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

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  • Neurocomputing 71 (200 io t $ , niv e 9 ion l c f fi fish Ne has some disadvantages to deal with bionic robot which has changing needs. The biologic research results showed the undulatory fin experimental system which imitated from a fin experimental system 2.1. Inspirations from ‘‘Gymnarchus niloticus’’ ARTICLE IN PRESS $This work is supported by the National Basic Research Program of ‘‘Gymnarchus niloticus’’, as shown in Fig. 1, is a fresh water flesh-eater that mainly lives in Nile of Egypt [4]. 0925-2312/$ - 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 computing complexity and unadaptable with changing needs [11,13,6]. The other is bionic neural network control method which imitated the biological neural network of the animals. The rhythmic movements of vertebrates include swimming (fishes), running (human or quadruped), flying (birds) are produced by central pattern-generating neural networks whose output is shaped by sensor and neuromodulatory inputs to allow the animal to adapt its movements to flesh-eater fish and its dynamic model are given. In Section 3, the bionic neural network which based on biological CPGs principles and constructed with our novel neural oscillator is presented. Then the experimental results of primary move- ments are given in Section 4 to demonstrate our control method. Finally, conclusions are drawn in Section 5. 2. Dynamic modeling and implementation of the undulatory Aquatic animals, most of which are fishes, have higher locomotion performance than man-made underwater vehicles [9,2,17]. Many scientists and engineers have built different kinds of fish-robots replicating the animal’s locomotion abilities [13,6,19,24]. There are two different ways to control all the joints to achieve high performances. One is the reverse kinematic control method which consists of observation and recording of animal’s movements, mimic modeling of bionic robot’s movement and gaits planning in real-time [12,18]. It network for fish-robots [1,5,8,7,26]. The main objective of this paper is to investigate the bionic neural network control method for fish-robots. Our team [21] built a novel fish-robot with a long dorsal fin propeller, which has nine joints with individual control modules and parallel connections to the vehicle base. It is worthwhile to mention that our approach just concentrated on the movements of the undulatory fin propeller, and the locomotion of the fish-robot in the water will be presented in our future papers. The rest of this paper is organized as follows. In Section 2, the 1. Introduction possibility and validity to construct such an artificial neural Design of an artificial b control fish-robo Daibing Zhang, Dewen Hu� College of Mechatronics and Automation, National U Available onlin Abstract An artificial bionic neural network to control fish-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 efficiency. 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 fish-robot, which is inspired from ‘‘Gymnarchus onnections and composed of several motors. The principle of the sh is analyzed. An artificial neural network which has many -robot. Experimental results of startup, stop, forward swimming ural oscillator; Bionic neural network 8) 648–654 nic neural network to www.elsevier.com/locate/neucom
  • The long dorsal fin produces the main propulsion force for hunting or cruising in low speed, which belongs to median and paired fin (MPF) mode according to the swimming classification [22]. The first inspiration is that we can build such a bionic propeller to be mounted on the straight axis base of underwater vehicles. It can be used as an assistant propeller for a normal underwater vehicle maneuvering at low speed or the main propeller for special fish-robots. The second inspiration is that the undulatory fin is composed of a lot of joints and an elastic membrane. Each joint consists of one servo motor and one steel ‘‘fin ray’’ which moves ‘‘left– right’’. The last important inspiration is that we can create a novel bionic neural network control system to perform the ‘‘manager’’ role of the bionic propeller. 2.2. Dynamic modeling of the bionic propeller The bionic propeller can be modeled as a group of actuators, spring elements and damping elements, as shown actuator for its low cost and easy control with pulse wide length of fin rays is 150 or 100mm. 3. Bionic neural network 3.1. Principles of fish central neural system Fish locomotion is governed by central neural system which is called ‘‘central pattern generators’’ (CPGs) [1,15,3,26,5,14] and modeled as shown in Fig. 4. The two CPGs located in each segment of spine cord have reciprocal inhibitory connections and can stimulate each side muscles to contract or stretch alternately. The supraspinal inputs from cerebrum play a major role in startup, stop and turn. When the steady locomotion is formed, the inputs from the high controller are not needed ARTICLE IN PRESS Fig. 3. Experimental system of the undulatory fin propeller and the test- D. Zhang et al. / Neurocomp in Fig. 2. Each joint has one turning freedom and one servo motor. The dynamics of the joint is given as J €yþ D_yþ ksy ¼ t, (1) where y is the joint angle of fin moves from balance position which in the vertical plane, _y is the angular velocity, €y is the angular acceleration, J is the rotating inertia, D is the damping coefficient, ks is the restore moment and t is the driving moment of the motor. Parameters of head, tail and middle joints have different values according to the undulatory parameters and traveling wave’s direction. Since all joints drive the membrane undulating in the water by steel fin rays, the feedback forces and moments from the water cannot be Fig. 1. Structure of ‘‘Gymnarchus niloticus’’. fin base fin joint Fig. 2. Dynamic model of the undulatory fin propeller. modulation(PWM) signals. The test-bed has a long straight track and is equipped with sensors to measure the changing parameters in locomotion. The measure parameters include power supply voltage, electric current, axial force, lateral force, propulsion acceleration, propulsion speed and swing angles of all joints. The final experimental system and the test-bed are shown in Fig. 3. The number of joints is nine, the distance between adjacent joints is 45mm and the neglected. To the best of our knowledge, however, it involves complicated nonlinear, unsteady flow hydrody- namics and cannot be modeled accurately. Fortunately, we have obtained one essential rule from the experiments: water feedback effects result in the steady increasing of damping coefficients, rotating inertia and decreasing of restore moment. 2.3. Implementation of experimental system An undulatory fin experimental system was built to validate the expectation of the novel bionic propeller. Its mechanism was designed by three-dimensional CAD soft- ware. Futaba S3003 servo motor was selected as joint bed. uting 71 (2008) 648–654 649 any longer, and the locomotion patterns are produced and modulated by CPGs network.
  • 3.2. Design of bionic neural network There are several key points in the design of bionic neural network. Firstly, the bionic propeller just adopts one servomotor to drive a joint while the fish has two group muscles in each joint. We can design one CPG in each segment to control the corresponding joint. Secondly, a discrete computational model is adopted to simulate the continuous biological tissues. Lastly, the connection lag time between neurons always exists and determines the intersegmental phase lag. The lag time function in the computational model is necessary. Since the CPG is often modeled as a neural oscillator with intersegmental descend- ing command and segmental sensor feedback, we propose a novel neural oscillator which is different from the Wilson–Cowan oscillator [23,20] and Matsuoka oscillator [16]. It is based on the sine–cosine oscillator model and all oscillatory parameters can be modulated individually [25]. The dynamics of the novel oscillator is described as _u ¼ ov þ k �u r þ 4 p tan�1 u r � �� � ; _v ¼ �ou þ k �v r þ 4 p tan�1 v r � �� � ; 8>>>< >>>: (2) where u and v denote the activity of inhibitory neuron and excitatory neuron, respectively. And o is a parameter which mainly determines the angular frequency of oscilla- tion, k denotes the sustain strength of limit cycles and r denotes the approximate radius of the limit cycles. The nonlinear function f ðx; k; rÞ is adopted to represent the complicated self-feedback effect, described as f ðx; k; rÞ ¼ k � x r þ 4 p tan�1 x r � �� � . (3) The limit cycles trajectory in this oscillator with k ¼ 5, r ¼ 1, o ¼ 2p is shown in Fig. 5(a). The original point is the 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) 648–654650 CPG CPG CPG CPG CPG CPG CPG CPGc e r e b r u m M M M Excitatory connection Inhibitory connection Stretch receptor M Fig. 4. Central neural system for fish locomotion. -3 -2 -1 0 1 2 -2 -1 0 1 2 u v 3 Fig. 5. Limit cycles of the novel oscillator (a) and by a small disturbing signal and transfer to the limit cycles. We designed the segmental CPG which is illustrated in Fig. 5(b) based on the oscillator. The dynamics of the CPG is _u ¼ ov þ f ðu; k; rÞ þ puðtÞ; _v ¼ �ou þ f ðv; k; rÞ þ pvðtÞ; y ¼ u; 8>< >: (4) where puðtÞ and pvðtÞ denote the external inputs composed of descending commands and sensor feedback and yðtÞ denotes the output from the inhibitory neuron to the motor. The bionic neural network we finally designed is shown in Fig. 6. The high level controller controls the undulatory angular 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 ¼ ov1 þ f ðu1; k; rÞ þ sfdðt � DTÞðu2 � u1Þ þsbdðt � DTÞquðtÞ; _v1 ¼ �ou1 þ f ðv1; k; rÞ þ sfdðt � DTÞðv2 � v1Þ þsbdðt � DTÞqvðtÞ; y1 ¼ u1; 8>>>>>>< >>>>>>: (5) where quðtÞ and qvðtÞ denote the high level commands of startup or stop, and sf and sb are the intersegmental u v ωω u v f f u v y Motor CPG model based on the novel oscillator (b).
  • ARTICLE IN PRESS PG M3 u v u u rk f mp connection’s logical status defined as sb ¼ 1; sf ¼ 0 ðswimming forwardÞ; sb ¼ 0; sf ¼ 1 ðswimming backwardÞ: ( (6) And dðt � DTÞ means the lag time between adjacent segments. To sustain a whole travel wave on the undulatory fin, the lag time is calculated as DT ¼ 2p no , (7) where n is the number of undulatory fin joints. The dynamics of middle segments has an uniform expression as _ui ¼ ovi þ f ðui; k; rÞ þ sfdðt � DTÞðuiþ1 � uiÞ8>> ω u v M1 CPG1 CPG2 C M2 u v High Level Controller r Fig. 6. Bionic neural netwo D. Zhang et al. / Neuroco þsbdðt � DTÞðui�1 � uiÞ; _vi ¼ �oui þ f ðvi; k; rÞ þ sfdðt � DTÞðviþ1 � viÞ þsbdðt � DTÞðvi�1 � viÞ; yi ¼ ui; i ¼ 2; 3; . . . ; n � 1: >>>>< >>>>>>: (8) And the dynamics of the tail segment is _un ¼ ovn þ f ðun; k; rÞ þ sbdðt � DTÞðun�1 � unÞ þsfdðt � DTÞquðtÞ; _vn ¼ �oun þ f ðvn; k; rÞ þ sbdðt � DTÞðvn�1 � vnÞ þsfdðt � DTÞqvðtÞ; yn ¼ un: 8>>>>>>< >>>>>>: (9) 4. Results and analysis The bionic propeller’s locomotion are classified as startup, stop, forward swimming and backward swimming. Experiments of the experimental system and simulations by Matlab/Simulink have been performed to testify the bionic neural network control method. 4.1. Startup experiment The startup of the locomotion is actually to activate the nonlinear coupled neural network. We imposed a short time width pulse on the head segment. The startup function is given as quðtÞ ¼ stepðt � tsÞ � stepðt � ts � tdÞ qvðtÞ ¼ 0 ( stepðtÞ ¼ 0; tp0; stepðtÞ ¼ 1; t40; ( ð10Þ 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 fin propeller. uting 71 (2008) 648–654 651 experimental system is shown in Fig. 7, where ts ¼ 0:1 s, td ¼ 0:01 s, o ¼ 4p, r ¼ 15�, k ¼ 5. The inhibitory neuron of the first CPG is excited at t ¼ ts. Then each CPG is excited in turn without external inputs. The ninth CPG holds up the same phase with but different amplitude from the first CPG. The locomotion of the bionic propeller has the same process with the bionic neural network. The process control by bionic neural network is quite different from the reverse kinematic planning method but similar with the natural fish. It avoids sudden startup and destroying of servo motors. Another advantage is keeping the fluid around the undulatory fin steady and away from turbulence. 4.2. Stop experiment The stop process is to weaken and cease oscillation of the bionic neural network. A direct way is to set all neurons to zero at one time. This method neglects the transition from locomotion to stillness and may destroy the propeller hardware. We instead use a descending function which applied to all oscillators in the artificial neural network to
  • ARTICLE IN PRESS tim 1.5 2 2.5 3 6 time/sec t h e ta 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 C P G o u tp u t y 8 ta mp modulate the oscillation amplitude, given as rðtÞ ¼ r0 1� 2 p tan�1ðkcÞ Z t¼0 stepðt � tcÞdt � � , (11) where r0 is the original amplitude, tc is the time of stop and kc 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 ¼ 10 and kc ¼ 5. After one or two seconds, the oscillatory amplitude of the 0 0.5 1 0 2 4 jo in ts ' a n g le Fig. 7. Startup process of the bi 0 0.5 1 -0.4 -0.2 0 0.2 0.4 C P G o u tp u t y 8 CPG1 CPG2 CPG3 CPG4 D. Zhang et al. / Neuroco652 bionic neural network is restricted into small range, and the locomotion of the propeller seems ‘‘stop’’. It is believed that when the locomotion of animals stops, the oscillation in the neural network never diminish but just inhibited by basal ganglion. And once the inhibitory command is canceled by the high level controller, the locomotion resume again [3,1]. The amazing phenomenon we observed on the bionic neural network and propeller agree with the above viewpoint. 4.3. Forward and backward swimming experiments The external commands or sensory feedback are not necessary in the steady swimming process, and the forward swimming process of the bionic neural network and propeller is shown in Fig. 9. The phase lag between adjacent joints is hold up by the lag time function. The backward swimming process has similar properties with the forward swimming except the sequence reversal of CPGs and joints. There is no sensory feedback in our current control method, and the special swing amplitude and angular frequency of each joint still cannot affect the locomotion. 1.5 2 2.5 e/sec 5 CPG6 CPG7 CPG8 CPG9 uting 71 (2008) 648–654 5. Conclusions We have presented a novel bionic neural network to control the fish-robot. The basic unit of the bionic neural network is an artificial neural oscillator which consists of two neurons, and it has excellent control properties for almost independently modulating of undulatory angular velocity and amplitude. The bionic neural network has three parts including head segment, middle segments and tail segment. To testify the control performance of the bionic neural network, we have carried out several experiments on startup, stop, forward swimming and backward 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 jo in ts ' a n g le t h e Fig. 8. Stop process of the bionic neural network and propeller.
  • ARTICLE IN PRESS tim tim jo PG1 the mp indicate the importance of the oscillation in the neural network. Although we have built an undulatory fin propeller experimental installation and validated the novel control method, we have not consider the modern control theory 6.9 7 7.1 7.2 0 Fig. 9. Forward swimming process of 6.8 6.9 7 7.1 -0.4 -0.2 0 0.2 0.4 C P G o u tp u t y 2 4 6 8 in ts ' a n g le t h e ta CPG8 CPG9 CCPG7CPG6 D. Zhang et al. / Neuroco and technology, e.g., the feedback theory. And the bionic neural network is just used to produce the joint motion patterns. In the future, we’ll test the control method on the fish-robot and investigate the principles and dynamics of the feedback modulation and aim at the adaptive control with changing environments. References [1] A.H. Cohen, M.A. Lewis, Sensorimotor integration in Lampreys and robot I: CPG principles, Physiol. Rev. 76 (3) (1996) 687–709. [2] G.V. Lauder, E.D. Tytell, Hydrodynamics of undulatory propulsion, Fish Physiol. 23 (3) (2005) 425–468. [3] S. Grillner, Neural networks for vertebrate locomotion, Sci. Am. (1996) 64–69. [4] T.J. Hu, et al., Morpholocial measurement and analyses of Gymnarchus Niloticus, J. Bionics Eng. 2 (1) (2005) 25–31. [5] A.J. Ijspeert, A. Crespi, J.M. Cabelguen, Simulation and robotics studies of salamander locomotion, Neuroinformatics 3 (3) (2005) 171–196. [6] N. Kato, Control performance of fish robot with mechanical pectoral fins in horizontal plane, IEEE J. Ocean Eng. 25 (1) (2000) 121–129. [7] N. Kazuki, A. Tesuya, A. Yoshihito, Design of an artificial central pattern generator with feedback controller, Intelligent Autom. Soft Comput. 10 (2) (2004) 185–192. [8] H. Kimura, S. Akiyama, K. Sakurama, Realization of dynamic walking and running of the quadruped using neural oscillator, Autonomous Robots (7) (1999) 247–258. [9] M.J. Lighthill, Aquatic animal propulsion of high hydromechanical efficiency, J. Fluid Mech. 44 (1970) 265. [11] J. Liu, I. Dukes, H. Hu, Novel mechatronics design for a robotic fish, in: IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005, pp. 2077–2082. [12] J.D. Liu, H.S. Hu, A 3D simulator for autonomous robotic fish, Int. J. Autom. Comput. (2004) 42–50. [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) 648–654 653 robotic fish with modular flexiable fins, in: IEEE International Conference on Mechatronics and Automation, Niagara, Canada, 2005, pp. 958–963. [14] M. MacKay-Lyons, Central pattern generation of locomotion: a review of the evidence, Phys. Ther. 82 (1) (2002) 69–83. [15] E. Marder, D. Bucher, Central pattern generators and the control of rhythmic movements, Curr. Biol. 11 (23) (2001) 986–996. [16] K. Matsuoka, Mechanism of frequency and pattern control in the neural rhythm generators, Biol. Cybern. 56 (1987) 345–353. [17] G.K. Taylor, R.L. Nudds, A.L.R. Thomas, Flying and swimming animals cruise at a Stouhal Number tuned for high power efficiency, Nature 425 (2003) 707–711. [18] Y. Toda, K. Fukui, T. Sugiguchi, Laminar flow computation around a plate with two undulating side fins, J. Kansai Soc. Nav. Archit. 237 (2002) 71–78. [19] M.S. Triantafyllou, G.S. Triantafyllou, D.K.P. Yue, Hydrodynamics of fishlike swimming, Fluid Mech. 32 (2000) 33–53. [20] T. Ueta, G.R. Chen, On synchronization and control of coupled Wilson Cowan neural oscillators, Int. J. Bifurcation Chaos 13 (1) (2003) 163–175. [21] G.M. Wang, et al., New underwater robot propelled by undulations of long-based fin, in: International Conference on Mechanical Engineering and Mechanics, Nanjing, 2005, pp. 475–478. [22] P.W. Webb, Form and function in fish swimming, Sci. Am. 251 (1984) 58–68. [23] H.R. Wilson, J.D. Cowan, Excitatory and inhibitory interactions in localized populations of model neurons, Biophysics (12) (1972) 1–24. [24] J.Z. Yu, et al., Motion control algorithms for a free-swimming biomimetic robot fish, Acta Automatica Sin. 31 (4) (2005) 537–542. [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. 1664–1669. [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(1–4). 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, fish-robot and neural network control. Dewen Hu received the B.S. degree and master’s degree in Automatic Control from Xi’an 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 Sheffield, 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, identification 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 field of control science and technology. His research interests include mission planning and control of unmanned aerial vehicles (UAVs), artificial 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 PRESS D. Zhang et al. / Neurocomputing 71 (2008) 648–654654 Design of an artificial bionic neural network to control fish-robot’s locomotion Introduction Dynamic modeling and implementation of the undulatory fin experimental system Inspirations from ’’Gymnarchus niloticus’’ Dynamic modeling of the bionic propeller Implementation of experimental system Bionic neural network Principles of fish central neural system Design of bionic neural network Results and analysis Startup experiment Stop experiment Forward and backward swimming experiments Conclusions References