Design of an artificial bionic neural network to control fish-robot's locomotion

  • Published on
    10-Sep-2016

  • View
    227

  • Download
    2

Transcript

  • Neurocomputing 71 (200

    iot $

    ,

    niv

    e 9

    ion

    l c

    f

    sh

    Ne

    has some disadvantages to deal with bionic robot which has

    changing needs. The biologic research results showed the

    undulatory n experimental system which imitated from a

    n experimental system

    2.1. Inspirations from Gymnarchus niloticus

    ARTICLE IN PRESS

    $This work is supported by the National Basic Research Program ofGymnarchus niloticus, as shown in Fig. 1, is a freshwater esh-eater that mainly lives in Nile of Egypt [4].

    0925-2312/$ - see front matter r 2007 Elsevier B.V. All rights reserved.

    doi:10.1016/j.neucom.2007.09.007

    China (2007CB311001).Corresponding author.E-mail address: dwhu@nudt.edu.cn (D. Hu).large numbers of joints such as unbearable computingcomplexity and unadaptable with changing needs [11,13,6].The other is bionic neural network control method whichimitated the biological neural network of the animals. Therhythmic movements of vertebrates include swimming(shes), running (human or quadruped), ying (birds) areproduced by central pattern-generating neural networkswhose output is shaped by sensor and neuromodulatoryinputs to allow the animal to adapt its movements to

    esh-eater sh and its dynamic model are given. In Section 3,the bionic neural network which based on biological CPGsprinciples and constructed with our novel neural oscillator ispresented. Then the experimental results of primary move-ments are given in Section 4 to demonstrate our controlmethod. Finally, conclusions are drawn in Section 5.

    2. Dynamic modeling and implementation of the undulatoryAquatic animals, most of which are shes, have higherlocomotion performance than man-made underwater vehicles[9,2,17]. Many scientists and engineers have built differentkinds of sh-robots replicating the animals locomotionabilities [13,6,19,24]. There are two different ways to controlall the joints to achieve high performances. One is the reversekinematic control method which consists of observation andrecording of animals movements, mimic modeling of bionicrobots movement and gaits planning in real-time [12,18]. It

    network for sh-robots [1,5,8,7,26].The main objective of this paper is to investigate the bionic

    neural network control method for sh-robots. Our team [21]built a novel sh-robot with a long dorsal n propeller, whichhas nine joints with individual control modules and parallelconnections to the vehicle base. It is worthwhile to mentionthat our approach just concentrated on the movements of theundulatory n propeller, and the locomotion of the sh-robotin the water will be presented in our future papers. The rest ofthis paper is organized as follows. In Section 2, the1. Introduction possibility and validity to construct such an articial neuralDesign of an articial bcontrol sh-robo

    Daibing Zhang, Dewen Hu

    College of Mechatronics and Automation, National U

    Available onlin

    Abstract

    An articial bionic neural network to control sh-robot locomot

    niloticus, is modeled as a multi-joint dynamic system with paralle

    central pattern generators (CPGs) governing the locomotion o

    comparability with the biological CPGs is designed to control the

    and backward swimming show its validity and efciency.

    r 2007 Elsevier B.V. All rights reserved.

    Keywords: Central pattern generators; Fish-robot; Swimming locomotion;s locomotion

    Lincheng Shen, Haibin Xie

    ersity of Defense Technology, Changsha, PR China

    October 2007

    is presented. The sh-robot, which is inspired from Gymnarchus

    onnections and composed of several motors. The principle of the

    sh is analyzed. An articial neural network which has many

    -robot. Experimental results of startup, stop, forward swimming

    ural oscillator; Bionic neural network8) 648654

    nic neural network to

    www.elsevier.com/locate/neucom

  • The long dorsal n produces the main propulsion force forhunting or cruising in low speed, which belongs to medianand paired n (MPF) mode according to the swimmingclassication [22].The rst inspiration is that we can build such a bionic

    propeller to be mounted on the straight axis base ofunderwater vehicles. It can be used as an assistant propellerfor a normal underwater vehicle maneuvering at low speedor the main propeller for special sh-robots. The secondinspiration is that the undulatory n is composed of a lot ofjoints and an elastic membrane. Each joint consists of oneservo motor and one steel n ray which moves leftright. The last important inspiration is that we can createa novel bionic neural network control system to performthe manager role of the bionic propeller.

    2.2. Dynamic modeling of the bionic propeller

    The bionic propeller can be modeled as a group ofactuators, spring elements and damping elements, as shown

    actuator for its low cost and easy control with pulse wide

    length of n rays is 150 or 100mm.

    3. Bionic neural network

    3.1. Principles of fish central neural system

    Fish locomotion is governed by central neural systemwhich is called central pattern generators (CPGs)[1,15,3,26,5,14] and modeled as shown in Fig. 4. The twoCPGs located in each segment of spine cord havereciprocal inhibitory connections and can stimulate eachside muscles to contract or stretch alternately. Thesupraspinal inputs from cerebrum play a major role instartup, stop and turn. When the steady locomotion isformed, the inputs from the high controller are not needed

    ARTICLE IN PRESS

    Fig. 3. Experimental system of the undulatory n propeller and the test-

    D. Zhang et al. / Neurocompin Fig. 2. Each joint has one turning freedom and one servomotor. The dynamics of the joint is given as

    J y D_y ksy t, (1)where y is the joint angle of n moves from balanceposition which in the vertical plane, _y is the angularvelocity, y is the angular acceleration, J is the rotatinginertia, D is the damping coefcient, ks is the restoremoment and t is the driving moment of the motor.Parameters of head, tail and middle joints have differentvalues according to the undulatory parameters andtraveling waves direction. Since all joints drive themembrane undulating in the water by steel n rays, thefeedback forces and moments from the water cannot be

    Fig. 1. Structure of Gymnarchus niloticus.

    fin base

    fin

    jointFig. 2. Dynamic model of the undulatory n propeller.modulation(PWM) signals. The test-bed has a long straighttrack and is equipped with sensors to measure the changingparameters in locomotion. The measure parameters includepower supply voltage, electric current, axial force, lateralforce, propulsion acceleration, propulsion speed and swingangles of all joints. The nal experimental system and thetest-bed are shown in Fig. 3. The number of joints is nine,the distance between adjacent joints is 45mm and theneglected. To the best of our knowledge, however, itinvolves complicated nonlinear, unsteady ow hydrody-namics and cannot be modeled accurately. Fortunately, wehave obtained one essential rule from the experiments:water feedback effects result in the steady increasing ofdamping coefcients, rotating inertia and decreasing ofrestore moment.

    2.3. Implementation of experimental system

    An undulatory n experimental system was built tovalidate the expectation of the novel bionic propeller. Itsmechanism was designed by three-dimensional CAD soft-ware. Futaba S3003 servo motor was selected as joint

    bed.uting 71 (2008) 648654 649any longer, and the locomotion patterns are produced andmodulated by CPGs network.

  • 3.2. Design of bionic neural network

    There are several key points in the design of bionicneural network. Firstly, the bionic propeller just adoptsone servomotor to drive a joint while the sh has twogroup muscles in each joint. We can design one CPG ineach segment to control the corresponding joint. Secondly,a discrete computational model is adopted to simulate thecontinuous biological tissues. Lastly, the connection lagtime between neurons always exists and determines theintersegmental phase lag. The lag time function in thecomputational model is necessary. Since the CPG is oftenmodeled as a neural oscillator with intersegmental descend-ing command and segmental sensor feedback, we propose anovel neural oscillator which is different from theWilsonCowan oscillator [23,20] and Matsuoka oscillator[16]. It is based on the sinecosine oscillator model and alloscillatory parameters can be modulated individually [25].The dynamics of the novel oscillator is described as

    _u ov k ur 4ptan1

    u

    r

    ;

    _v ou k vr 4ptan1

    v

    r

    ;

    8>>>>>:

    (2)

    where u and v denote the activity of inhibitory neuron andexcitatory neuron, respectively. And o is a parameterwhich mainly determines the angular frequency of oscilla-tion, k denotes the sustain strength of limit cycles and rdenotes the approximate radius of the limit cycles. Thenonlinear function f x; k; r is adopted to represent thecomplicated self-feedback effect, described as

    f x; k; r k xr 4ptan1

    x

    r

    . (3)

    The limit cycles trajectory in this oscillator with k 5,r 1, o 2p is shown in Fig. 5(a). The original point isthe sole unsteady balance point which would be push away

    ARTICLE IN PRESS

    M M M M

    p

    p

    D. Zhang et al. / Neurocomputing 71 (2008) 648654650CPG

    CPG

    CPG

    CPG

    CPG

    CPG

    CPG

    CPGcerebrum

    M M M

    Excitatory connection

    Inhibitory connection

    Stretch receptor

    M

    Fig. 4. Central neural system for sh locomotion.

    -3 -2 -1 0 1 2

    -2

    -1

    0

    1

    2

    u

    v

    3Fig. 5. Limit cycles of the novel oscillator (a) andby a small disturbing signal and transfer to the limit cycles.We designed the segmental CPG which is illustrated inFig. 5(b) based on the oscillator. The dynamics of theCPG is

    _u ov f u; k; r put;_v ou f v; k; r pvt;y u;

    8>: (4)where put and pvt denote the external inputs composedof descending commands and sensor feedback and ytdenotes the output from the inhibitory neuron to themotor.The bionic neural network we nally designed is shown

    in Fig. 6. The high level controller controls the undulatoryangular frequency o and the undulatory amplitude r.The bionic neural network can be divided into three

    sections: head segment, tail segment and middle segments.The dynamics of head segment is presented as

    _u1 ov1 f u1; k; r sfdt DTu2 u1sbdt DTqut;

    _v1 ou1 f v1; k; r sfdt DTv2 v1sbdt DTqvt;

    y1 u1;

    8>>>>>>>>>>>:

    (5)

    where qut and qvt denote the high level commands ofstartup or stop, and sf and sb are the intersegmental

    u

    v

    u

    v

    f

    f

    u

    v

    y

    MotorCPG model based on the novel oscillator (b).

  • ARTICLE IN PRESS

    PG

    M3

    u

    v

    u u

    rk f

    mpconnections logical status dened as

    sb 1; sf 0 swimming forward;sb 0; sf 1 swimming backward:

    ((6)

    And dt DT means the lag time between adjacentsegments. To sustain a whole travel wave on theundulatory n, the lag time is calculated as

    DT 2pno

    , (7)

    where n is the number of undulatory n joints.The dynamics of middle segments has an uniform

    expression as

    _ui ovi f ui; k; r sfdt DTui1 ui8>>

    u

    v

    M1

    CPG1 CPG2 C

    M2

    u

    v

    High

    Level

    Controller

    r

    Fig. 6. Bionic neural netwo

    D. Zhang et al. / Neurocosbdt DTui1 ui;_vi oui f vi; k; r sfdt DTvi1 vi

    sbdt DTvi1 vi;yi ui; i 2; 3; . . . ; n 1:

    >>>>>>>>>:

    (8)

    And the dynamics of the tail segment is

    _un ovn f un; k; r sbdt DTun1 unsfdt DTqut;

    _vn oun f vn; k; r sbdt DTvn1 vnsfdt DTqvt;

    yn un:

    8>>>>>>>>>>>:

    (9)

    4. Results and analysis

    The bionic propellers locomotion are classied asstartup, stop, forward swimming and backward swimming.Experiments of the experimental system and simulations byMatlab/Simulink have been performed to testify the bionicneural network control method.4.1. Startup experiment

    The startup of the locomotion is actually to activate thenonlinear coupled neural network. We imposed a shorttime width pulse on the head segment. The startup functionis given as

    qut stept ts stept ts tdqvt 0

    (

    stept 0; tp0;stept 1; t40;

    (10

    where ts is the onset and td is the time width of the pulse.The startup process of the bionic neural network and

    Forward Connection

    Backward Connection

    3 CPG(n-1) CPG(n)

    v v

    M(n-1) M(n)

    or undulatory n propeller.uting 71 (2008) 648654 651experimental system is shown in Fig. 7, where ts 0:1 s,td 0:01 s, o 4p, r 15, k 5. The inhibitory neuronof the rst CPG is excited at t ts. Then each CPG isexcited in turn without external inputs. The ninth CPGholds up the same phase with but different amplitude fromthe rst CPG. The locomotion of the bionic propeller hasthe same process with the bionic neural network. Theprocess control by bionic neural network is quite differentfrom the reverse kinematic planning method but similarwith the natural sh. It avoids sudden startup anddestroying of servo motors. Another advantage is keepingthe uid around the undulatory n steady and away fromturbulence.

    4.2. Stop experiment

    The stop process is to weaken and cease oscillation of thebionic neural network. A direct way is to set all neurons tozero at one time. This method neglects the transition fromlocomotion to stillness and may destroy the propellerhardware. We instead use a descending function whichapplied to all oscillators in the articial neural network to

  • ARTICLE IN PRESS

    tim

    1.5 2 2.5 3

    6

    time/sec

    th

    eta

    CPG

    onic neural network and propeller.

    9 9.5 10 10.5 11 11.5 12 12.5-0.4

    -0.2

    0

    0.2

    0.4

    time/sec

    CP

    G o

    utp

    ut

    y

    8

    ta

    mpmodulate the oscillation amplitude, given as

    rt r0 12

    ptan1kc

    Zt0

    stept tcdt

    , (11)

    where r0 is the original amplitude, tc is the time of stop andkc is the parameter to control amplitude descending speed.The stop process of the bionic neural network and

    propeller are shown in Fig. 8, where tc 10 and kc 5.After one or two seconds, the oscillatory amplitude of the

    0 0.5 1

    0

    2

    4

    join

    ts' angle

    Fig. 7. Startup process of the bi0 0.5 1

    -0.4

    -0.2

    0

    0.2

    0.4

    CP

    G o

    utp

    ut y

    8

    CPG1

    CPG2

    CPG3

    CPG4

    D. Zhang et al. / Neuroco652bionic neural network is restricted into small range, and thelocomotion of the propeller seems stop. It is believedthat when the locomotion of animals stops, the oscillationin the neural network never diminish but just inhibited bybasal ganglion. And once the inhibitory command iscanceled by the high level controller, the locomotionresume again [3,1]. The amazing phenomenon we observedon the bionic neural network and propeller agree with theabove viewpoint.

    4.3. Forward and backward swimming experiments

    The external commands or sensory feedback are notnecessary in the steady swimming process, and the forwardswimming process of the bionic neural network andpropeller is shown in Fig. 9. The phase lag betweenadjacent joints is hold up by the lag time function. Thebackward swimming process has similar properties with theforward swimming except the sequence reversal of CPGsand joints. There is no sensory feedback in our currentcontrol method, and the special swing amplitude andangular frequency of each joint still cannot affect thelocomotion.1.5 2 2.5

    e/sec

    5

    CPG6

    CPG7

    CPG8

    CPG9

    uting 71 (2008) 6486545. Conclusions

    We have presented a novel bionic neural network tocontrol the sh-robot. The basic unit of the bionic neuralnetwork is an articial neural oscillator which consists oftwo neurons, and it has excellent control properties foralmost independently modulating of undulatory angularvelocity and amplitude. The bionic neural network hasthree parts including head segment, middle segments andtail segment. To testify the control performance of thebionic neural network, we have carried out severalexperiments on startup, stop, forward swimming andbackward swimming. The phenomenons in these experi-ments quite agree with the biological viewpoints and

    9 9.5 10 10.5 11 11.5 12 12.5

    time/sec

    2

    0

    4

    6

    join

    ts' a

    ng

    le t

    he

    Fig. 8. Stop process of the bionic neural network and propeller.

  • ARTICLE IN PRESS

    tim

    tim

    jo

    PG1

    the

    mpindicate the importance of the oscillation in the neuralnetwork.Although we have built an undulatory n propeller

    experimental installation and validated the novel controlmethod, we have not consider the modern control theory

    6.9 7 7.1 7.20

    Fig. 9. Forward swimming process of6.8 6.9 7 7.1-0.4

    -0.2

    0

    0.2

    0.4

    CP

    G o

    utp

    ut

    y

    2

    4

    6

    8

    ints

    'a

    ngle

    th

    eta

    CPG8 CPG9 CCPG7CPG6

    D. Zhang et al. / Neurocoand technology, e.g., the feedback theory. And the bionicneural network is just used to produce the joint motionpatterns. In the future, well test the control method on thesh-robot and investigate the principles and dynamics ofthe feedback modulation and aim at the adaptive controlwith changing environments.

    References

    [1] A.H. Cohen, M.A. Lewis, Sensorimotor integration in Lampreys and

    robot I: CPG principles, Physiol. Rev. 76 (3) (1996) 687709.

    [2] G.V. Lauder, E.D. Tytell, Hydrodynamics of undulatory propulsion,

    Fish Physiol. 23 (3) (2005) 425468.

    [3] S. Grillner, Neural networks for vertebrate locomotion, Sci. Am.

    (1996) 6469.

    [4] T.J. Hu, et al., Morpholocial measurement and analyses of

    Gymnarchus Niloticus, J. Bionics Eng. 2 (1) (2005) 2531.

    [5] A.J. Ijspeert, A. Crespi, J.M. Cabelguen, Simulation and robotics

    studies of salamander locomotion, Neuroinformatics 3 (3) (2005)

    171196.

    [6] N. Kato, Control performance of sh robot with mechanical pectoral

    ns in horizontal plane, IEEE J. Ocean Eng. 25 (1) (2000) 121129.

    [7] N. Kazuki, A. Tesuya, A. Yoshihito, Design of an articial central

    pattern generator with feedback controller, Intelligent Autom. Soft

    Comput. 10 (2) (2004) 185192.

    [8] H. Kimura, S. Akiyama, K. Sakurama, Realization of dynamic

    walking and running of the quadruped using neural oscillator,

    Autonomous Robots (7) (1999) 247258.

    [9] M.J. Lighthill, Aquatic animal propulsion of high hydromechanical

    efciency, J. Fluid Mech. 44 (1970) 265.[11] J. Liu, I. Dukes, H. Hu, Novel mechatronics design for a robotic sh,

    in: IEEE/RSJ International Conference on Intelligent Robots and

    Systems, 2005, pp. 20772082.

    [12] J.D. Liu, H.S. Hu, A 3D simulator for autonomous robotic sh, Int.

    J. Autom. Comput. (2004) 4250.

    [13] K.H. Low, A. Willy, Development and initial investigation of NTU

    7.2 7.3 7.4 7.5 7.6

    e/sec

    7.3 7.4 7.5 7.6 7.7

    e/sec

    CPG2 CPG3 CPG4 CPG5 CPG6

    bionic neural network and propeller.

    uting 71 (2008) 648654 653robotic sh with modular exiable ns, in: IEEE International

    Conference on Mechatronics and Automation, Niagara, Canada,

    2005, pp. 958963.

    [14] M. MacKay-Lyons, Central pattern generation of locomotion: a

    review of the evidence, Phys. Ther. 82 (1) (2002) 6983.

    [15] E. Marder, D. Bucher, Central pattern generators and the control of

    rhythmic movements, Curr. Biol. 11 (23) (2001) 986996.

    [16] K. Matsuoka, Mechanism of frequency and pattern control in the

    neural rhythm generators, Biol. Cybern. 56 (1987) 345353.

    [17] G.K. Taylor, R.L. Nudds, A.L.R. Thomas, Flying and swimming

    animals cruise at a Stouhal Number tuned for high power efciency,

    Nature 425 (2003) 707711.

    [18] Y. Toda, K. Fukui, T. Sugiguchi, Laminar ow computation around

    a plate with two undulating side ns, J. Kansai Soc. Nav. Archit. 237

    (2002) 7178.

    [19] M.S. Triantafyllou, G.S. Triantafyllou, D.K.P. Yue, Hydrodynamics

    of shlike swimming, Fluid Mech. 32 (2000) 3353.

    [20] T. Ueta, G.R. Chen, On synchronization and control of coupled

    Wilson Cowan neural oscillators, Int. J. Bifurcation Chaos 13 (1)

    (2003) 163175.

    [21] G.M. Wang, et al., New underwater robot propelled by undulations

    of long-based n, in: International Conference on Mechanical

    Engineering and Mechanics, Nanjing, 2005, pp. 475478.

    [22] P.W. Webb, Form and function in sh swimming, Sci. Am. 251

    (1984) 5868.

    [23] H.R. Wilson, J.D. Cowan, Excitatory and inhibitory interactions

    in localized populations of model neurons, Biophysics (12) (1972)

    124.

    [24] J.Z. Yu, et al., Motion control algorithms for a free-swimming

    biomimetic robot sh, Acta Automatica Sin. 31 (4) (2005) 537542.

    [25] D.B. Zhang, et al., Design of a central pattern generator for

    bionic-robot joint with angular frequency modulation, in: IEEE

  • International Conference on Robotics and Biomimetics, Kunming,

    2006, pp. 16641669.

    [26] L. Zhaoping, L.A. Lewis, S. Scarpetta, Mathematical analysis and

    simulations of the neural circuit for locomotion in Lampreys, Phys.

    Rev. Lett. 92 (19) (2004) 198106(14).

    Daibing Zhang was born in Chongqing, PR

    China. He received the B.S., M.S. and Ph.D.

    degrees in College of Mechatronics and Automa-

    tion, National University of Defense Technology

    (NUDT), PR China, in 1999, 2002 and 2007

    respectively. He is a lecturer in the Institute of

    Automation, NUDT. He has research interests in

    snake-robot, sh-robot and neural network

    control.

    Dewen Hu received the B.S. degree and masters

    degree in Automatic Control from Xian

    Jiaotong University, PR China, in 1983, 1986,

    and the Ph.D. degree in Automatic Control from

    the National University of Defense Technology

    in 1999. He was a visiting scholar from October

    1995 to October 1996 in University of Shefeld,

    UK, and from September 2003 to January 2004

    in the Hong Kong Polytechnic University. He has

    been a full professor in the Department of

    Automatic Control at the NUDT since 1996. His research interests

    include image processing, neural networks, identication and control,

    cognitive neuroscience. He was awarded the Distinguished Young

    Scholars Fund of China in 2002. He is currently an action editor of

    Neural Networks.

    Lincheng Shen was born in 1965 and received

    B.S., M.S. and Ph.D. degrees in College of

    Mechatronics and Automation, National Uni-

    versity of Defense Technology (NUDT), in 1986,

    1990 and 1994, respectively. He has been a full

    professor in the eld of control science and

    technology. His research interests include mission

    planning and control of unmanned aerial vehicles

    (UAVs), articial intelligence (AI) and bionic

    robot control technology.

    Haibin Xie received the B.S. and M.S. degrees in

    Automatic Control, and the Ph.D. degree in

    Control Science and Engineering from the

    National University of Defense Technology

    (NUDT), PR China, in 1999, 2002 and 2006,

    respectively. He is a lecturer in the Institute of

    Automation, NUDT. His research interests

    include bionic robot, underwater robot locomo-

    tion control system and fuzzy neural networks.

    ARTICLE IN PRESSD. Zhang et al. / Neurocomputing 71 (2008) 648654654

    Design of an artificial bionic neural network to control fish-robots locomotionIntroductionDynamic modeling and implementation of the undulatory fin experimental systemInspirations from Gymnarchus niloticusDynamic modeling of the bionic propellerImplementation of experimental system

    Bionic neural networkPrinciples of fish central neural systemDesign of bionic neural network

    Results and analysisStartup experimentStop experimentForward and backward swimming experiments

    ConclusionsReferences