construction and central pattern generator-based control of a … · 2009-02-19 · construction...

Advanced Robotics 23 (2009) 19–43www.brill.nl/ar

Full paper

Construction and Central Pattern Generator-Based Controlof a Flipper-Actuated Turtle-Like Underwater Robot

Wei Zhao ∗, Yonghui Hu and Long Wang

Intelligent Control Laboratory, Department of Mechanics and Space Technologies,College of Engineering, Peking University, Beijing 100871, PRC

Received 29 February 2008; accepted 18 July 2008

AbstractThis paper deals with the construction and control of a turtle-like underwater robot with four mechanicalflippers. Each flipper consists of two joints generating a rowing motion by a combination of lead-lag andfeathering motions. With cooperative movements of four flippers, the robot can propel and maneuver inany direction without rotation of its main body and execute complicated three-dimensional movements,including ascending, submerging, rolling and hovering. The control architecture is constructed based ona central pattern generator (CPG). A model for a system of coupled nonlinear oscillators is established toconstruct a CPG and has been successfully applied to the eight-joint turtle-like robot. The CPGs are modeledas nonlinear oscillators for joints and inter-joint coordination is achieved by altering the connection weightsbetween joints. Rowing action can be produced by modulating the control parameters in the CPG model.The CPG-based method performs elegant and smooth transitions between swimming gaits, and enhancedadaptation to the transient perturbations due to nonlinear characteristics. The effectiveness of the proposedmethod is confirmed via simulations and experimental results.© Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2009

KeywordsTurtle-like underwater robot, 2-d.o.f. flippers, central pattern generator, swimming patterns, rowing action

1. Introduction

Robotics research has shown much progress with the development of robotic tech-nologies to complex and dynamic environments, especially those inaccessible tohumans like outer space and the deep oceans. In the fields of ocean development andocean investigation, various autonomous underwater vehicles (AUVs) have beendeveloped to survey the complex and dynamic undersea environments. However,the state of the art in AUV technology can hardly meet the mission requirements

* To whom correspondence should be addressed. E-mail: [email protected]

© Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2009 DOI:10.1163/156855308X392663

20 W. Zhao et al. / Advanced Robotics 23 (2009) 19–43

of high propulsive efficiency, excellent maneuverability and low noise. Swimminganimals have been evolving their aquatic locomotion abilities for thousands of mil-lions of years, achieving superb swimming performances and surpassing man-madeunderwater vehicles in many respects such as propulsive efficiency, maneuverabil-ity and acceleration. Based on recent progress in mechanics, materials, computing,electronics and bionics, many biologically inspired underwater vehicles that employbiomimetic swimming mechanisms have been created to bridge the gap between themission requirements and available technologies.

In the area of biorobotic AUVs, the fish-like robot is the early focus and fish-likeswimming has become one of the interesting research topics. Significant work in ro-botic fish was initiated in the 1990s by Triantafyllou et al. [1, 2]. An eight-link, foil-flapping robotic mechanism, i.e., RoboTuna, was developed and its drag-reductionmechanism was experimentally investigated. The authors have also undertakenbiomimetic robotics research with special efforts focused on the mechatronic de-sign and motion control of biomimetic robotic fish [3, 4]. The robotic fish calledBlackBass developed by Kato used the rowing mode of oscillatory pectoral finpropulsion and demonstrated high maneuverability [5]. With further research onunderwater biorobotics, other animals with rowing or flapping appendages suchas turtles and penguins are receiving more and more attention. Their paired ap-pendages are used for propulsion and maneuvering without deformation of thebody. Since biological observations have shown that pectoral fins or flippers un-dergoing a combination of lead-lag, feathering and flapping motions can producelarge lift, side force and thrust, biorobotic AUVs with a rigid body can also use theirflipper apparatus as the sole source of propulsion and maneuvering forces. Severalunderwater robots of this kind have been developed to investigate the swimmingperformance, including efficiency, maneuvering, etc. Based on sea turtles, Konnoet al. developed a turtle-like submergence vehicle, whose fore fins flap for propul-sion and maneuvering by a combination of flapping and feathering motions [6]. In2004 at MIT, Licht et al. developed a biomimetic flapping foil AUV that propelswith four oscillating foils and analyzed the generation of thrust [7]. Dudek et al.designed a visually guided amphibious robot named AQUA at McGill University,which uses six paddles to achieve movements with 6 d.o.f. [8]. In 2006, Long etal. constructed an aquatic robot named Madeleine in Vassar College, which waspropelled by four flippers with 1 d.o.f. oscillating only in pitch [9].

In this paper, a novel turtle-like underwater robot equipped with four mechanicalflippers is constructed and controlled based on a central pattern generator (CPG).The robot has a number of biologically inspired features and the contributions ofthis paper lie in the following. (i) A four-symmetrical-flippered, top-shell-covered,turtle-like architecture is constructed. (ii) The 2-d.o.f. mechanical flippers, that con-sist of two joints generating a rowing motion, share the locomotion mechanism withthe rowing forelimbs of softshell turtles. (iii) The configuration of the robot is forhigh maneuverability; as a result, it can propel and maneuver in any direction with-out rotation of its main body, and execute complicated three-dimensional (3-D)

W. Zhao et al. / Advanced Robotics 23 (2009) 19–43 21

movements, including ascending, submerging, rolling and hovering, by cooperativemovements of four flippers. (iv) Based on CPGs, multiple swimming patterns aredesigned and implemented on the robot. (v) The advantages of bio-gaits generatedby the CPG model are investigated and the influence of model parameter setting onthe swimming gaits is studied. This robot shows great promise of utility in prac-tical applications such as seabed exploration, oil-pipe leakage detection, oceanicsupervision, aquatic life-form observation, military detection, etc.

The rest of the paper is organized as follows. Section 2 provides the biologicalbasis of turtle swimming. In Section 3, an overall description of the turtle-like un-derwater robot’s configuration is given in detail. In Section 4, we describe the CPGmodel and its application to the robot, presenting the advantages of the CPG-basedmethod and the influence of parameter setting on the swimming gaits via simula-tions. The experimental results are shown in Section 5. Finally, Section 6 concludesthe paper and summarizes the future work.

2. Review of Turtle Swimming

The locomotor system of turtles is uncommon among vertebrates in respect thatits body axis is largely inflexible. In most turtle species, their dorsal vertebrae arefused to the carapace and are immobile, additionally the tail is highly reduced, sothat they depend exclusively on limb movements for propulsion and maneuvering.

Sea turtles and freshwater turtles exhibit a number of specific differences inswimming mode. The flippers of sea turtles are elongated from hypertrophied fore-limbs to produce lift-based thrust during flapping strokes in open-ocean swimming[10–13]. In contrast, for freshwater turtles, the hindlimb has previously been re-garded as the dominant propulsive part during aquatic locomotion because thehindfoot can form a broad paddle to generate drag-based thrust during rowingstrokes [10, 14]. However, as a typical kind of freshwater turtle, softshell turtles(e.g., Apalone spinifera shown in Fig. 1) take the forelimb as an effective thrustgenerator during aquatic locomotion, and their forelimb has two joints similar to theelbow and wrist [15]. Extensive investigations have revealed the contrast between

Figure 1. Spiny softshell turtle (Apalone spinifera).


the flapping forelimb strokes used by swimming sea turtles and the rowing forelimbstrokes used by most swimming freshwater turtles [11–13, 16–18]. As mentionedbefore, in flapping strokes, dorsoventral forelimb movements are involved predom-inantly, while anteroposterior forelimb movements combined with rotation of thefoot are involved predominantly in rowing strokes. Although the flapping motionmechanism is widely used by vertebrates in aquatic environments for generatingthrust, the persistence of rowing motion among aquatic species has been attributedto diverse factors [18, 19]. Despite the lower velocity in rowing, drag-based propul-sion is frequently used by aquatic species with high maneuverability, and by speciesthat have the ability to travel both on land and in water [18, 19].

3. Construction of a Turtle-Like Underwater Robot

3.1. General Structure of a Turtle-Like Robot Prototype

Inspired by softshell turtles, a turtle-like underwater robot equipped with four me-chanical flippers is being developed in our laboratory. The robot assumes a modularstructure including a cylindrical main body, four identical flipper actuator modulesand their attached wing-shaped foils. Figure 2a shows a photograph of the turtle-like

(a)

(b)

Figure 2. (a) Prototype and (b) general structure of a turtle-like underwater robot.


(a) (b)

Figure 3. Illustration of 2-d.o.f. movements. (a) Lead-lag motion. (b) Feathering motion.

Table 1.Technical parameters of the turtle-like robot prototype

Item Value

Dimension (L × W × H ) ∼200 mm × 200 mm × 175 mmWeight ∼5.0 kgNumber of flipper actuator modules 4Maximum oscillating frequency 4.0 HzPower supply for motors DC, 6.0 V, 2500 mAhPower supply for control unit DC, 4.8 V, 2500 mAhMicrocontroller AT91SAM7A3, 48 MHzActuator mode R/C servomotorOperation mode radio control, 444 MHz

robot prototype. The mechanical configuration of the turtle-like robot is illustratedin Fig. 2b.

Each flipper can perform lead-lag and feathering motions, which can be con-trolled independently and combined to form a rowing action. The lead-lag motionactuated by the servomotor inside the main body through a gear set is character-ized by posterior and anterior motions in the horizontal plane, while the feather-ing motion actuated by the servomotor inside the flipper actuator module denotesthe rotation motion of the foil. Figure 3 illustrates the 2-d.o.f. movements of thefoil.

The basic technical parameters of this prototype are described in Table 1.

3.2. Structure of the Main Body

The main body can be regarded as a sealed hard body with several connected parts.As shown in Fig. 2b, the sealing-connected parts in top–bottom order include aspherical cap-shaped top shell, an aluminum circle, an aluminum top circular cover,a cylindrical body cover and an aluminum bottom cover. The top shell and bodycover made of polymethyl methacrylate are transparent for leakage detection. The


Figure 4. Structure of the main body.

aluminum circle is glued to the shell. Both the top circular cover and bottom coverare glued to the body cover. The aluminum circle and the top circular cover arescrewed together with O-rings between them. Four semicirques are stretched outaround the top circular cover and bottom cover. At the end of each semicirque is ahole for bearing installation.

The main body accommodates the power and electronics of the robot, and alsoprovides four inside joints for the lead-lag motion of the flippers. As shown inFig. 4, the elements inside the main body include an AT91SAM7A3-centeredprinted circuit board, a duplex wireless communication module (GW100B) withits antenna, four servomotors (Futaba S9451), and two battery groups supplying thecontrol unit and motors, respectively. The antenna is stretched out of the center ofthe top shell for remote control. The waterproofed power switch and the rechargeplug are fixed on the backside of the bottom cover.

Each of the four servomotors sealed inside the main body actuates its neighbor-ing flipper module’s lead-lag movement, respectively. A rotating shaft connectedto the axis of each servomotor sticks out through the dynamic sealing structure toactuate its neighboring flipper module through a gear set fixed under the bottomcover.

3.3. Structure of the Flipper Actuator Module

Each flipper actuator module is waterproofed separately. The attached four foilsare made of polyvinyl chloride, a material with a density a little greater than thatof water. The material is rigid enough to generate high thrust in water. Figure 5ashows a photograph of one flipper actuator module. The cylinder-shaped modulesplits into two semicylindrical pieces, which are screwed together with O-rings be-tween them. A cutaway view of the module is shown in Fig. 5b. A high torqueservomotor (Hitec HSR-5995TG) sits in the interior cavity of the semicylindricalpart to actuate the foil’s feathering movement. A big gear connected to the axis of


(a) (b)

Figure 5. Flipper actuator module. (a) Photograph. (b) Cutaway view.

the servomotor drives a small gear through which a rotating shaft sticks out pass-ing the dynamic sealing structure at the smaller protruding cylinder-shaped tube.The end of the rotating shaft connects to the foil. The rotational motion of the shaftgenerates feathering motion of the foil. The transmission ratio of gear transmissionis 1:2 so that the oscillatory amplitude of the foil is twice that of the servomotor.Since the rotational range of the servomotor is limited to 180◦ (−90◦ to 90◦), thefull range of feathering motion is doubled to 360◦ (−180◦ to 180◦). The maximumoscillating frequency of the foil is limited to 4 Hz with an oscillating amplitude of40◦ due to the operating speed limitation of servomotor.

3.4. Electronics and Sensors

An embedded AT91SAM7A3-centered controller is used for generating real-timegaits, communicating with a personal computer and collecting the sensor data foranalysis. A two-axis accelerometer (ADXL202) is used to measure the accelera-tions on the pitch and roll axes. Figure 6 presents the hardware architecture of thecontrol system for the turtle-like robot.

The motion of the turtle-like robot is controlled by the microcontrollerAT91SAM7A3 that incorporates a high-performance 32-bit RISC, ARM7TDMIprocessor and a wide range of peripherals from Atmel Corporation. The con-troller connects the wireless communication module through a UART port andmeasures the duty cycle of the pulse width modulation (PWM) signal generatedby the accelerometer for calculating acceleration. The servomotor has internal po-sition feedback and the degree of turn of the axis depends upon the input PWMsignal from the microcontroller. The microcontroller generates eight PWM signalsto adjust the movements of a total of eight joints. Other interfaces like a USB port,CAN bus, IIC bus and analog-to-digital converter have been designed for futureapplications.


Figure 6. Hardware architecture of the control system.

4. CPG-Based Control

4.1. CPG Model

Neurobiology studies have shown that the locomotion of animals is controlledhierarchically by the central nervous system, from the cerebral cortex level, thebrainstem level to the spinal cord level. Fundamental rhythmic movements in loco-motion, such as walking, running, swimming and flying, are generated by CPGs atthe spinal cord level. A CPG is a neuronal circuit capable of producing rhythmicpatterns of neural activity automatically and unconsciously. The rhythmic patternactivates motor neurons that control the muscles generating the rhythmic move-ments. CPGs are networks of neurons that can produce coordinated oscillatorysignals without oscillatory inputs. The sensory input or descending input fromhigher elements can regulate the frequency and phase of the rhythmic patterns byaltering the intrinsic properties of the neurons, and the synaptic strengths and con-nectivity among them [20].

A typical example of a CPG is found in the lamprey and has been studied ex-tensively [21, 22]. It is known that the lamprey is one of the earliest and simplestvertebrates, and swims by propagating a traveling wave along its body from head totail. Thus, the CPG has been an interesting source of inspiration for motion controlof robots.

4.1.1. Mathematical Model for a Singular JointIn the earliest research, the most fundamental CPG model using the neural oscil-lator was proposed by Brown [23]. It consists of two neurons and has interactionsbetween neurons by reciprocal inhibition. Gradually, a number of artificial neuralnetworks have been proposed as the CPG model [23–25]. As a biologically in-


spired approach, the CPG-based method has been applied to locomotion of robotssuccessfully [26–30].

For our robot, each bionic flipper adopts two servomotors to drive two joints.We can design one CPG to control the corresponding joint. In this paper, the CPGmodel to produce rhythmic control signals consists of an excitatory neuron and aninhibitory neuron with excitatory–inhibitory connections. The original sine–cosineoscillator model is described by: {

υ̇ = −ωθ

θ̇ = ωυ,(1)

where υ is the activity of excitatory neuron, θ denotes the activity of inhibitoryneuron and ω is the synaptic strength between them.

The main problem with this simple oscillator (1) is that the oscillatory amplitudewill be absolutely determined by the initial conditions (θ0, υ0). Hence, we have nocontrol over the amplitude of the signal. Furthermore, the signal’s amplitude willalso change when the system is perturbed by an external input. As a result, theoriginal system has no ability to form steady oscillation and cannot cope with theexternal perturbations. To improve that and to make the oscillatory status control-lable, a new term has been added to (1) as follows:{

υ̇ = −ωθ + f (υ, θ)

θ̇ = ωυ + f (θ,υ).(2)

If the function f is a linear function, the oscillator becomes a typical 2-D linearsystem which cannot produce steady oscillation. We choose the nonlinear functionf (x, y) added to fix the energy of the oscillator, described as:

f (x, y) = ωx − x

A(x2 + y2). (3)

The complete dynamic model of the nonlinear oscillator is presented as follows:⎧⎪⎨⎪⎩

υ̇ = −ωθ + ωυ − υ

A(θ2 + υ2)

θ̇ = ωυ + ωθ − θ

A(θ2 + υ2).

(4)

Without loss of generality, the dynamics of the model (4) is expressed by thefollowing equations: {

Aυ̇ = Aω(υ − θ) − υ(θ2 + υ2)

Aθ̇ = Aω(υ + θ) − θ(θ2 + υ2).(5)

Equation (5) has two particular solutions: one is the origin (0,0), which is anunstable fixed point, and the other is a stable limit cycle, which is a sinusoidal signalwith amplitude

√Aω and period 2π/ω. θ will indeed converge to the particular

solution θ̃ (t) = √Aω sin(ωt + φ) from any initial conditions (θ0, υ0) (except the

origin (0,0) in the phase plane), where φ is determined by the initial conditions.In (5), Aω represents the desired energy and θ2 +υ2 represents the actual energy

of the oscillator. Rather than explicitly prescribing an oscillatory signal for the joint


(a) (b)

Figure 7. (a) Solution θ(t) of (6) where the parameters are: ω = 10, A = 40, θ̄ = 10 and θ quicklyconverges to its particular solution. (b) Corresponding limit cycle and the oscillator quickly reachesits limit cycle from different initial conditions (θ0, υ0) in each run.

angles, in which time-varying amplitudes and frequencies must be dictated in orderto prevent discontinuous joint angle signals, motivated by studies of CPG signalsin neurobiology, the nonlinear two-state model (5) is adopted and in this model theoutput θ from the inhibitory neuron will be used to prescribe joint angle motion.The positive parameter ω determines the oscillatory frequency of the joint angle.Thus, the bigger ω is, the faster the oscillator will reach its limit cycle.

The joint angle θ oscillates around θ = 0 in the above nonlinear oscillator. Sincethe turtle-like robot can propel and maneuver in any direction by modulating theoscillatory angle’s offset for each joint of mechanical flippers, we expect that the os-cillator of each joint can oscillate around an arbitrary offset θ̄ to implement flexiblemotion control in 3-D space. An offset value θ̄ is introduced and then (5) changesto (6) as:

⎧⎨⎩

�θ = θ − θ̄

Aυ̇ = Aω(υ − �θ) − υ(�θ2 + υ2)

A�̇θ = Aω(υ + �θ) − �θ(�θ2 + υ2).

(6)

The solution will converge to θ̃ (t) = θ̄ + √Aω sin(ωt + φ) in (6). The solution

and its limit cycle are shown in Fig. 7 as an example.

4.1.2. Coupling Joints TogetherThe above nonlinear oscillator illustrates a singular joint’s behavior property. Thegait pattern can be generated by coupling joints together, so a coupling term shouldbe added to (6) in the following way:

⎧⎪⎪⎨⎪⎪⎩

�θi = θi − θ̄i

Aiυ̇i = Aiω(υi − �θi) − υi(�θ2i + υ2

i ) + Ai

∑j

(aij θj + bijυj )

Ai�̇θi = Aiω(υi + �θi) − �θi(�θ2i + υ2

i ),

(7)


where θi denotes the desired angle of the ith joint of the robot, θ̄i indicates theangular offset added to the ith joint, and aij and bij are the connection weights todefine the coupling between the ith and the j th joints (i.e., the influence that the j thjoint has on the ith one). Cooperative movements can be obtained by modulating thephase-lag or phase-lead relationship between coupled joins, which is determined bythe coupling coefficients aij and bij .

In mathematics and computational science, the Euler method, named after Leon-hard Euler, is a numerical procedure for solving ordinary differential equations.In the Euler method, [υ(k + 1) − υ(k)]/T is used instead of υ̇ , so the differen-tial equations are transformed into difference equations. As a result, the differentialequations in (7) are then changed to difference equations using the Euler method inthe following way:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

�θi(k) = θi(k) − θ̄i

Ai

υi(k + 1) − υi(k)

T= Aiω(υi(k) − �θi(k)) − υi(k)

(�θ2

i (k) + υ2i (k)

)

+ Ai

∑j

(aij θj (k) + bijυj (k))

Ai

�θi(k + 1) − �θi(k)

T= Aiω(υi(k) + �θi(k))

− �θi(k)(�θ2

i (k) + υ2i (k)

),

(8)

where θi(k) represents the ith joint’s angle at the kth time, T denotes the step size oftime, and the initial conditions can be set as θi(0) = 0, υi(0) �= 0. Through recursivealgorithms, θi(k) can be calculated from (8) in real-time.

4.2. CPG-Based Method

The control for the turtle-like robot is based on the above CPG model that generatesthe rhythmic movements for real-time gait generation. Since the robot is composedof four mechanical flippers with two joints each, the CPG model of (8) can be ap-plied to an eight-joint system established for the turtle-like robot, as illustrated inFig. 8. By connecting the CPG of each joint, CPGs are mutually entrained, andoscillate at the same frequency and with a fixed phase difference. This mutual en-trainment between the CPGs of the flippers results in a swimming gait.

As observed from (8), a parametric vector E = {A1–A8,ω, θ̄1–θ̄8, aij , bij } regu-lating the swimming gaits of the turtle-like robot can be summarized. The settingof these parameters is to generate a proper swimming pattern according to turtlesswimming character. In the CPG model, θ̄1–θ̄8 determine the propulsive orientationof the robot, the connection weights aij , bij determine the phase difference ��ij

between connected joins, A1–A8 determine small or large amplitude swimmingmodes, and ω determines the oscillatory frequency. Based on the proposed CPGmodel, several swimming patterns and actions will be described next, and the ad-vantages of bio-gaits and the influence of parameter setting on the swimming gaitswill be given in detail in the simulations.


Figure 8. CPG network for the turtle-like robot. Joints 1, 2, 3 and 4 correspond to lead-lag motion,while joints 5, 6, 7 and 8 correspond to feathering motion. L, R, F and H denote the left, right, fore orhind flippers, respectively.

4.2.1. Typical Swimming PatternsConsidering parameter setting in swimming pattern design, the following points areproposed beforehand:

• The angular offset θ̄i added to feathering joints (i = 5–8) can range from −π

to π rad, as illustrated in Fig. 9.

• In the case of Ai = 0, whatever value ω, aij and bij are set to, the solution willconverge to θ̃i (t) = θ̄i in (8).

• In the case of Ai �= 0, the oscillatory amplitude for joint i is approximately√Aiω.

Based upon the joints used, the swimming can be classified into two basic modes:FJ (feathering joints) mode and LFJ (combination of lead-lag and feathering joints)mode. By modulating the oscillatory angle’s offset for each foil, the turtle-like robotcan accomplish complex movements in 3-D space. By cooperative movements offour symmetrical flippers combining lead-lag motion and feathering motion, theturtle-like robot can propel and maneuver in any direction without any rotationof its main body. The following typical swimming patterns with two modes havebeen designed and implemented on the robot by adopting different CPG modelparameters.

FJ forward swimming (Fig. 10a). The robot swims forward in a straight line bythe synchronized oscillations of all foils around the horizontal plane, with fixedpositions of lead-lag joints, in which case the CPG model parameters are set asA1 = A2 = A3 = A4 = 0, θ̄1 = θ̄2 = θ̄3 = θ̄4 = 0; ω ∈ [2π,8π], A5 = A6 = A7 =A8 > 0 (S.t.

√Aiω ∈ [5◦,40◦], i = 5,6,7,8), θ̄5 = θ̄6 = θ̄7 = θ̄8 = 0, all connection

weights aij and bij to be near-zero values.


Figure 9. Illustration of angular offset for a foil.

Figure 10. Illustrations of eight typical swimming patterns designed for the turtle-like underwaterrobot. (a) FJ forward swimming. (b) FJ backward swimming. (c) FJ turning. (d) FJ rolling. (e) FJascending. (f) FJ submerging. (g) LFJ leftward swimming. (h) LFJ rightward swimming.

FJ backward swimming (Fig. 10b). The robot swims backwards by the synchro-nized oscillations of all foils around the horizontal plane in the contrary directionto forward swimming, with fixed positions of lead-lag joints, in which case theCPG model parameters are set as A1 = A2 = A3 = A4 = 0, θ̄1 = θ̄2 = θ̄3 = θ̄4 = 0;ω ∈ [2π,8π], A5 = A6 = A7 = A8 > 0 (S.t.

√Aiω ∈ [5◦,40◦], i = 5,6,7,8),

θ̄5 = θ̄6 = θ̄7 = θ̄8 = π, all connection weights aij and bij to be near-zero values.FJ turning (Fig. 10c). The differentiation of hydrodynamic forces in the hor-

izontal plane between the pair of foils on the left side and the right side willcause a yawing moment that is necessary to execute turning maneuvers on the ro-bot. An effective method to produce the yawing moment is to produce anteriorlydirected force on one side and posteriorly directed force on the other side, onecase of which is A1 = A2 = A3 = A4 = 0, θ̄1 = θ̄2 = θ̄3 = θ̄4 = 0; ω ∈ [2π,8π],


A5 = A6 = A7 = A8 > 0 (S.t.√

Aiω ∈ [5◦,40◦], i = 5,6,7,8), θ̄5 = θ̄6 = π,θ̄7 = θ̄8 = 0, all connection weights aij and bij to be near-zero values.

FJ ascending (Fig. 10e). The robot swims upwards with all foils oscillating syn-chronously around the vertical plane functioning to generate lift forces, in whichcase the CPG model parameters are set as A1 = A2 = A3 = A4 = 0, θ̄1 = θ̄2 =θ̄3 = θ̄4 = 0; ω ∈ [2π,8π], A5 = A6 = A7 = A8 > 0 (S.t.

√Aiω ∈ [5◦,40◦],

i = 5,6,7,8), θ̄5 = θ̄6 = θ̄7 = θ̄8 = −π/2, all connection weights aij and bij tobe near-zero values.

FJ submerging (Fig. 10f). The robot swims downwards with all foils oscillatingsynchronously around the vertical plane in contrary direction to ascending, in whichcase the CPG model parameters are set as A1 = A2 = A3 = A4 = 0, θ̄1 = θ̄2 =θ̄3 = θ̄4 = 0; ω ∈ [2π,8π], A5 = A6 = A7 = A8 > 0 (S.t.

√Aiω ∈ [5◦,40◦], i =

5,6,7,8), θ̄5 = θ̄6 = θ̄7 = θ̄8 = π/2, all connection weights aij and bij to be near-zero values.

FJ rolling (Fig. 10d). The differentiation of hydrodynamic forces in the verti-cal plane between the pair of foils on the left side and the right side will cause arolling moment on the robot, in which case the CPG model parameters are set asA1 = A2 = A3 = A4 = 0, θ̄1 = θ̄2 = θ̄3 = θ̄4 = 0; ω ∈ [2π,8π], A5 = A6 = A7 =A8 > 0 (S.t.

√Aiω ∈ [5◦,40◦], i = 5,6,7,8), θ̄5 = θ̄6 = −π/2, θ̄7 = θ̄8 = π/2, all

connection weights aij and bij to be near-zero values.LFJ leftward swimming (Fig. 10g). With each lead-lag joint turning to the posi-

tion perpendicular to that in FJ forward swimming, respectively, the robot swimsleftwards without any rotation of its main body by the synchronized oscillations ofall foils around the horizontal plane to generate leftward thrust, in which case theCPG model parameters are set as A1 = A2 = A3 = A4 = 0, θ̄1 = θ̄2 = θ̄3 = θ̄4 =π/2; ω ∈ [2π,8π], A5 = A6 = A7 = A8 > 0 (S.t.

√Aiω ∈ [5◦,40◦], i = 5,6,7,8),

θ̄5 = θ̄7 = π, θ̄6 = θ̄8 = 0, all connection weights aij and bij to be near-zero values.LFJ rightward swimming (Fig. 10h). With each lead-lag joint turning to the po-

sition perpendicular to that in FJ forward swimming, respectively, the robot swimsrightwards without any rotation of its main body by the synchronized oscillationsof all foils around the horizontal plane in contrary direction to leftward swimming,in which case the CPG model parameters are set as A1 = A2 = A3 = A4 = 0,θ̄1 = θ̄2 = θ̄3 = θ̄4 = π/2; ω ∈ [2π,8π], A5 = A6 = A7 = A8 > 0 (S.t.

√Aiω ∈

[5◦,40◦], i = 5,6,7,8), θ̄5 = θ̄7 = 0, θ̄6 = θ̄8 = π, all connection weights aij andbij to be near-zero values.

4.2.2. Rowing ActionRowing action, by coupling lead-lag motion and feathering motion together, canalso perform forward swimming, backward swimming and turning in the horizontalplane. In rowing action, the foils of our robot are brought ‘forward almost edge-wise and back broadside’ [31]. A sequence of the rowing action is illustrated inFig. 11. Rowing involves anteroposterior movements and rotations of the foils. Theoscillations of the lead-lag joint and feathering joint of one flipper are of the same


Figure 11. A sequence of the rowing action. Swimming forward edgewise (from (a) to (b)) and swim-ming back broadside (from (c) to (d)).

frequency. The setting of CPG model parameters in the rowing action will be stud-ied via simulations.

4.3. Simulations

4.3.1. Study of the Characteristics of CPG-Based Bio-gait GenerationWe conducted a series of simulation experiments to demonstrate the coordination,swiftness, adaptation and diversity of the proposed CPG-based method. First, tak-ing rolling, for example, the ability of the CPG-based method was tested to showelegant and smooth transitions between swimming gaits and enhanced ability tocope with transient perturbations due to nonlinear characteristic.

An example of such solutions that generate rolling movement is given in Fig. 12,where θ5(t)–θ8(t) represent oscillatory angles of all four foils of the robot and theCPG model parameters are set as A1 = A2 = A3 = A4 = 0, θ̄1 = θ̄2 = θ̄3 = θ̄4 = 0,ω = 4π, A5 = A6 = A7 = A8 = 32 (S.t.

√Aiω ≈ 20◦, i = 5,6,7,8), θ̄5 = θ̄6 =

−π/2, θ̄7 = θ̄8 = π/2, aij = bij = 0.03; t = 0–2.5 s. In particular, the frequencyand amplitude of all foils are modulated by changing the parameters ω → 8π, Ai →36 (i = 5,6,7,8) at time t = 1.5 s. As a consequence, the oscillatory frequency(almost ω/2π) rises approximately from 2 to 4 Hz and the oscillatory amplitude


(a) (b)

Figure 12. Modulation of both the oscillatory frequency and amplitude of the foils by changing theCPG model parameters at time t = 1.5 s.

(a) (b)

Figure 13. Random perturbation of the oscillatory angles of the foils at time t = 1 s.

for the ith joint (nearly√

Aiω, i = 5,6,7,8) is approximately modulated from 20◦to 30◦ at the same time t = 1.5 s. As shown in Fig. 12, the oscillation of eachfoil can smoothly and easily adapt to the abrupt change of oscillatory frequencyand oscillatory amplitude determined by CPG model parameters. As a result, theadjustment of the speed of the robot can be smooth and easy.

Furthermore, nonlinear oscillators of the CPG model have an enhanced ability tocope with transient perturbations due to nonlinear characteristics. When correctlycoupled, the oscillators in a circle will produce stable limit cycle behaviors after anytype of transient perturbation. Figure 13 illustrates this property. At a given time,random perturbations are applied to all oscillatory angles of the foils θ5–θ8. Aftera short transitory period, the system quickly and smoothly returns to the originalswimming gait.

In conclusion, the CPG-based method possesses a range of advantages overprevious gait generation algorithms: (i) the oscillatory angle of each joint can becalculated from the nonlinear difference equations utilizing recursive algorithms inreal-time, without large numbers of calculative operations (see (8)), (ii) the oscilla-


tion of each joint can smoothly and easily adapt to the abrupt change of oscillatoryfrequency and oscillatory amplitude determined by CPG model parameters (seeFig. 12), and (iii) enhanced ability to cope with transient perturbations due to non-linear characteristic (see Fig. 13). As a result, this CPG-based method providesgood adaptation to both modifications of the control parameter and random pertur-bations in the environment.

4.3.2. Study of a Flipper System With Two Coupled Nonlinear Oscillators inRowing ActionSince the behaviors of the four mechanical flippers in rowing action are almost thesame, a system is investigated to get an idea of how interconnected oscillators in thesame flipper behave, especially how the phase relation between them is determinedby the connection weights. Figure 14 shows the quarter-CPG we are going to study.In this system, the CPG model parameters include Ai , Ai+4, ω, θ̄i , θ̄i+4, ai+4,i ,bi+4,i , ai,i+4 and bi,i+4.

In rowing action, the phase difference �φi,i+4 between lead-lag joint i (i =1,2,3,4) and feathering joint i +4 will determine different types of rowing strokes.To perform ‘forward almost edgewise and back broadside’, the rule of setting thesemodel parameters to produce a rowing stroke is given by:

�φi,i+4 ∈[−π

4,π

4

], i = 1,2,3,4. (9)

As mentioned before, the amplitude and the frequency of each oscillator can beeasily controlled through Ai and ω. In addition, in the CPG network, it is also cru-cial to control the phase relation between coupled oscillators, which will be carriedout by the connections between the oscillators. After the system starts the phaseof each oscillator is first defined by its initial conditions θ0 and υ0, and the con-nections will quickly force a particular phase relation. Through simulations on theCPG model (8), the influence of the connection weights on the oscillations of cou-pled joints has been investigated. On the other hand, based on the simulation resultsthat give the dependence of phase difference on connection weights, the CPG modelparameters can be chosen obeying the rule in (9).

The following example will illustrate how the phase difference �φ between thetwo coupled joints is determined by the connection weights a and b by some simu-lation results. For simplicity, we supposed that only the feathering joint can receivea signal from its lead-lag one, i.e., ai,i+4 and bi,i+4 were set to 0. All of the parame-

Figure 14. A flipper system made of two nonlinear oscillators linked together.


Figure 15. Phase difference ��i,i+4 (rad) with ai,i+4 = 0 and bi,i+4 = 0.

ters were set as follows: ω = 4π, Ai = Ai+4 = 161 (S.t.√

Aiω = √Ai+4ω ≈ 45◦),

θ̄i = 0, θ̄i+4 = π/4, ai,i+4 = bi,i+4 = 0, only ai+4,i and bi+4,i were free variables.In the case of ai+4,i = 0 and bi+4,i = 0, there is no coupling term and the two jointsof a same flipper both run freely with phase differences ��i,i+4 = 0, which exactlyfits the condition in rule (9). As a result, the values of ai+4,i and bi+4,i could be setaround 0 for simulating. In this example, the values of ai+4,i and bi+4,i were iter-atively changed between −3 and 3. The simulation results in this case are given inFig. 15, stating how the phase difference ��i,i+4 changes with the modification ofai+4,i and bi+4,i . It can be concluded that the phase difference ��i,i+4 depends onthe quadrant in which the point (ai+4,i , bi+4,i ) locates regularly. The plane is ap-proximately split into two symmetric areas by the line ai+4,i = 0. In the area whereai+4,i > 0, the oscillation of the lead-lag joint lags that of the corresponding feath-ering joint in phase, while the phase-lead relation happens in the area of ai+4,i < 0.As observed from Fig. 15, the phase difference ��i,i+4 satisfies the rule in (9)stably in the areas of bi+4,i > ai+4,i > 0 and bi+4,i > −ai+4,i > 0.

Considering the rule and the simulation results, a set of solutions that generaterowing action have been obtained in our simulation and experiments. An example ofsuch solutions θi(t) and θi+4(t) that, respectively, represent oscillatory angles of thelead-lag joint and feathering joint of the same flipper is illustrated in Fig. 16, whereω = 4π, Ai = Ai+4 = 161 (S.t.

√Aiω = √

Ai+4ω ≈ 45◦), θ̄i = 0, θ̄i+4 = π/4,ai+4,i = −0.5, bi+4,i = 0.6, ai,i+4 = 0, bi,i+4 = 0 and t = 0–4 s. As shown inFig. 16, the phase relationship between the two coupled nonlinear oscillators ofeach flipper produces an appropriate type of rowing motion.


Figure 16. Oscillatory angles of the lead-lag joint and feathering joint of the same flipper based onthe CPG model during the rowing action.

5. Experiments and Results

5.1. Evaluation of Swimming Speed

The swimming performance of the turtle-like underwater robot was tested in a staticswimming tank with a size of 2250 mm × 1250 mm and with still water of 400 mmin depth. The robot was marked with specified colors and the information withinthe swimming tank was captured by an overhead CCD camera (see Fig. 17). Theimage was transmitted to a personal computer and processed with a visual trackingsoftware platform developed to obtain the position and orientation of the robot inreal-time. In this way, the speed and orientation of the turtle-like robot could bemeasured in the platform to test its swimming performance.

For the FJ forward swimming pattern, the average linear speed was tested byvarying the frequency and amplitude of foil oscillations. Steady-state speed wasmeasured at different levels of frequencies and amplitudes of all foils. Three groupsof foil oscillatory amplitudes were employed while the frequency was varied in eachcase. As illustrated in Fig. 18, the swimming speed increased with the oscillatoryamplitude until the peak value on amplitude of 30◦ and almost linearly with theoscillatory frequency. The swimming speed decreased with the enhancement of theamplitude after reaching its peak value because the oscillations became so largeas to generate braking waves. Overall, the robot could swim up to the speed of19.8 cm/s at a frequency of 4 Hz and amplitude of 30◦.

5.2. Testing of Swimming Patterns Sequentially

The ability of the CPG-based method was tested to produce different types ofswimming patterns presented above. The turtle-like robot can change its posturefrom one pattern to another smoothly. Figure 19 presents the variations of os-cillatory angles of eight joints when executing a sequence of typical swimmingpatterns. The sequentially executed swimming patterns include FJ forward swim-ming (t � 5 s), FJ backward swimming (5 < t � 10 s), FJ turning (10 < t � 15 s),


Figure 17. Experimental environments captured from the overhead camera.

Figure 18. Average linear speed in FJ forward swimming with different frequencies and amplitudes.The amplitudes used in each case are: A = {Ai = 400/ω} (S.t.

√Aiω = 20◦), B = {Ai = 900/ω} (S.t.√

Aiω = 30◦) and C = {Ai = 1600/ω} (S.t.√

Aiω = 40◦), i = 5,6,7,8.

FJ ascending (15 < t � 20 s), FJ submerging (20 < t � 25 s), FJ rolling (25 <

t � 30 s), LFJ leftward swimming (30 < t � 35 s) and LFJ rightward swimming(35 < t � 40 s). For convenience of clearly observing swimming patterns in 3-Dspace, the tests of sequential patterns were conducted in a transparent water tank(100 cm × 80 cm × 50 cm). Figure 20 shows an image sequence of the transi-tion from FJ forward swimming to LFJ rightward swimming and the correspondingmoving trajectory of the robot is illustrated in Fig. 21.

6. Conclusions and Future Work

In this paper, a flipper-propelled turtle-like underwater robot was constructed andcontrolled based on a CPG. Each of the four flippers can perform lead-lag andfeathering motions, which can be controlled independently and combined to forma rowing action. The cooperative movements of four symmetrical flippers can gen-


Figure 19. Variations of oscillatory angles of eight joints when executing a sequence of typical swim-ming patterns.

Figure 20. Image sequence of the transition from FJ forward swimming to LFJ rightward swimming.


Figure 21. Experimental trajectory estimated from the corresponding video of the above transition.

erate propulsion and maneuvering in any direction without any rotation of the mainbody. A CPG model of a nonlinear oscillator was introduced and the CPG-basedmethod was applied to the robot. Several typical swimming patterns, including turn-ing, up-and-down motion and rolling, were designed and implemented on the robot.The advantages of CPG-based gait generation were proposed and demonstrated viasimulations. The experimental results demonstrated high maneuverability of the ro-bot and presented its speed evaluation, and showed that the control method waseffective to produce different types of swimming patterns sequentially.

Further research will focus on developing more effective swimming patternsbased on the optimization of control parameters. Sensors like infrared detectors,ultrasonics and cameras will be incorporated for perception of the environments.Finally, a turtle-like underwater robot with various swimming skills and capable ofautonomous operation will be constructed.

Acknowledgements

This work was supported by National 863 Program (2006AA04Z258), 11-5 project(A2120061303), NSFC (60674050 and 60528007) and National 973 Program(2002CB312200). The authors would like to express their appreciation to Mr LeZhang and Mr Qi Wang for their daily technical assistance. They would also liketo thank Mr Guangming Xie, Ms Dandan Zhang and Ms. Jinyan Shao for theirconstructive discussions.

References

1. M. S. Triantafyllou and G. S. Triantafyllou, An efficient swimming machine, Sci. Am. 272, 64–70(1995).

2. D. Barrett, M. Grosenbaugh and M. Triantafyllou, The optimal control of a flexible hull roboticundersea vehicle propelled by an oscillating foil, in: Proc. 1996 IEEE AUV Symp., Monterrey, CA,pp. 1–9 (1996).


3. W. Zhao, J. Yu, Y. Fang and L. Wang, Development of multi-mode biomimetic robotic fish basedon central pattern generator, in: Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems,Beijing, pp. 3891–3896 (2006).

4. Y. Hu, L. Wang, W. Zhao, Q. Wang and L. Zhang, Modular design and motion control of re-configurable robotic fish, in: Proc. IEEE Int. Conf. on Decision and Control, New Orleans, LA,pp. 5156–5161 (2007).

5. N. Kato, Control performance in the horizontal plane of a fish robot with mechanical fins, IEEEJ. Oceanic Eng. 25, 121–129 (2000).

6. A. Konno, T. Furuya, A. Mizuno, K. Hishinuma, K. Hirata and M. Kawada, Development of turtle-like submergence vehicle, in: Proc. Int. Symp. on Marine Engineering, Tokyo, pp. 1–5 (2005).

7. S. Licht, V. Polidoro, M. Flores, F. Hover and M. Triantafyllou, Design and projected performanceof a flapping foil AUV, IEEE J. Oceanic Eng. 29, 786–794 (2004).

8. G. Dudek, M. Jenkin, C. Prahacs, A. Hogue, J. Sattar, P. Giguere, A. German, H. Liu, S. Saunder-son, A. Ripsman, S. Simhon, L.-A. Torres, E. Milios, P. Zhang and I. Rekletis, A visually guidedswimming robot, in: Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Edmonton, AB,pp. 3604–3609 (2005).

9. J. H. Long, J. Schumacher, N. Livingston and M. Kemp, Four flippers or two? Tetrapodal swim-ming with an aquatic robot, Bioinspirat. Biomimet. 1, 20–29 (2006).

10. W. F. Walker, The locomotor apparatus of Testudines, in: Biology of the Reptilia 4, Morphology D,(C. Gans and T. S. Parsons, Eds), pp. 1–100. Academic Press, New York, NY (1973).

11. J. Davenport, S. A. Monks and P. J. Oxford, A comparison of the swimming in marine and fresh-water turtles, Proc. Roy. Soc. Lond. B 220, 447–475 (1984).

12. S. Renous and V. Bels, Comparison between aquatic and terrestrial locomotions of the leatherbacksea turtle (Dermochelys coriacea), J. Zool., Lond. 230, 357–378 (1993).

13. J. Wyneken, Sea turtle locomotion: mechanisms, behavior and energetics, in: The Biology of SeaTurtles (P. L. Lutz and J. A. Musick, Eds), pp. 165–198. CRC Press, Boca Raton, FL (1997).

14. G. R. Zug, Buoyancy, locomotion, morphology of the pelvic girdle and hind limb and systematicsof cryptodiran turtles, Misc. Publ. Mus. Zool. Univ. Michigan 142, 1–98 (1971).

15. C. M. Pace, R. W. Blob and M. W. Westneat, Comparative kinematics of the forelimb duringswimming in red-eared slider (Trachemys scripta) and spiny softshell (Apalone spinifera) turtles,J. Exp Biol. 204, 3261–3271 (2001).

16. W. F. Walker, Swimming in sea turtles of the family Cheloniidae, Copeia, 00, 229–233 (1971).17. J. Davenport and G. A. Pearson, Observations on the swimming of the Pacific Ridley, Lepidochelys

olivacea (Eschscholtz 1829): comparisons with other sea turtles, Herpetol. J. 4, 60–63 (1994).18. J. A. Walker and M. W. Westneat, Mechanical performance of aquatic rowing and flying, Proc.

Roy. Soc. Lond. B 267, 1875–1881 (2000).19. S. Vogel, Life in Moving Fluids. Princeton University Press, Princeton, NJ (1994).20. F. Delcomyn, Neural basis for rhythmic behaviour in animals, Science 210, 492–498 (1980).21. J. Buchanan and S. Grillner, Newly identified ‘glutamate interneurons’ and their role in locomo-

tion in the lamprey spinal cord, Science 236, 312–314 (1987).22. S. Grillner, P. Wallen and L. Brodin, Neuronal network generating locomotor behavior in lamprey:

circuitry, transmitters, membrane properties, and simulation, Annu. Rev. Neurosci. 14, 169–199(1991).

23. G. Brown, On the nature of the fundamental activity of the nervous centers; together with ananalysis of the conditioning of the rhythmic activity in progression, and a theory of the evolutionof function in the nervous system, J. Physiol. 48, 18–46 (1914).


24. G. Taga, Y. Yamaguchi and H. Shimizu, Self-organized control of bipedal locomotion by neuraloscillators in unpredictable environment, Biol. Cybernet. 65, 147–159 (1991).

25. S. Ito, H. Yuasa, Z. W. Luo, M. Ito and D. Yanagihara, A mathematical model of adaptive behaviorin quadruped locomotion, Biol. Cybernet. 78, 337–347 (1998).

26. H. Kimura, Y. Fukuoka and K. Konaga, Adaptive dynamic walking of a quadruped robot using aneural system model, Adv. Robotics 15, 859–876 (2001).

27. A. Crespi, A. Badertscher, A. Guignard and A. J. Ijspeert, Amphibot I: an amphibious snake-likerobot, Robotics Autonomous Syst. 50, 163–175 (2005).

28. K. Inoue, T. Sumi and S. Ma, CPG-based control of a simulated snake-like robot adaptable tochanging ground friction, in: Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, SanDiego, CA, pp. 1957–1962 (2007).

29. Z. Lu, S. Ma, B. Li and Y. Wang, Gaits-transferable CPG controller for a snake-like robot, Sci.China Ser. F Inf. Sci. 51, 293–305 (2008).

30. D. Zhang, D. Hu, L. Shen and H. Xie, Design of an artificial bionic neural network to controlfish-robot’s locomotion, Neurocomputing 71, 648–654 (2008).

31. M. W. Westneat and J. A. Walker, Applied aspects of mechanical design, behavior, and perfor-mance of pectoral fin swimming in fishes, in: Proc. Conf. on Unmanned, Untethered SubmersibleTechnology. Autonomous Underwater Systems Institute, Durham, NH, pp. 1–14 (1997).

About the Authors

Wei Zhao received the BE degree in automation from Beijing Institute of Tech-nology in 2004 and is currently pursuing the PhD degree in Dynamics and Controlat Peking University. Her research interests include biomimetic robotics, motioncontrol, autonomous systems and multirobot coordination.

Yonghui Hu received the BE degree in Automation from Beijing Institute of Tech-nology in 2004 and is currently working toward the PhD degree in Dynamics andControl at Peking University. His research interests include mechatronics, bio-mimetic robotics and multirobot cooperation.

Long Wang received his Bachelor, Master, and Doctor’s degrees in Dynamicsand Control from Tsinghua University and Peking University in 1986, 1989 and1992, respectively. He has held research positions at the University of Toronto, theUniversity of Alberta, Canada, and the German Aerospace Center, Munich, Ger-many. He is currently Cheung Kong Chair Professor of Dynamics and Control,Director of the Center for Systems and Control of Peking University. He is alsoJian-Zhi Professor of Wuhan University, and Director of the Center for IntelligentAerospace Systems, Academy for Advanced Technology, Peking University. He

serves as Vice-Chairman of the Chinese Intelligent Aerospace Systems Committee, and Vice-Director


of National Key Laboratory of Complex Systems and Turbulence. He is a Panel Member of the Di-vision of Information Science, National Natural Science Foundation of China and a Member of theIFAC Technical Committee on Networked Systems. He is on the Editorial Boards of Progress inNatural Science, Journal of Intelligent Systems, Acta Automatica Sinica, Journal of Control Theoryand Applications, Control and Decision, Information and Control, Journal of Applied Mathematicsand Computation, International Journal of Computer Systems, etc. His research interests are in thefields of complex networked systems, information dynamics, collective intelligence and biomimeticrobotics.

construction and central pattern generator-based control of a … · 2009-02-19 · construction...

Documents