star fish2 nus 021511

NUS Presentation Title 2001

Study of Modular Undulating Fin Rays

in Bio-inspired Robotic Fish.


Why Fins and not propellers?

• Propeller strikes produce greater amount of marine debris,

marine creatures mortality and shallow waters ecosystem

disturbance• Broadband noise have severe acoustic effects on marine wildlife• Maneuvering ships reduce their speed by more than 50 percent,

and their turning radius is at least 10 times larger than

corresponding, value for fish • Fish-like robots are expected to be quieter, more maneuverable

(lesser accidents), and possible more energy efficient (longer

missions).


Piscine propulsion vs. Propellers

• Undulating-finned robot preserve undisturbed condition of its

surroundings for data acquisition and exploration (stealth).

• Fish can reverse direction without slowing down and turning

radius only 10 to 30 percent of length of body.

• At low speeds, traditional propeller propulsion mechanisms can

have efficiencies below 50%, while energy efficiency of fish

propulsion in nature is estimated to range from 70% to 90%

• Able to stay still in currents. Moves through water without

creating ripples and eddies.


Propeller Mechanism

• Projection of mass of water in a direction opposite to that of required vessel

motion.• Relation between mass of water acted upon and acceleration imparted to it

should be such that product shall equal estimated resistance of ship, and size

and rate of motion of propelling apparatus• In a motor-driven craft, efficiency is ratio of useful power (thrust times forward

velocity) divided by power expended by motor to drive foil or propeller.• Efficiency is always less than one, because some of motor’s power is wasted

in wayward vortices and other undesirable turbulence as well as heat. • For performance, most important factor is propulsor efficiency at reasonably

high levels of thrust.


Hydrodynamics of Piscine Propulsion•Any object in a flow, like a swimming swordfish, creates a trail of spinning vortices. •Tail of a fish pushes water backward (jet),set a column of moving fluid that includes thrust-producing vortices. •These Jet vortices play Fig 1 central role in generation of thrust, and their optimal formation would increase efficiency tremendously.

Fig 1


Vortices / Strouhal Number

•Fluid-dynamics parameter known as Strouhal number to study Vortices.

•Product of frequency of vortex formation behind an object in a flow and width of wake, divided by speed of the flow. For a swimming fish, Strouhal number is defined as product of frequency of tail and width of Jet, divided by the speed of fish.

•Number indicates, how often vortices are created in wake and how close they are.

•Ratio remains constant at about 0.2 for a variety of flow conditions and object shapes.

•Analyzed data from flapping foils, indicate that thrust-inducing vortices form optimally when Strouhal number lies between 0.25 and 0.35.

•Efficiency should be at a maximum for these values.


Fish Swimming Modes

•Classification of fish is based on two main factors •Extend to which propelling process is based on undulatory motion versus oscillatory motion, and •Body structures or fin segments that contribute most in generating propulsion.

•Fish swim either by using •Body and/or caudal fin (BCF) locomotion,•Median and/or paired fin (MPF) locomotion, •Combination of both BCF and MPF locomotion.

NUS Presentation Title 2001MPF Propulsion

Swimming types identified by the MPF propulsion

Fig 2

NUS Presentation Title 2001Rajiform Mode

Fin propulsion is generated by passing vertical undulations along wide pectorals with increasing amplitude from anterior part to fin apex and tapers again towards posterior Fig. 3.

Mostly, body of fish is held straight when swimming.

Fig 3


Typical examples are stingrays, skates and mantas, characterized by large, triangular-shaped and flexible pectoral fins

Fig 4

NUS Presentation Title 2001Other Swimming Forms

Propulsion in Amiiform is achieved by undulations of a long-based dorsal fin with body held straight

Propulsion in Gymnotiform is by undulations of a long-based anal fin. Example knifefish does not have dorsal and caudal fins.

Fig 6

Fig 5


Fig. 7 shows fin diagram of any fish, including that of cuttlefish, performing undulations.

Universal Joint that permits two degree of freedom movements at base of each fin ray.

Fig 8

Fig 7


Mechanical Modeling of Undulating Fins

Motion in one degree of freedom from originally two degrees of freedom at base of each fin ray.

A servomotor serves as a muscle producing one degree of freedom at base of each ray. A crank is attached at each servomotor to function as a fin ray.

Fig 9 (a)


To exhibit undulations similar to any undulating fin, each servomotor is programmed so that crank attached to servomotor oscillates based on a sinusoidal function with a specified phase lead or lag defined by β

Fig 9 (b)

NUS Presentation Title 2001Undulating Fin Mechanism Models-Robotic ribbon fin by the Northwestern University

Fig 10


Squid-type underwater vehicle by the Osaka University

Fig 11

NUS Presentation Title 2001Nanyang Knifefish (NKF-I) robot by the NTU

Fig 12


Modeling of Fin Mechanism NTU

•Produce undulation motion by virtue of designed crank-slider linkages.•Complete fin mechanism is able to provide various waveform shapes.

Fig 13 Fig 14


Crank Slider Linkages•Fin consists of specified number of servomotors. •Each of them drives a crank that is connected to slider. •Sliders can retract and extend on their own within an allowable length

Fig 15


Kinematics Diagram •Rotational Axis is perpendicular to Longitudinal wave direction•With slider, Amplitude of fin motion can be varied.

Fig 16

Fig 17

NUS Presentation Title 2001Kinematics Modeling of Fin rays

Modeled as a ruled surface in 3-D space.

Fin baseline is directrix of the ruled surface, while fin ray is generatrix.

Fig 18


Undulation can be generated through a sequential oscillating of generatrix on ruled surface.

Given by ruled-surface expression Fig 18.

P (r, s, t) = b (s, t) + r.d (s).c (s, t) , 0 ≤ r ≤ 1

b (s, t) is fin base curve that describes change of respective fin

ray’s starting point along fin base,

c (s, t) is a time-varying vector overlapping fin ray at y = s

d (s) is length of fin ray at y = s,

t is time

r is normalized

…(1)


In order to model multi-degree-of-freedom propulsor / undulating fin motion function used :

x is amplitude of undulating wave,

y-axis is centre line of wave,

c0 is profile of undulating fin at initial or starting point.

c1 is linear wave amplitude envelope

c2 is quadratic wave amplitude envelope,

α is wave frequency

k = 2π/λ is wave number

…(2)


Discrete Model of Sinusoidal waveforms•Crank’s root point at horizontal line shows position of each respective servomotor. •Lines away from root points represent respective cranks (example, ac and db)•Lines connecting tip points of cranks form resulting fin wave, which is pushing away water to provide locomotion.

•Basic sinusoidal function, formed by roots of fin rays oscillating at same

frequency but out of phase.

Fig 19

NUS Presentation Title 2001Waveform of Fin Rays generated by Servomotors and Inter-Connected Sliders

R is crank length,

L is distance between two servomotors,

S is length of slider,

• Smin minimum (when slides are fully retracted),

• Smax maximum (when sliders are fully extended),

θ1 angular position of a crank attached to 1st servomotor,

θ2 angular position of a crank attached to 2nd servomotor.

Fig 20


Basic Layout for the Waveform

A is amplitude of a resulting sinusoidal movement,

x is vertical height from crank end to reference line,

θi is angular position of a crank attached to ith servomotor, where i

= 1, 2,. . . ,m, where m is total number of motors

Fig 21


To provide an arbitrary and predictable fin wave (a fin profile), with arbitrary amplitudes along fin, at each individual segment by controlling actuator angles, θn.

Joint variables θn are related to wave amplitude, crank length and phase angle γn

Substitution yields

…(3)

…(4)

…(5)

NUS Presentation Title 2001Joint Control Law to drive Servomotors

Since γn rotates reciprocately, we can assume that it subjects to following function phase angle γ2 is only variable

Substituting general expression for angular position θn(t) of a crank attached to nth servos at time ‘t’ can be written in nonlinear form as n is servomotor number along longitudinal axis, α is fin undulating frequency,

β = γn - γn1 is phase difference (difference of the two adjacent phase angles),

An is amplitude of nth undulating fin crank

…(6)

…(7)


Use fin segment to generate a sinusoidal wave, say, a harmonic wave.

Resulting wave can x be interpreted as vibrations of infinite successive particles.

λ is wavelength of whole undulating fin

Distal end point of crank, B, acts as oscillating particle to generate harmonic wave described above.

Independent variable y will then be discretized as

…(8)

…(9)


Wave equation in discrete form associated to distal end of individual cranks as

If crank rotates at a constant speed, projection of point B on x axis satisfies a harmonic vibration equation, which provides a harmonic wave along undulating fin segments.

Control law for a single motor in one vibration cycle can be simply expressed by linear equations as

where

in which θmax is extreme position of crank, which is determined by waveform amplitude A

…(12)

…(10)

…(11)


Parametric Study of Workspace•Workspace: Space generated by motion of two cranks with parameters defined Fig 22.•Parameter study is concerned with fin design to provide an arbitrary sinusoidal movement with amplitudes as larger as possible with phase range of 30–90 deg•All crank angles in series are in the range of -90 to +90 ; Three designated positions have been marked

Fig22


(a) Slider moves smoothly within working area, position P1,

(b) Slider reaches end of track when it hits blue lines, position P2 (left-right boundaries),

(c) Slider gets disconnected when hitting red lines (up-down boundaries), position P3.

Fig 23

NUS Presentation Title 2001Effect of Phase Difference β on fin waveforms

Assuming L = 70 mm, R = 60 mm, and A = 41 mm.

For a suitable fin design, phase difference β should be between 30 deg and 90 deg to generate a sinusoidal locomotion.

Fig 24 Illustrates workspace and wave profiles of fin segments in terms of various phase differences β

Motion with phase difference, β = 10°. Not a sinusoidal movement of fin locomotion

Fig24(a)

NUS Presentation Title 2001Workspace and Waveform of the respective Fin segments

Motion with phase difference, β = 30°. Producing a sine wave of 180°, suitable for fin locomotion

Motion with phase difference, β = 90°. Producing one and a half unsmooth sine wave.

Motion with phase difference, β = 120°. The wave produced is not a sinusoidal movement

Fig24(d)

Fig24(c)

Fig24(b)


Resulted workspace of the selected fin dimension with five different phase differences (30–90 deg).

Fig 25


Effect of Amplitude on Fin Waveforms

• Different amplitude trends of crank series will generate different

sinusoidal waveforms. • Change in amplitude (with same phase difference) will have a

significant effect on waveform, i.e. larger amplitude will lead to

bigger waveform, and vice versa. • Maximum allowable amplitude will depend on allowable

workspace


Fin sinusoidal waves vs Amplitudes

Maximum allowable amplitude will depend on allowable workspace

Fig26(a)

Fig26(b)

Fig26(c)

NUS Presentation Title 2001Effect of sliders length on Fin Waveforms• Length of slider S between two cranks is changeable by combination of two independent joint angles. • Length of slider S can be derived Fig 20 as follows:

in which

…13

…14

…15


• S in terms of two crank angles, range of angles θ1

and θ2 is between -90 and +90 deg.

• Larger crank angle will produce higher amplitude. • Increase of crank angle will however decrease allowable phase

difference, which constrains performance of whole fin. • Devise a method to balance both of them.

…16


Workspace Area RatioArea ratio is introduced to compare different workspaces for a comprehensible solution

Q is a constant (Q = 180) and P (P = min {P1, P2}) is the smaller length to determine the working square area (P2).

Fig 27


•With area ratio η, find out a set of parameters of single fin segment by investigating different workspaces Table 1. •Ratio implies how much usable area of workspace, limits set as P1, P2 and P3 •Maximum ranges can be obtained for a given fin waveform in terms of joint angles

Table 1


Specifications of NKF-II.•Fin dimensions obtained in parametric study,

L = 70 mm and R = 60mm, used for all cranks.

•Fish robot comprises of three individual modules:

•Buoyancy tank module,

•Motor compartment module,

•Undulating fin module

• Control for buoyancy tank and undulating fins require μP one BasicX-24p μP while undulating fins required another BasicX-24p μP and one servomotor controller – Servo 8 T.

• Power source for two systems consists of two separate 7.2 V 3A-batteries in order to prevent problems in transmission of data and signals between microprocessors.

NUS Presentation Title 2001Fully Assembled Nanyang Knifefish II (NKF-II)

Fig 28 Fig 29

Nanyang Knifefish II Detailed View of crank’s dimension

NUS Presentation Title 2001Features

•Modular and scalable design, various types of bio-mimetic can be modeled by different number and arrangement of undulating fin(s).•Modular concept enables to easily and conveniently construct various bio-mimetic fish robots swimming by fin undulations in different forms, while re-configurable assembly allows us to construct fish robots in different forms•Approximation of Sinusoidal (Fin) wave with adjustable amplitudes.•Able to attach single or multiple sets of fin spines to any position of fish body

.


Limitations /Improvements RequiredScenarios introducing Errors

• Distal end point of cranks doesn’t perfectly fit a sinusoidal wave at a specified time

• Connecting segment between two cranks is a straight and rigid link, which is unable to resemble a sinusoidal curve.

• Actual path of distal point of crank is a circular arc, which is not exactly same as desired vertical path (dash line) shown.

Fig 29


Basis of Assumptions are not given:

•Larger amplitude of fin motion provides higher thrust force

in workspace q = 180 •In following computation, crank length and distance

between servomotors are selected as R = 60 mm and L =

70 mm


Exploring Research Areas

•Understand impact of design parameters to robot’s performance and efficiency.•Investigating different undulating layouts depicted for more energy efficiency. •Hydrodynamics incorporated for efficient swimming and a better controlling of fish robot response to external disturbances. •Improve design of existing prototype for compactness, easier waterproofing, energy-saving fin motion, etc. •Useful body/fin materials, effective payload capability, communication, and team coordination of fish robot


•Study of Swarm Intelligence and other Control strategies can provide insight in designing bio-mimetic underwater robots for complex group coordination tasks. •Hybrid driving system with smart materials and servomotors for Actuation, •Passive or elastic components (EAP) could be a way to optimize energy application of flexible fin materials.


Videos

• Northwestern Uni Knifefish

• Osaka Uni SquidFish

• NTU RoboFish 1

• NTU RoboFish 2


References

• Low K H: Modelling and parametric study of modular undulating fin

rays for fish robots. Mechanism and Machine Theory, 2009, 44(3):

pp.615–632.

• Low K H and Willy A: Development and Initial Experiments of NTU

Robotic Fish with Modular Fins Proceedings of 2005 IEEE

International Conference on Mechatronics and Automation

(ICMA2005), Niagara Falls, Canada, Jul-Aug 2005, pp. 958-963.

• Jing-Fa, T., & Chung-Wen, L. (2002). Study on the resistance and

propulsion performance of biomimetic autonomous underwater

vehicle. Proceedings of the 2002 International Symposium on

Underwater Technology,pp. 167-171.

• Biomemetic Robotic Swimming

www.stanford.edu/~hoffert/projects/robots/robots.pdf

star fish2 nus 021511

Technology

fish fish

mpf propulsion fig

dorsal fin

swimming fish

fin segments

anal fin

fin diagram

body of fish