively controlled by the PSOELM and ELM and theresults are respectively given as shown in Figures 7(a) and7(b) Determinant coefficient 1198772 is 1 and mean square errorof pitch angles respectively reaches 64198 times 10ndash35 and 10272times 10minus32 when the obstacle height 5 cm lt ℎ lt 8 cm pitch

Mathematical Problems in Engineering 7

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

Expected outputPSOELM output

(mse = 64198e minus 35 R2 = 1)

(a)

Expected outputELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 32 R2 = 1)

(b)

Expected outputPSOELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 41087e minus 33 R2 = 1)

(c)

Expected outputELM output

(mse = 13132e minus 32 R2 = 1)

1 2 3Joint number

0807060504030201

0

Pitc

h an

gle (

rad)

minus01

(d)

Expected outputPSOELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 33 R2 = 1)

(e)

Expected outputELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 12326e minus 32 R2 = 1)

(f)

Figure 7 (a) Pitch angles optimized by the PSOELM (ℎ lt 5 cm) (b) Pitch angles controlled by the ELM (ℎ lt 5 cm) (c) Pitch angles optimizedby the PSOELM (5 cm lt ℎ lt 8 cm) (d) Pitch angles controlled by the ELM (5 cm lt ℎ lt 8 cm) (e) Pitch angles optimized by the PSOELM(8 cm lt ℎ lt 12 cm) (f) Pitch angles controlled by the ELM (8 cm lt ℎ lt 12 cm)

8 Mathematical Problems in Engineering

Table 1 MSE comparison between PSOELM and ELM

Algorithm types MSE of pitch angle(ℎ lt 5 cm)

MSE of pitch angle(5 cm lt ℎ lt 8 cm)

MSE of pitch angle(8 cm lt ℎ lt 12 cm)

PSOELM 64198 times 10minus35 41087 times 10minus33 10272 times 10minus33

ELM 10272 times 10minus32 13132 times 10minus32 12326 times 10minus32

018

016

014

012

01

008

006

004

0021 2 3 4 5 6 7 8 9 10

Model number

Runt

ime (

s)

POSELMELM

Figure 8 Comparison of the runtime of the 10 models (POSELMversus ELM)

angles of the first three joints are respectively controlled bythe PSOELMand ELM and the results are respectively givenas shown in Figures 7(c) and 7(d) Determinant coefficient1198772 is 1 and mean square error of pitch angles respectivelyreaches 41087 times 10ndash33 and 13132 times 10minus32 when the obstacleheight 8 cm lt ℎ lt 12 cm pitch angles of the first three jointsare respectively controlled by the PSOELM and ELM andthe results are respectively given as shown in Figures 7(e)and 7(f) Determinant coefficient 1198772 is 1 and mean squareerror of pitch angles respectively reaches 10272 times 10ndash33 and12326 times 10minus32 MSE based on PSOELM and ELM is shown inTable 1 It can be seen from Figure 7 and Table 1 comparedwith ELM the smaller mean square error and better controlaccuracy and generalization ability are acquired by PSOELMOptimal control of joint pitch angles can be realized

(2) The Model Runtime Since the training set and the testset are generated randomly each runtime of the model isdifferentThe above-mentioned 10 identical ELMmodels and10 identical POSELMmodels are respectively selected to testtheir computation speedThemaximumnumber of iterationsis 3 As shown in Figure 8 the average runtime of the 10 ELMmodels and the 10 POSELM models is respectively 00426 Sand 00535 S So the runtime of the ELM and POSELMmodels is roughly the same and it is all around 50ms It canbe seen that the POSELMmodel continues the characteristicsof the fast learning of the ELMmodel

j

times10minus5

PSOELMELM

6571

5459

4347

3235

2123

10112 64 8 10 12 14 16

MRE

Figure 9 Hidden layer nodes andmean relative error (MRE) curves(POSELM versus ELM)

(3) The Stability of the Model The effect of the numberof hidden layer nodes on MRE is analyzed to evaluate thestability of the model The relationship curves between thehidden layer node 119895 and MRE are shown in Figure 9 Asobtained from Figure 9 the ELMmodel shows great volatilitywith the change of 119895 which is caused by random selectionof input weight and hidden layer node bias In the POSELMmodel the fluctuation of MRE is smaller with the change of119895 and the smaller hidden layer nodes can ensure that MRE isthe smallestWhen 119895 is 6 MRE is the smallest which is 13673times 10minus16 The POSELM model has the characteristic of fastsearching for the optimal and stability and it has significantadvantages in the control of the joint pitch angles of the snakerobot

5 Conclusion

A coal mine rescue snake robot is developed and takingthe robot as an experimental platform aiming at the robotrsquosobstacle surmounting behavior a pose control algorithmbased on particle swarm optimization weight coefficient ofextreme learningmachine (PSOELM) is studied in this paperThe following conclusions are drawn

(1) The mechanical structure and control system ofthe coal mine rescue snake robot are designed and maderespectively The mechanical part is consisted of five unitmodules five connecting plates four orthogonal joints andtwo speed servomotors The robot has better capability to

Mathematical Problems in Engineering 9

surmount the obstacle because of using the self-made bladeswheels The control system is made up of the power sourceenvironmental detection system pose control system mastercontroller mobile mechanism obstacle avoidance modulecommunication module and host computer system Thesnake robot can walk on the rugged grounds By controllingthe direction servomotors serpentine straight concertinaand head rising posture of the snake robot can be acquiredand the speed of the snake robot can be changed by control-ling the speed servomotors

(2) The pose control algorithm based on PSOELM isproposed and discussed compared with simulation resultsof the algorithm based on ELM the PSOELM algorithmhas the following advantages the smaller mean square errorand better control accuracy and generalization ability areacquired the characteristics of fast learning of ELM arecontinued having the characteristic of fast searching for theoptimal and better stability so optimal control of robotrsquos jointpitch angles is achieved by the PSOELM algorithm

(3)ThePSOELMalgorithm is applied to the surmountingobstacle control of the developed snake robot and it lays thefoundation for further implement of the coal mine rescue

Disclosure

The coal mine rescue snake robot developed won specialaward in 2016 Chinese Education Robot Contest

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research has been supported by Foundation of Scienceand Technology Innovation Project of China Coal Technol-ogy Engineering Group (no KJ3013-XBMJ-03) and cultivat-ing fund of Xirsquoan University of Science And Technology (no2013024)

References

[1] A Crespi A Badertscher A Guignard and A J IjspeertldquoAmphiBot I An amphibious snake-like robotrdquo Robotics andAutonomous Systems vol 50 no 4 pp 163ndash175 2005

[2] S Hirose Biologically Inspired Robots (Snake-like Locomotorsand Manipulators) Oxford University Press Oxford UK 1993

[3] Y C Wang L Chen S G Ma et al ldquoStudies on lateral roilinglocomotion of a snake robotrdquo in Proceedings of the IntemationalConference on Robotics and Automation IEEE pp 5070ndash5074Piscataway NJ USA 2004

[4] C Ye S Ma B Li and Y Wang ldquoTurning and side motionof snake-like robotrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation (ICRA rsquo04) pp 5075ndash5080 IEEE May 2004

[5] R L Hatton and H Choset ldquoGenerating gaits for snakerobots Annealed chain fitting and keyframe wave extractionrdquoAutonomous Robots vol 28 no 3 pp 271ndash281 2010

[6] Y Xie U Zhenli and X Huigang ldquoResearch on underwa-ter snake-like robots mechanism design and their serpentineswimming performancerdquo Chinese High Technology Letters vol26 no 6 pp 599ndash605 2016

[7] J Ostrowski and J Burdick ldquoThe geometricmechanics of undu-latory robotic locomotionrdquo International Journal of RoboticsResearch vol 17 no 7 pp 683ndash701 1998

[8] P Liljeback K Y Pettersen and K Stavdahl ldquoModelling andcontrol of obstacle-aided snake robot locomotion based onjam resolutionrdquo in Proceedings of the 2009 IEEE InternationalConference on Robotics and Automation ICRA rsquo09 pp 3807ndash3814 Japan May 2009

[9] L Chen Y-C Wang S-G Ma and B Li ldquoStudy of laterallocomotion of snake robotrdquo JiqirenRobot vol 25 no 3 p 2462003

[10] W Wei and C Sun ldquoResearch on Gait Generation and Controlof Snake-like Robot for Bridge Cable Climbing [J]rdquo ChinaMechanicalengineering vol 23 no 10 pp 1230ndash1235 2012

[11] X Guo S-GMa B Li M-HWang and Y-CWang ldquoVelocitytracking control of a snake-like robot with a dynamics andcontrol unified modelrdquo Zidonghua XuebaoActa AutomaticaSinica vol 41 no 11 pp 1847ndash1856 2015

[12] Q Cheng G Wu S Li et al ldquoStatic mechanism of a climbingsnake robot navigating obstaclerdquoMachinery DesignampManufac-ture vol 3 pp 37ndash40 2016

[13] A Crespi and A J Ijspeert ldquoOnline optimization of swimmingand crawling in an amphibious snake robotrdquo IEEE Transactionson Robotics vol 24 no 1 pp 75ndash87 2008

[14] Z Lu S Ma B Li and Y Wang ldquoSnake-like robot con-troller with cyclic inhibitory CPG modelrdquo Jixie GongchengXuebaoChinese Journal of Mechanical Engineering vol 42 no5 pp 137ndash143 2006

[15] X Lian Guo W X Lian et al ldquoCPG model parametersoptimization based on genetic algorithm for snake-like robotrdquoComputure Engineeing And Design vol 36 pp 1859ndash1864 2015

[16] Q Gao Z-L Wang W-J Hu and L-Y Zhao ldquoResearch onrealization and environmental adaptability of serpentine loco-motion for a snake robotrdquoDalian Ligong Daxue XuebaoJournalof Dalian University of Technology vol 55 no 2 pp 203ndash2082015

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 5

robot 119899 is the number of unit modules 119899 minus 1 is the numberof joints 119894 represents 119894th joint 119894 = 1 2 119899 minus 1

120593119894 is defined as the relative rotation angle between the119894th joint and the (119894 minus 1)th joint The relative rotation anglefunction of the 119894th joint in dynamic condition can be obtainedas follows

120593119894 (119905) = minus21198860 sin (1198961119897) sin (120596119905 + 1198961 (119904 minus 2 (119894 minus 1) 119897)) (2)

where 1198860 is the initial angle of serpenoid curve 1198961 is the scalefactor of jointrsquos relative rotation angle 119904 is the total lengthof serpenoid curve 2119897 is the length of unit module of snakerobot 119894 represents 119894th joint 119894 = 1 2 119899 minus 1 Here 1198961 =2120587(119904 + 119888) 119888 is the adjustment parameter

Amodel of extreme learningmachine (ELM) algorithm isa feed-forward neural network with single hidden layer Thebasic idea is that all the hidden node parameters (includingthe weight between the hidden layer and the input layer andthe bias of the hidden layer nodes) are randomly generatedand are independent of the objective functions and thetraining sample and do not need iterative adjustment Onlythe number of hidden layer nodes needs to be set and thenthe weight between the hidden layer and the output layeris analyzed and calculated The optimal weight coefficientis obtained by using the particle swarm optimization (PSO)algorithm and the final network output acquired is the opti-mal solution If the pitch angle is optimized the algorithm isused to optimize formula (1) If the relative rotation angle isoptimized the algorithm is used to optimize formula (2)Thefollowing is mainly aimed at the optimization of pitch anglein the second step

The systemmodel is the 3-6-1 type networkThe networkinput is three kinds of random permitted solution 120579119894 =[1205791198941 1205791198942 1205791198943]119879 (119894 = 1 2 3) which indicates the first three jointangles of snake robot when the obstacle is three differentheights The hidden layer nodes are 6 The output node ofnetwork is 1 which corresponds to the actual angles of thefirst three joints of the snake robot when surmounting theobstacle The angles specified by each expert rule in thefirst step are used as the expected angles The error betweenthe actual angles and the expected angles of the joints isminimized by the extreme learning algorithm that is theerror between the network output (actual angles) and theexpected output (expected angles) is minimized and Δ120579119894 rarr 0is accomplished

The extreme learning algorithm is equivalent to solvingthe objective function 119871

min 119871

= 12100381710038171003817100381712057310038171003817100381710038172 + 12119862

3

sum119894=1

1003817100381710038171003817Δ12057911989410038171003817100381710038172

minus3

sum119894=1

6

sum119895=1

120582119894 (ℎ (120579119894) 120573119895 minus 119910119894 minus Δ120579119894)

(3)

where 120579119894 = [1205791198941 1205791198942 1205791198943]119879 (119894 = 1 2 3) are input neurons forextreme learning machine 119884 = [1199101 1199102 1199103]119879 is expectedoutput for extreme learning machine 120573 is weight between

hidden layer and output layer Δ120579119894 is pitch angle errorof snake robot of network training 119862 is correspondingpenalty factor of Δ120579119894 120582119894 is Lagrange multiplier ℎ(120579119894) =[119866(1198861 1198871 120579119894) 119866(1198862 1198872 120579119894) 119866(119886119871 119887119871 120579119894)] is the output vec-tor of hidden layer about 120579119894 where119866(119886119895 119887119895 120579119894) is the output ofthe 119895th hidden node through the activation function 119886119895 is theweight between the 119895th hidden layer node and the networkinput 119887119895 is the bias of the 119895th hidden layer node Here thehyperbolic function is chosen as the activation function theinput of the 119895th hidden node of the network is gained as thefollowing formula

119902119895 =6

sum119895=1

119886119895120579119894 + 119887119895 (4)

So the output vector of the 119895th hidden node about 120579119894 is asfollows

ℎ119895 (120579119894) = 1 minus 119890minus1199011199021198951 + 119890minus119901119902119895 (5)

where 119901 is the optimal weight coefficientCalculate the partial derivative for each variable of the

objective function 119871120597119871120597120573119895 = 0 997888rarr

120573119895 =3

sum119894=1

120582119894ℎ (120579119894)119879 997888rarr

120573 = 119867119879120582120597119871

120597 (Δ120579119894) = 0 997888rarr120582119894 = 119862 (Δ120579119894)120597119871120597120582119894 = 0 997888rarr

ℎ (120579119894) 120573 minus 119910119879119894 + (Δ120579119894)119879 = 0

(6)

where119867 is a 3 times 6-dimensional hidden layer output matrix

119867 = [ℎ (1205791) ℎ (1205792) ℎ (1205793)]119879 (7)

because

119884 = [1199101 1199102 1199103]119879 (8)

From formula (3) we obtain 120597119871(120597120573119895 120597(Δ120579119894) 120597120582119894) gt 0So according to the principle of least squares the followingformula can be derived

( 119868119862 + 119867119867119879)120582 = 119884 (9)

Then the weight 120573 can be deduced as shown in thefollowing formula

120573 = 119867119879120582 = 119867119879 ( 119868119862 + 119867119867119879)minus1 119884 (10)

6 Mathematical Problems in Engineering

(a) (b)

Figure 6 (a) Action 1 of surmounting the obstacle (b) Action 2 of surmounting the obstacle

Therefore the output formula (11) of the extreme learningmachine is obtained

119891 (120579119894) = ℎ (120579119894) 120573 =6

sum119895=1

ℎ119895 (120579119894)119867119879 ( 1119862 + 119867119867119879)minus1 119884 (11)

33 The Third Step Particle Swarm Optimization WeightCoefficient 119901 In formula (11) in order to solve the optimalweight coefficient 119901 of hidden layer matrix the particleswarm optimization algorithm is used In the process ofsolving the particle is updated by tracking the two optimalvaluesThe first one is the optimal solution which is searchedby the particle itself and the other is the optimal solutionsearched by the whole swarm so far The formula used is asfollows

V119894 (119905 + 1) = 120596V119894 (119905) + 11988811199031 (119909119901best119894 minus 119909119894 (119905))+ 11988821199032 (119909119892best119894 minus 119909119894 (119905))

119909119894 (119905 + 1) = 119909119894 (119905) + V119894 (119905 + 1) (12)

where 119894 represents a particle 119909119894 indicates the position ofthe particle at 119905 moment (corresponding to the optimalweight coefficient 119901 of output matrix of the hidden layer at119905moment) V119894 indicates the velocity of particles at 119905moment119909119901best119894 represents the best position of the particle so far 119909119892best119894represents the best position searched by the whole swarmso far 0 lt 120596 lt 1 is inertial coefficient 1198881 and 1198882 arelearning factors 1199031 and 1199032 are the randomnumbers uniformlydistributed on interval (0 1) After calculating V119894(119905 + 1) theposition 119909119894(119905 + 1) of the particle 119894 at next moment can becalculatedThat is position 119909119894 is changed bymodifying speedV119894 to make Δ119901119894 rarr 0 achieving optimal weight coefficient 119901

In this system the weight coefficient of hidden layermatrix is optimized by the particle swarm optimizationalgorithm It makes that the error between the actual outputof extreme learning machine 119891(120579) and the expected output119884 is minimized that is Δ120579119894 rarr 0 The optimal pitch angle ofeach joint is obtained

4 Simulation Experiment and Result Analysis

Combined with the snake robotrsquos behavior of surmountingobstacle which are shown in Figures 6(a) and 6(b) the 15

training samples and 5 test samples were randomly selectedInput variables are pitch angles of the first three jointswhen the obstacle is three different heights that is 120579119894 =[1205791198941 1205791198942 1205791198943]119879 119894 = 1 2 3 and input layer nodes are 3 Outputvariables are the actual pitch angles of the first three jointsthat is 119891(120579) = [119891(1205791) 119891(1205792) 119891(1205793)]119879 and the output nodeis 1 The computer simulation is carried out in MATLAB

The effects of the ELM and POSELM control modelsare evaluated by comparing the following 4 indicators Theperformance and generalization ability of the model areevaluated by calculating MSE (mean square error) and deter-minant coefficient 1198772 The computation speed is evaluated bycomparing the runtime of models The stability of the modelis evaluated by analyzing the effect of the number of hiddenlayer nodes on MRE (mean relative error)

(1) MSE (Mean Square Error) and Determinant Coefficient 1198772Here

MSE = 1119899119899

sum119894=1

(119891 (120579119894) minus 119910119894)2

1198772

= (119899sum119899119894=1 119891 (120579119894) 119910119894 minus sum119899119894=1 119891 (120579119894)sum119899119894=1 119910119894)2(119899sum119899119894=1 119891 (120579119894)2 minus (sum119899119894=1 119891 (120579119894))2) (119899sum119899119894=1 1199101198942 minus (sum119899119894=1 119910119894)2)

(13)

In formula (13) 119899 represents the number of samples119891(120579119894) is the output of the optimal control model and 119910119894 isthe expected output The smaller the MSE the better theperformance of themodelThe value of1198772 is in the interval of[0 1]The closer to 1 the better the performance of themodel

PSOELM and ELM are used respectively to control thejoint pitch angles of snake robot and the simulation resultsare shown in Figure 7 The 119909-axis represents the first threejoints of snake robot and the 119910-axis indicates the joint pitchangle During surmounting the obstacle when the obstacleheight ℎ lt 5 cm pitch angles of the first three joints arerespectively controlled by the PSOELM and ELM and theresults are respectively given as shown in Figures 7(a) and7(b) Determinant coefficient 1198772 is 1 and mean square errorof pitch angles respectively reaches 64198 times 10ndash35 and 10272times 10minus32 when the obstacle height 5 cm lt ℎ lt 8 cm pitch

Mathematical Problems in Engineering 7

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

Expected outputPSOELM output

(mse = 64198e minus 35 R2 = 1)

(a)

Expected outputELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 32 R2 = 1)

(b)

Expected outputPSOELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 41087e minus 33 R2 = 1)

(c)

Expected outputELM output

(mse = 13132e minus 32 R2 = 1)

1 2 3Joint number

0807060504030201

0

Pitc

h an

gle (

rad)

minus01

(d)

Expected outputPSOELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 33 R2 = 1)

(e)

Expected outputELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 12326e minus 32 R2 = 1)

(f)

Figure 7 (a) Pitch angles optimized by the PSOELM (ℎ lt 5 cm) (b) Pitch angles controlled by the ELM (ℎ lt 5 cm) (c) Pitch angles optimizedby the PSOELM (5 cm lt ℎ lt 8 cm) (d) Pitch angles controlled by the ELM (5 cm lt ℎ lt 8 cm) (e) Pitch angles optimized by the PSOELM(8 cm lt ℎ lt 12 cm) (f) Pitch angles controlled by the ELM (8 cm lt ℎ lt 12 cm)

8 Mathematical Problems in Engineering

Table 1 MSE comparison between PSOELM and ELM

Algorithm types MSE of pitch angle(ℎ lt 5 cm)

MSE of pitch angle(5 cm lt ℎ lt 8 cm)

MSE of pitch angle(8 cm lt ℎ lt 12 cm)

PSOELM 64198 times 10minus35 41087 times 10minus33 10272 times 10minus33

ELM 10272 times 10minus32 13132 times 10minus32 12326 times 10minus32

018

016

014

012

01

008

006

004

0021 2 3 4 5 6 7 8 9 10

Model number

Runt

ime (

s)

POSELMELM

Figure 8 Comparison of the runtime of the 10 models (POSELMversus ELM)

angles of the first three joints are respectively controlled bythe PSOELMand ELM and the results are respectively givenas shown in Figures 7(c) and 7(d) Determinant coefficient1198772 is 1 and mean square error of pitch angles respectivelyreaches 41087 times 10ndash33 and 13132 times 10minus32 when the obstacleheight 8 cm lt ℎ lt 12 cm pitch angles of the first three jointsare respectively controlled by the PSOELM and ELM andthe results are respectively given as shown in Figures 7(e)and 7(f) Determinant coefficient 1198772 is 1 and mean squareerror of pitch angles respectively reaches 10272 times 10ndash33 and12326 times 10minus32 MSE based on PSOELM and ELM is shown inTable 1 It can be seen from Figure 7 and Table 1 comparedwith ELM the smaller mean square error and better controlaccuracy and generalization ability are acquired by PSOELMOptimal control of joint pitch angles can be realized

(2) The Model Runtime Since the training set and the testset are generated randomly each runtime of the model isdifferentThe above-mentioned 10 identical ELMmodels and10 identical POSELMmodels are respectively selected to testtheir computation speedThemaximumnumber of iterationsis 3 As shown in Figure 8 the average runtime of the 10 ELMmodels and the 10 POSELM models is respectively 00426 Sand 00535 S So the runtime of the ELM and POSELMmodels is roughly the same and it is all around 50ms It canbe seen that the POSELMmodel continues the characteristicsof the fast learning of the ELMmodel

j

times10minus5

PSOELMELM

6571

5459

4347

3235

2123

10112 64 8 10 12 14 16

MRE

Figure 9 Hidden layer nodes andmean relative error (MRE) curves(POSELM versus ELM)

(3) The Stability of the Model The effect of the numberof hidden layer nodes on MRE is analyzed to evaluate thestability of the model The relationship curves between thehidden layer node 119895 and MRE are shown in Figure 9 Asobtained from Figure 9 the ELMmodel shows great volatilitywith the change of 119895 which is caused by random selectionof input weight and hidden layer node bias In the POSELMmodel the fluctuation of MRE is smaller with the change of119895 and the smaller hidden layer nodes can ensure that MRE isthe smallestWhen 119895 is 6 MRE is the smallest which is 13673times 10minus16 The POSELM model has the characteristic of fastsearching for the optimal and stability and it has significantadvantages in the control of the joint pitch angles of the snakerobot

5 Conclusion

A coal mine rescue snake robot is developed and takingthe robot as an experimental platform aiming at the robotrsquosobstacle surmounting behavior a pose control algorithmbased on particle swarm optimization weight coefficient ofextreme learningmachine (PSOELM) is studied in this paperThe following conclusions are drawn

(1) The mechanical structure and control system ofthe coal mine rescue snake robot are designed and maderespectively The mechanical part is consisted of five unitmodules five connecting plates four orthogonal joints andtwo speed servomotors The robot has better capability to

Mathematical Problems in Engineering 9

surmount the obstacle because of using the self-made bladeswheels The control system is made up of the power sourceenvironmental detection system pose control system mastercontroller mobile mechanism obstacle avoidance modulecommunication module and host computer system Thesnake robot can walk on the rugged grounds By controllingthe direction servomotors serpentine straight concertinaand head rising posture of the snake robot can be acquiredand the speed of the snake robot can be changed by control-ling the speed servomotors

(2) The pose control algorithm based on PSOELM isproposed and discussed compared with simulation resultsof the algorithm based on ELM the PSOELM algorithmhas the following advantages the smaller mean square errorand better control accuracy and generalization ability areacquired the characteristics of fast learning of ELM arecontinued having the characteristic of fast searching for theoptimal and better stability so optimal control of robotrsquos jointpitch angles is achieved by the PSOELM algorithm

(3)ThePSOELMalgorithm is applied to the surmountingobstacle control of the developed snake robot and it lays thefoundation for further implement of the coal mine rescue

Disclosure

The coal mine rescue snake robot developed won specialaward in 2016 Chinese Education Robot Contest

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research has been supported by Foundation of Scienceand Technology Innovation Project of China Coal Technol-ogy Engineering Group (no KJ3013-XBMJ-03) and cultivat-ing fund of Xirsquoan University of Science And Technology (no2013024)

References

[1] A Crespi A Badertscher A Guignard and A J IjspeertldquoAmphiBot I An amphibious snake-like robotrdquo Robotics andAutonomous Systems vol 50 no 4 pp 163ndash175 2005

[2] S Hirose Biologically Inspired Robots (Snake-like Locomotorsand Manipulators) Oxford University Press Oxford UK 1993

[3] Y C Wang L Chen S G Ma et al ldquoStudies on lateral roilinglocomotion of a snake robotrdquo in Proceedings of the IntemationalConference on Robotics and Automation IEEE pp 5070ndash5074Piscataway NJ USA 2004

[4] C Ye S Ma B Li and Y Wang ldquoTurning and side motionof snake-like robotrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation (ICRA rsquo04) pp 5075ndash5080 IEEE May 2004

[5] R L Hatton and H Choset ldquoGenerating gaits for snakerobots Annealed chain fitting and keyframe wave extractionrdquoAutonomous Robots vol 28 no 3 pp 271ndash281 2010

[6] Y Xie U Zhenli and X Huigang ldquoResearch on underwa-ter snake-like robots mechanism design and their serpentineswimming performancerdquo Chinese High Technology Letters vol26 no 6 pp 599ndash605 2016

[7] J Ostrowski and J Burdick ldquoThe geometricmechanics of undu-latory robotic locomotionrdquo International Journal of RoboticsResearch vol 17 no 7 pp 683ndash701 1998

[8] P Liljeback K Y Pettersen and K Stavdahl ldquoModelling andcontrol of obstacle-aided snake robot locomotion based onjam resolutionrdquo in Proceedings of the 2009 IEEE InternationalConference on Robotics and Automation ICRA rsquo09 pp 3807ndash3814 Japan May 2009

[9] L Chen Y-C Wang S-G Ma and B Li ldquoStudy of laterallocomotion of snake robotrdquo JiqirenRobot vol 25 no 3 p 2462003

[10] W Wei and C Sun ldquoResearch on Gait Generation and Controlof Snake-like Robot for Bridge Cable Climbing [J]rdquo ChinaMechanicalengineering vol 23 no 10 pp 1230ndash1235 2012

[11] X Guo S-GMa B Li M-HWang and Y-CWang ldquoVelocitytracking control of a snake-like robot with a dynamics andcontrol unified modelrdquo Zidonghua XuebaoActa AutomaticaSinica vol 41 no 11 pp 1847ndash1856 2015

[12] Q Cheng G Wu S Li et al ldquoStatic mechanism of a climbingsnake robot navigating obstaclerdquoMachinery DesignampManufac-ture vol 3 pp 37ndash40 2016

[13] A Crespi and A J Ijspeert ldquoOnline optimization of swimmingand crawling in an amphibious snake robotrdquo IEEE Transactionson Robotics vol 24 no 1 pp 75ndash87 2008

[14] Z Lu S Ma B Li and Y Wang ldquoSnake-like robot con-troller with cyclic inhibitory CPG modelrdquo Jixie GongchengXuebaoChinese Journal of Mechanical Engineering vol 42 no5 pp 137ndash143 2006

[15] X Lian Guo W X Lian et al ldquoCPG model parametersoptimization based on genetic algorithm for snake-like robotrdquoComputure Engineeing And Design vol 36 pp 1859ndash1864 2015

[16] Q Gao Z-L Wang W-J Hu and L-Y Zhao ldquoResearch onrealization and environmental adaptability of serpentine loco-motion for a snake robotrdquoDalian Ligong Daxue XuebaoJournalof Dalian University of Technology vol 55 no 2 pp 203ndash2082015

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

6 Mathematical Problems in Engineering

(a) (b)

Figure 6 (a) Action 1 of surmounting the obstacle (b) Action 2 of surmounting the obstacle

Therefore the output formula (11) of the extreme learningmachine is obtained

119891 (120579119894) = ℎ (120579119894) 120573 =6

sum119895=1

ℎ119895 (120579119894)119867119879 ( 1119862 + 119867119867119879)minus1 119884 (11)

33 The Third Step Particle Swarm Optimization WeightCoefficient 119901 In formula (11) in order to solve the optimalweight coefficient 119901 of hidden layer matrix the particleswarm optimization algorithm is used In the process ofsolving the particle is updated by tracking the two optimalvaluesThe first one is the optimal solution which is searchedby the particle itself and the other is the optimal solutionsearched by the whole swarm so far The formula used is asfollows

V119894 (119905 + 1) = 120596V119894 (119905) + 11988811199031 (119909119901best119894 minus 119909119894 (119905))+ 11988821199032 (119909119892best119894 minus 119909119894 (119905))

119909119894 (119905 + 1) = 119909119894 (119905) + V119894 (119905 + 1) (12)

where 119894 represents a particle 119909119894 indicates the position ofthe particle at 119905 moment (corresponding to the optimalweight coefficient 119901 of output matrix of the hidden layer at119905moment) V119894 indicates the velocity of particles at 119905moment119909119901best119894 represents the best position of the particle so far 119909119892best119894represents the best position searched by the whole swarmso far 0 lt 120596 lt 1 is inertial coefficient 1198881 and 1198882 arelearning factors 1199031 and 1199032 are the randomnumbers uniformlydistributed on interval (0 1) After calculating V119894(119905 + 1) theposition 119909119894(119905 + 1) of the particle 119894 at next moment can becalculatedThat is position 119909119894 is changed bymodifying speedV119894 to make Δ119901119894 rarr 0 achieving optimal weight coefficient 119901

In this system the weight coefficient of hidden layermatrix is optimized by the particle swarm optimizationalgorithm It makes that the error between the actual outputof extreme learning machine 119891(120579) and the expected output119884 is minimized that is Δ120579119894 rarr 0 The optimal pitch angle ofeach joint is obtained

4 Simulation Experiment and Result Analysis

Combined with the snake robotrsquos behavior of surmountingobstacle which are shown in Figures 6(a) and 6(b) the 15

training samples and 5 test samples were randomly selectedInput variables are pitch angles of the first three jointswhen the obstacle is three different heights that is 120579119894 =[1205791198941 1205791198942 1205791198943]119879 119894 = 1 2 3 and input layer nodes are 3 Outputvariables are the actual pitch angles of the first three jointsthat is 119891(120579) = [119891(1205791) 119891(1205792) 119891(1205793)]119879 and the output nodeis 1 The computer simulation is carried out in MATLAB

The effects of the ELM and POSELM control modelsare evaluated by comparing the following 4 indicators Theperformance and generalization ability of the model areevaluated by calculating MSE (mean square error) and deter-minant coefficient 1198772 The computation speed is evaluated bycomparing the runtime of models The stability of the modelis evaluated by analyzing the effect of the number of hiddenlayer nodes on MRE (mean relative error)

(1) MSE (Mean Square Error) and Determinant Coefficient 1198772Here

MSE = 1119899119899

sum119894=1

(119891 (120579119894) minus 119910119894)2

1198772

= (119899sum119899119894=1 119891 (120579119894) 119910119894 minus sum119899119894=1 119891 (120579119894)sum119899119894=1 119910119894)2(119899sum119899119894=1 119891 (120579119894)2 minus (sum119899119894=1 119891 (120579119894))2) (119899sum119899119894=1 1199101198942 minus (sum119899119894=1 119910119894)2)

(13)

In formula (13) 119899 represents the number of samples119891(120579119894) is the output of the optimal control model and 119910119894 isthe expected output The smaller the MSE the better theperformance of themodelThe value of1198772 is in the interval of[0 1]The closer to 1 the better the performance of themodel

PSOELM and ELM are used respectively to control thejoint pitch angles of snake robot and the simulation resultsare shown in Figure 7 The 119909-axis represents the first threejoints of snake robot and the 119910-axis indicates the joint pitchangle During surmounting the obstacle when the obstacleheight ℎ lt 5 cm pitch angles of the first three joints arerespectively controlled by the PSOELM and ELM and theresults are respectively given as shown in Figures 7(a) and7(b) Determinant coefficient 1198772 is 1 and mean square errorof pitch angles respectively reaches 64198 times 10ndash35 and 10272times 10minus32 when the obstacle height 5 cm lt ℎ lt 8 cm pitch

Mathematical Problems in Engineering 7

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

Expected outputPSOELM output

(mse = 64198e minus 35 R2 = 1)

(a)

Expected outputELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 32 R2 = 1)

(b)

Expected outputPSOELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 41087e minus 33 R2 = 1)

(c)

Expected outputELM output

(mse = 13132e minus 32 R2 = 1)

1 2 3Joint number

0807060504030201

0

Pitc

h an

gle (

rad)

minus01

(d)

Expected outputPSOELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 33 R2 = 1)

(e)

Expected outputELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 12326e minus 32 R2 = 1)

(f)

Figure 7 (a) Pitch angles optimized by the PSOELM (ℎ lt 5 cm) (b) Pitch angles controlled by the ELM (ℎ lt 5 cm) (c) Pitch angles optimizedby the PSOELM (5 cm lt ℎ lt 8 cm) (d) Pitch angles controlled by the ELM (5 cm lt ℎ lt 8 cm) (e) Pitch angles optimized by the PSOELM(8 cm lt ℎ lt 12 cm) (f) Pitch angles controlled by the ELM (8 cm lt ℎ lt 12 cm)

8 Mathematical Problems in Engineering

Table 1 MSE comparison between PSOELM and ELM

Algorithm types MSE of pitch angle(ℎ lt 5 cm)

MSE of pitch angle(5 cm lt ℎ lt 8 cm)

MSE of pitch angle(8 cm lt ℎ lt 12 cm)

PSOELM 64198 times 10minus35 41087 times 10minus33 10272 times 10minus33

ELM 10272 times 10minus32 13132 times 10minus32 12326 times 10minus32

018

016

014

012

01

008

006

004

0021 2 3 4 5 6 7 8 9 10

Model number

Runt

ime (

s)

POSELMELM

Figure 8 Comparison of the runtime of the 10 models (POSELMversus ELM)

angles of the first three joints are respectively controlled bythe PSOELMand ELM and the results are respectively givenas shown in Figures 7(c) and 7(d) Determinant coefficient1198772 is 1 and mean square error of pitch angles respectivelyreaches 41087 times 10ndash33 and 13132 times 10minus32 when the obstacleheight 8 cm lt ℎ lt 12 cm pitch angles of the first three jointsare respectively controlled by the PSOELM and ELM andthe results are respectively given as shown in Figures 7(e)and 7(f) Determinant coefficient 1198772 is 1 and mean squareerror of pitch angles respectively reaches 10272 times 10ndash33 and12326 times 10minus32 MSE based on PSOELM and ELM is shown inTable 1 It can be seen from Figure 7 and Table 1 comparedwith ELM the smaller mean square error and better controlaccuracy and generalization ability are acquired by PSOELMOptimal control of joint pitch angles can be realized

(2) The Model Runtime Since the training set and the testset are generated randomly each runtime of the model isdifferentThe above-mentioned 10 identical ELMmodels and10 identical POSELMmodels are respectively selected to testtheir computation speedThemaximumnumber of iterationsis 3 As shown in Figure 8 the average runtime of the 10 ELMmodels and the 10 POSELM models is respectively 00426 Sand 00535 S So the runtime of the ELM and POSELMmodels is roughly the same and it is all around 50ms It canbe seen that the POSELMmodel continues the characteristicsof the fast learning of the ELMmodel

j

times10minus5

PSOELMELM

6571

5459

4347

3235

2123

10112 64 8 10 12 14 16

MRE

Figure 9 Hidden layer nodes andmean relative error (MRE) curves(POSELM versus ELM)

(3) The Stability of the Model The effect of the numberof hidden layer nodes on MRE is analyzed to evaluate thestability of the model The relationship curves between thehidden layer node 119895 and MRE are shown in Figure 9 Asobtained from Figure 9 the ELMmodel shows great volatilitywith the change of 119895 which is caused by random selectionof input weight and hidden layer node bias In the POSELMmodel the fluctuation of MRE is smaller with the change of119895 and the smaller hidden layer nodes can ensure that MRE isthe smallestWhen 119895 is 6 MRE is the smallest which is 13673times 10minus16 The POSELM model has the characteristic of fastsearching for the optimal and stability and it has significantadvantages in the control of the joint pitch angles of the snakerobot

5 Conclusion

A coal mine rescue snake robot is developed and takingthe robot as an experimental platform aiming at the robotrsquosobstacle surmounting behavior a pose control algorithmbased on particle swarm optimization weight coefficient ofextreme learningmachine (PSOELM) is studied in this paperThe following conclusions are drawn

(1) The mechanical structure and control system ofthe coal mine rescue snake robot are designed and maderespectively The mechanical part is consisted of five unitmodules five connecting plates four orthogonal joints andtwo speed servomotors The robot has better capability to

Mathematical Problems in Engineering 9

surmount the obstacle because of using the self-made bladeswheels The control system is made up of the power sourceenvironmental detection system pose control system mastercontroller mobile mechanism obstacle avoidance modulecommunication module and host computer system Thesnake robot can walk on the rugged grounds By controllingthe direction servomotors serpentine straight concertinaand head rising posture of the snake robot can be acquiredand the speed of the snake robot can be changed by control-ling the speed servomotors

(2) The pose control algorithm based on PSOELM isproposed and discussed compared with simulation resultsof the algorithm based on ELM the PSOELM algorithmhas the following advantages the smaller mean square errorand better control accuracy and generalization ability areacquired the characteristics of fast learning of ELM arecontinued having the characteristic of fast searching for theoptimal and better stability so optimal control of robotrsquos jointpitch angles is achieved by the PSOELM algorithm

(3)ThePSOELMalgorithm is applied to the surmountingobstacle control of the developed snake robot and it lays thefoundation for further implement of the coal mine rescue

Disclosure

The coal mine rescue snake robot developed won specialaward in 2016 Chinese Education Robot Contest

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research has been supported by Foundation of Scienceand Technology Innovation Project of China Coal Technol-ogy Engineering Group (no KJ3013-XBMJ-03) and cultivat-ing fund of Xirsquoan University of Science And Technology (no2013024)

References

[1] A Crespi A Badertscher A Guignard and A J IjspeertldquoAmphiBot I An amphibious snake-like robotrdquo Robotics andAutonomous Systems vol 50 no 4 pp 163ndash175 2005

[2] S Hirose Biologically Inspired Robots (Snake-like Locomotorsand Manipulators) Oxford University Press Oxford UK 1993

[3] Y C Wang L Chen S G Ma et al ldquoStudies on lateral roilinglocomotion of a snake robotrdquo in Proceedings of the IntemationalConference on Robotics and Automation IEEE pp 5070ndash5074Piscataway NJ USA 2004

[4] C Ye S Ma B Li and Y Wang ldquoTurning and side motionof snake-like robotrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation (ICRA rsquo04) pp 5075ndash5080 IEEE May 2004

[5] R L Hatton and H Choset ldquoGenerating gaits for snakerobots Annealed chain fitting and keyframe wave extractionrdquoAutonomous Robots vol 28 no 3 pp 271ndash281 2010

[6] Y Xie U Zhenli and X Huigang ldquoResearch on underwa-ter snake-like robots mechanism design and their serpentineswimming performancerdquo Chinese High Technology Letters vol26 no 6 pp 599ndash605 2016

[7] J Ostrowski and J Burdick ldquoThe geometricmechanics of undu-latory robotic locomotionrdquo International Journal of RoboticsResearch vol 17 no 7 pp 683ndash701 1998

[8] P Liljeback K Y Pettersen and K Stavdahl ldquoModelling andcontrol of obstacle-aided snake robot locomotion based onjam resolutionrdquo in Proceedings of the 2009 IEEE InternationalConference on Robotics and Automation ICRA rsquo09 pp 3807ndash3814 Japan May 2009

[9] L Chen Y-C Wang S-G Ma and B Li ldquoStudy of laterallocomotion of snake robotrdquo JiqirenRobot vol 25 no 3 p 2462003

[10] W Wei and C Sun ldquoResearch on Gait Generation and Controlof Snake-like Robot for Bridge Cable Climbing [J]rdquo ChinaMechanicalengineering vol 23 no 10 pp 1230ndash1235 2012

[11] X Guo S-GMa B Li M-HWang and Y-CWang ldquoVelocitytracking control of a snake-like robot with a dynamics andcontrol unified modelrdquo Zidonghua XuebaoActa AutomaticaSinica vol 41 no 11 pp 1847ndash1856 2015

[12] Q Cheng G Wu S Li et al ldquoStatic mechanism of a climbingsnake robot navigating obstaclerdquoMachinery DesignampManufac-ture vol 3 pp 37ndash40 2016

[13] A Crespi and A J Ijspeert ldquoOnline optimization of swimmingand crawling in an amphibious snake robotrdquo IEEE Transactionson Robotics vol 24 no 1 pp 75ndash87 2008

[14] Z Lu S Ma B Li and Y Wang ldquoSnake-like robot con-troller with cyclic inhibitory CPG modelrdquo Jixie GongchengXuebaoChinese Journal of Mechanical Engineering vol 42 no5 pp 137ndash143 2006

[15] X Lian Guo W X Lian et al ldquoCPG model parametersoptimization based on genetic algorithm for snake-like robotrdquoComputure Engineeing And Design vol 36 pp 1859ndash1864 2015

[16] Q Gao Z-L Wang W-J Hu and L-Y Zhao ldquoResearch onrealization and environmental adaptability of serpentine loco-motion for a snake robotrdquoDalian Ligong Daxue XuebaoJournalof Dalian University of Technology vol 55 no 2 pp 203ndash2082015

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 7

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

Expected outputPSOELM output

(mse = 64198e minus 35 R2 = 1)

(a)

Expected outputELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 32 R2 = 1)

(b)

Expected outputPSOELM output

08

07

06

05

04

03

02

01

0

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 41087e minus 33 R2 = 1)

(c)

Expected outputELM output

(mse = 13132e minus 32 R2 = 1)

1 2 3Joint number

0807060504030201

0

Pitc

h an

gle (

rad)

minus01

(d)

Expected outputPSOELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 10272e minus 33 R2 = 1)

(e)

Expected outputELM output

08

075

07

065

06

055

05

045

04

Pitc

h an

gle (

rad)

1 2 3Joint number

(mse = 12326e minus 32 R2 = 1)

(f)

Figure 7 (a) Pitch angles optimized by the PSOELM (ℎ lt 5 cm) (b) Pitch angles controlled by the ELM (ℎ lt 5 cm) (c) Pitch angles optimizedby the PSOELM (5 cm lt ℎ lt 8 cm) (d) Pitch angles controlled by the ELM (5 cm lt ℎ lt 8 cm) (e) Pitch angles optimized by the PSOELM(8 cm lt ℎ lt 12 cm) (f) Pitch angles controlled by the ELM (8 cm lt ℎ lt 12 cm)

8 Mathematical Problems in Engineering

Table 1 MSE comparison between PSOELM and ELM

Algorithm types MSE of pitch angle(ℎ lt 5 cm)

MSE of pitch angle(5 cm lt ℎ lt 8 cm)

MSE of pitch angle(8 cm lt ℎ lt 12 cm)

PSOELM 64198 times 10minus35 41087 times 10minus33 10272 times 10minus33

ELM 10272 times 10minus32 13132 times 10minus32 12326 times 10minus32

018

016

014

012

01

008

006

004

0021 2 3 4 5 6 7 8 9 10

Model number

Runt

ime (

s)

POSELMELM

Figure 8 Comparison of the runtime of the 10 models (POSELMversus ELM)

angles of the first three joints are respectively controlled bythe PSOELMand ELM and the results are respectively givenas shown in Figures 7(c) and 7(d) Determinant coefficient1198772 is 1 and mean square error of pitch angles respectivelyreaches 41087 times 10ndash33 and 13132 times 10minus32 when the obstacleheight 8 cm lt ℎ lt 12 cm pitch angles of the first three jointsare respectively controlled by the PSOELM and ELM andthe results are respectively given as shown in Figures 7(e)and 7(f) Determinant coefficient 1198772 is 1 and mean squareerror of pitch angles respectively reaches 10272 times 10ndash33 and12326 times 10minus32 MSE based on PSOELM and ELM is shown inTable 1 It can be seen from Figure 7 and Table 1 comparedwith ELM the smaller mean square error and better controlaccuracy and generalization ability are acquired by PSOELMOptimal control of joint pitch angles can be realized

(2) The Model Runtime Since the training set and the testset are generated randomly each runtime of the model isdifferentThe above-mentioned 10 identical ELMmodels and10 identical POSELMmodels are respectively selected to testtheir computation speedThemaximumnumber of iterationsis 3 As shown in Figure 8 the average runtime of the 10 ELMmodels and the 10 POSELM models is respectively 00426 Sand 00535 S So the runtime of the ELM and POSELMmodels is roughly the same and it is all around 50ms It canbe seen that the POSELMmodel continues the characteristicsof the fast learning of the ELMmodel

j

times10minus5

PSOELMELM

6571

5459

4347

3235

2123

10112 64 8 10 12 14 16

MRE

Figure 9 Hidden layer nodes andmean relative error (MRE) curves(POSELM versus ELM)

(3) The Stability of the Model The effect of the numberof hidden layer nodes on MRE is analyzed to evaluate thestability of the model The relationship curves between thehidden layer node 119895 and MRE are shown in Figure 9 Asobtained from Figure 9 the ELMmodel shows great volatilitywith the change of 119895 which is caused by random selectionof input weight and hidden layer node bias In the POSELMmodel the fluctuation of MRE is smaller with the change of119895 and the smaller hidden layer nodes can ensure that MRE isthe smallestWhen 119895 is 6 MRE is the smallest which is 13673times 10minus16 The POSELM model has the characteristic of fastsearching for the optimal and stability and it has significantadvantages in the control of the joint pitch angles of the snakerobot

5 Conclusion

A coal mine rescue snake robot is developed and takingthe robot as an experimental platform aiming at the robotrsquosobstacle surmounting behavior a pose control algorithmbased on particle swarm optimization weight coefficient ofextreme learningmachine (PSOELM) is studied in this paperThe following conclusions are drawn

(1) The mechanical structure and control system ofthe coal mine rescue snake robot are designed and maderespectively The mechanical part is consisted of five unitmodules five connecting plates four orthogonal joints andtwo speed servomotors The robot has better capability to

Mathematical Problems in Engineering 9

surmount the obstacle because of using the self-made bladeswheels The control system is made up of the power sourceenvironmental detection system pose control system mastercontroller mobile mechanism obstacle avoidance modulecommunication module and host computer system Thesnake robot can walk on the rugged grounds By controllingthe direction servomotors serpentine straight concertinaand head rising posture of the snake robot can be acquiredand the speed of the snake robot can be changed by control-ling the speed servomotors

(2) The pose control algorithm based on PSOELM isproposed and discussed compared with simulation resultsof the algorithm based on ELM the PSOELM algorithmhas the following advantages the smaller mean square errorand better control accuracy and generalization ability areacquired the characteristics of fast learning of ELM arecontinued having the characteristic of fast searching for theoptimal and better stability so optimal control of robotrsquos jointpitch angles is achieved by the PSOELM algorithm

(3)ThePSOELMalgorithm is applied to the surmountingobstacle control of the developed snake robot and it lays thefoundation for further implement of the coal mine rescue

Disclosure

The coal mine rescue snake robot developed won specialaward in 2016 Chinese Education Robot Contest

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research has been supported by Foundation of Scienceand Technology Innovation Project of China Coal Technol-ogy Engineering Group (no KJ3013-XBMJ-03) and cultivat-ing fund of Xirsquoan University of Science And Technology (no2013024)

References

[1] A Crespi A Badertscher A Guignard and A J IjspeertldquoAmphiBot I An amphibious snake-like robotrdquo Robotics andAutonomous Systems vol 50 no 4 pp 163ndash175 2005

[2] S Hirose Biologically Inspired Robots (Snake-like Locomotorsand Manipulators) Oxford University Press Oxford UK 1993

[3] Y C Wang L Chen S G Ma et al ldquoStudies on lateral roilinglocomotion of a snake robotrdquo in Proceedings of the IntemationalConference on Robotics and Automation IEEE pp 5070ndash5074Piscataway NJ USA 2004

[4] C Ye S Ma B Li and Y Wang ldquoTurning and side motionof snake-like robotrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation (ICRA rsquo04) pp 5075ndash5080 IEEE May 2004

[5] R L Hatton and H Choset ldquoGenerating gaits for snakerobots Annealed chain fitting and keyframe wave extractionrdquoAutonomous Robots vol 28 no 3 pp 271ndash281 2010

[6] Y Xie U Zhenli and X Huigang ldquoResearch on underwa-ter snake-like robots mechanism design and their serpentineswimming performancerdquo Chinese High Technology Letters vol26 no 6 pp 599ndash605 2016

[7] J Ostrowski and J Burdick ldquoThe geometricmechanics of undu-latory robotic locomotionrdquo International Journal of RoboticsResearch vol 17 no 7 pp 683ndash701 1998

[8] P Liljeback K Y Pettersen and K Stavdahl ldquoModelling andcontrol of obstacle-aided snake robot locomotion based onjam resolutionrdquo in Proceedings of the 2009 IEEE InternationalConference on Robotics and Automation ICRA rsquo09 pp 3807ndash3814 Japan May 2009

[9] L Chen Y-C Wang S-G Ma and B Li ldquoStudy of laterallocomotion of snake robotrdquo JiqirenRobot vol 25 no 3 p 2462003

[10] W Wei and C Sun ldquoResearch on Gait Generation and Controlof Snake-like Robot for Bridge Cable Climbing [J]rdquo ChinaMechanicalengineering vol 23 no 10 pp 1230ndash1235 2012

[11] X Guo S-GMa B Li M-HWang and Y-CWang ldquoVelocitytracking control of a snake-like robot with a dynamics andcontrol unified modelrdquo Zidonghua XuebaoActa AutomaticaSinica vol 41 no 11 pp 1847ndash1856 2015

[12] Q Cheng G Wu S Li et al ldquoStatic mechanism of a climbingsnake robot navigating obstaclerdquoMachinery DesignampManufac-ture vol 3 pp 37ndash40 2016

[13] A Crespi and A J Ijspeert ldquoOnline optimization of swimmingand crawling in an amphibious snake robotrdquo IEEE Transactionson Robotics vol 24 no 1 pp 75ndash87 2008

[14] Z Lu S Ma B Li and Y Wang ldquoSnake-like robot con-troller with cyclic inhibitory CPG modelrdquo Jixie GongchengXuebaoChinese Journal of Mechanical Engineering vol 42 no5 pp 137ndash143 2006

[15] X Lian Guo W X Lian et al ldquoCPG model parametersoptimization based on genetic algorithm for snake-like robotrdquoComputure Engineeing And Design vol 36 pp 1859ndash1864 2015

[16] Q Gao Z-L Wang W-J Hu and L-Y Zhao ldquoResearch onrealization and environmental adaptability of serpentine loco-motion for a snake robotrdquoDalian Ligong Daxue XuebaoJournalof Dalian University of Technology vol 55 no 2 pp 203ndash2082015

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

8 Mathematical Problems in Engineering

Table 1 MSE comparison between PSOELM and ELM

Algorithm types MSE of pitch angle(ℎ lt 5 cm)

MSE of pitch angle(5 cm lt ℎ lt 8 cm)

MSE of pitch angle(8 cm lt ℎ lt 12 cm)

PSOELM 64198 times 10minus35 41087 times 10minus33 10272 times 10minus33

ELM 10272 times 10minus32 13132 times 10minus32 12326 times 10minus32

018

016

014

012

01

008

006

004

0021 2 3 4 5 6 7 8 9 10

Model number

Runt

ime (

s)

POSELMELM

Figure 8 Comparison of the runtime of the 10 models (POSELMversus ELM)

angles of the first three joints are respectively controlled bythe PSOELMand ELM and the results are respectively givenas shown in Figures 7(c) and 7(d) Determinant coefficient1198772 is 1 and mean square error of pitch angles respectivelyreaches 41087 times 10ndash33 and 13132 times 10minus32 when the obstacleheight 8 cm lt ℎ lt 12 cm pitch angles of the first three jointsare respectively controlled by the PSOELM and ELM andthe results are respectively given as shown in Figures 7(e)and 7(f) Determinant coefficient 1198772 is 1 and mean squareerror of pitch angles respectively reaches 10272 times 10ndash33 and12326 times 10minus32 MSE based on PSOELM and ELM is shown inTable 1 It can be seen from Figure 7 and Table 1 comparedwith ELM the smaller mean square error and better controlaccuracy and generalization ability are acquired by PSOELMOptimal control of joint pitch angles can be realized

(2) The Model Runtime Since the training set and the testset are generated randomly each runtime of the model isdifferentThe above-mentioned 10 identical ELMmodels and10 identical POSELMmodels are respectively selected to testtheir computation speedThemaximumnumber of iterationsis 3 As shown in Figure 8 the average runtime of the 10 ELMmodels and the 10 POSELM models is respectively 00426 Sand 00535 S So the runtime of the ELM and POSELMmodels is roughly the same and it is all around 50ms It canbe seen that the POSELMmodel continues the characteristicsof the fast learning of the ELMmodel

j

times10minus5

PSOELMELM

6571

5459

4347

3235

2123

10112 64 8 10 12 14 16

MRE

Figure 9 Hidden layer nodes andmean relative error (MRE) curves(POSELM versus ELM)

(3) The Stability of the Model The effect of the numberof hidden layer nodes on MRE is analyzed to evaluate thestability of the model The relationship curves between thehidden layer node 119895 and MRE are shown in Figure 9 Asobtained from Figure 9 the ELMmodel shows great volatilitywith the change of 119895 which is caused by random selectionof input weight and hidden layer node bias In the POSELMmodel the fluctuation of MRE is smaller with the change of119895 and the smaller hidden layer nodes can ensure that MRE isthe smallestWhen 119895 is 6 MRE is the smallest which is 13673times 10minus16 The POSELM model has the characteristic of fastsearching for the optimal and stability and it has significantadvantages in the control of the joint pitch angles of the snakerobot

5 Conclusion

A coal mine rescue snake robot is developed and takingthe robot as an experimental platform aiming at the robotrsquosobstacle surmounting behavior a pose control algorithmbased on particle swarm optimization weight coefficient ofextreme learningmachine (PSOELM) is studied in this paperThe following conclusions are drawn

(1) The mechanical structure and control system ofthe coal mine rescue snake robot are designed and maderespectively The mechanical part is consisted of five unitmodules five connecting plates four orthogonal joints andtwo speed servomotors The robot has better capability to

Mathematical Problems in Engineering 9

surmount the obstacle because of using the self-made bladeswheels The control system is made up of the power sourceenvironmental detection system pose control system mastercontroller mobile mechanism obstacle avoidance modulecommunication module and host computer system Thesnake robot can walk on the rugged grounds By controllingthe direction servomotors serpentine straight concertinaand head rising posture of the snake robot can be acquiredand the speed of the snake robot can be changed by control-ling the speed servomotors

(2) The pose control algorithm based on PSOELM isproposed and discussed compared with simulation resultsof the algorithm based on ELM the PSOELM algorithmhas the following advantages the smaller mean square errorand better control accuracy and generalization ability areacquired the characteristics of fast learning of ELM arecontinued having the characteristic of fast searching for theoptimal and better stability so optimal control of robotrsquos jointpitch angles is achieved by the PSOELM algorithm

(3)ThePSOELMalgorithm is applied to the surmountingobstacle control of the developed snake robot and it lays thefoundation for further implement of the coal mine rescue

Disclosure

The coal mine rescue snake robot developed won specialaward in 2016 Chinese Education Robot Contest

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research has been supported by Foundation of Scienceand Technology Innovation Project of China Coal Technol-ogy Engineering Group (no KJ3013-XBMJ-03) and cultivat-ing fund of Xirsquoan University of Science And Technology (no2013024)

References

[1] A Crespi A Badertscher A Guignard and A J IjspeertldquoAmphiBot I An amphibious snake-like robotrdquo Robotics andAutonomous Systems vol 50 no 4 pp 163ndash175 2005

[2] S Hirose Biologically Inspired Robots (Snake-like Locomotorsand Manipulators) Oxford University Press Oxford UK 1993

[3] Y C Wang L Chen S G Ma et al ldquoStudies on lateral roilinglocomotion of a snake robotrdquo in Proceedings of the IntemationalConference on Robotics and Automation IEEE pp 5070ndash5074Piscataway NJ USA 2004

[4] C Ye S Ma B Li and Y Wang ldquoTurning and side motionof snake-like robotrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation (ICRA rsquo04) pp 5075ndash5080 IEEE May 2004

[5] R L Hatton and H Choset ldquoGenerating gaits for snakerobots Annealed chain fitting and keyframe wave extractionrdquoAutonomous Robots vol 28 no 3 pp 271ndash281 2010

[6] Y Xie U Zhenli and X Huigang ldquoResearch on underwa-ter snake-like robots mechanism design and their serpentineswimming performancerdquo Chinese High Technology Letters vol26 no 6 pp 599ndash605 2016

[7] J Ostrowski and J Burdick ldquoThe geometricmechanics of undu-latory robotic locomotionrdquo International Journal of RoboticsResearch vol 17 no 7 pp 683ndash701 1998

[8] P Liljeback K Y Pettersen and K Stavdahl ldquoModelling andcontrol of obstacle-aided snake robot locomotion based onjam resolutionrdquo in Proceedings of the 2009 IEEE InternationalConference on Robotics and Automation ICRA rsquo09 pp 3807ndash3814 Japan May 2009

[9] L Chen Y-C Wang S-G Ma and B Li ldquoStudy of laterallocomotion of snake robotrdquo JiqirenRobot vol 25 no 3 p 2462003

[10] W Wei and C Sun ldquoResearch on Gait Generation and Controlof Snake-like Robot for Bridge Cable Climbing [J]rdquo ChinaMechanicalengineering vol 23 no 10 pp 1230ndash1235 2012

[11] X Guo S-GMa B Li M-HWang and Y-CWang ldquoVelocitytracking control of a snake-like robot with a dynamics andcontrol unified modelrdquo Zidonghua XuebaoActa AutomaticaSinica vol 41 no 11 pp 1847ndash1856 2015

[12] Q Cheng G Wu S Li et al ldquoStatic mechanism of a climbingsnake robot navigating obstaclerdquoMachinery DesignampManufac-ture vol 3 pp 37ndash40 2016

[13] A Crespi and A J Ijspeert ldquoOnline optimization of swimmingand crawling in an amphibious snake robotrdquo IEEE Transactionson Robotics vol 24 no 1 pp 75ndash87 2008

[14] Z Lu S Ma B Li and Y Wang ldquoSnake-like robot con-troller with cyclic inhibitory CPG modelrdquo Jixie GongchengXuebaoChinese Journal of Mechanical Engineering vol 42 no5 pp 137ndash143 2006

[15] X Lian Guo W X Lian et al ldquoCPG model parametersoptimization based on genetic algorithm for snake-like robotrdquoComputure Engineeing And Design vol 36 pp 1859ndash1864 2015

[16] Q Gao Z-L Wang W-J Hu and L-Y Zhao ldquoResearch onrealization and environmental adaptability of serpentine loco-motion for a snake robotrdquoDalian Ligong Daxue XuebaoJournalof Dalian University of Technology vol 55 no 2 pp 203ndash2082015

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 9

surmount the obstacle because of using the self-made bladeswheels The control system is made up of the power sourceenvironmental detection system pose control system mastercontroller mobile mechanism obstacle avoidance modulecommunication module and host computer system Thesnake robot can walk on the rugged grounds By controllingthe direction servomotors serpentine straight concertinaand head rising posture of the snake robot can be acquiredand the speed of the snake robot can be changed by control-ling the speed servomotors

(2) The pose control algorithm based on PSOELM isproposed and discussed compared with simulation resultsof the algorithm based on ELM the PSOELM algorithmhas the following advantages the smaller mean square errorand better control accuracy and generalization ability areacquired the characteristics of fast learning of ELM arecontinued having the characteristic of fast searching for theoptimal and better stability so optimal control of robotrsquos jointpitch angles is achieved by the PSOELM algorithm

(3)ThePSOELMalgorithm is applied to the surmountingobstacle control of the developed snake robot and it lays thefoundation for further implement of the coal mine rescue

Disclosure

The coal mine rescue snake robot developed won specialaward in 2016 Chinese Education Robot Contest

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research has been supported by Foundation of Scienceand Technology Innovation Project of China Coal Technol-ogy Engineering Group (no KJ3013-XBMJ-03) and cultivat-ing fund of Xirsquoan University of Science And Technology (no2013024)

References

[1] A Crespi A Badertscher A Guignard and A J IjspeertldquoAmphiBot I An amphibious snake-like robotrdquo Robotics andAutonomous Systems vol 50 no 4 pp 163ndash175 2005

[2] S Hirose Biologically Inspired Robots (Snake-like Locomotorsand Manipulators) Oxford University Press Oxford UK 1993

[3] Y C Wang L Chen S G Ma et al ldquoStudies on lateral roilinglocomotion of a snake robotrdquo in Proceedings of the IntemationalConference on Robotics and Automation IEEE pp 5070ndash5074Piscataway NJ USA 2004

[4] C Ye S Ma B Li and Y Wang ldquoTurning and side motionof snake-like robotrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation (ICRA rsquo04) pp 5075ndash5080 IEEE May 2004

[5] R L Hatton and H Choset ldquoGenerating gaits for snakerobots Annealed chain fitting and keyframe wave extractionrdquoAutonomous Robots vol 28 no 3 pp 271ndash281 2010

[6] Y Xie U Zhenli and X Huigang ldquoResearch on underwa-ter snake-like robots mechanism design and their serpentineswimming performancerdquo Chinese High Technology Letters vol26 no 6 pp 599ndash605 2016

[7] J Ostrowski and J Burdick ldquoThe geometricmechanics of undu-latory robotic locomotionrdquo International Journal of RoboticsResearch vol 17 no 7 pp 683ndash701 1998

[8] P Liljeback K Y Pettersen and K Stavdahl ldquoModelling andcontrol of obstacle-aided snake robot locomotion based onjam resolutionrdquo in Proceedings of the 2009 IEEE InternationalConference on Robotics and Automation ICRA rsquo09 pp 3807ndash3814 Japan May 2009

[9] L Chen Y-C Wang S-G Ma and B Li ldquoStudy of laterallocomotion of snake robotrdquo JiqirenRobot vol 25 no 3 p 2462003

[10] W Wei and C Sun ldquoResearch on Gait Generation and Controlof Snake-like Robot for Bridge Cable Climbing [J]rdquo ChinaMechanicalengineering vol 23 no 10 pp 1230ndash1235 2012

[11] X Guo S-GMa B Li M-HWang and Y-CWang ldquoVelocitytracking control of a snake-like robot with a dynamics andcontrol unified modelrdquo Zidonghua XuebaoActa AutomaticaSinica vol 41 no 11 pp 1847ndash1856 2015

[12] Q Cheng G Wu S Li et al ldquoStatic mechanism of a climbingsnake robot navigating obstaclerdquoMachinery DesignampManufac-ture vol 3 pp 37ndash40 2016

[13] A Crespi and A J Ijspeert ldquoOnline optimization of swimmingand crawling in an amphibious snake robotrdquo IEEE Transactionson Robotics vol 24 no 1 pp 75ndash87 2008

[14] Z Lu S Ma B Li and Y Wang ldquoSnake-like robot con-troller with cyclic inhibitory CPG modelrdquo Jixie GongchengXuebaoChinese Journal of Mechanical Engineering vol 42 no5 pp 137ndash143 2006

[15] X Lian Guo W X Lian et al ldquoCPG model parametersoptimization based on genetic algorithm for snake-like robotrdquoComputure Engineeing And Design vol 36 pp 1859ndash1864 2015

[16] Q Gao Z-L Wang W-J Hu and L-Y Zhao ldquoResearch onrealization and environmental adaptability of serpentine loco-motion for a snake robotrdquoDalian Ligong Daxue XuebaoJournalof Dalian University of Technology vol 55 no 2 pp 203ndash2082015

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom