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Star Fish2 Nus 021511

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BHUNESHWAR PRASAD

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Star Fish2 Nus 021511

  1. 1. Study of Modular Undulating Fin Rays in Bio-inspired Robotic Fish.
  2. 2. Why Fins and not propellers? <ul><li>Propeller strikes produce greater amount of marine debris, </li></ul><ul><li>marine creatures mortality and shallow waters ecosystem </li></ul><ul><li>disturbance </li></ul><ul><li>Broadband noise have severe acoustic effects on marine wildlife </li></ul><ul><li>Maneuvering ships reduce their speed by more than 50 percent, </li></ul><ul><li>and their turning radius is at least 10 times larger than </li></ul><ul><li>corresponding, value for fish </li></ul><ul><li>Fish-like robots are expected to be quieter, more maneuverable </li></ul><ul><li>(lesser accidents), and possible more energy efficient (longer </li></ul><ul><li>missions) . </li></ul>
  3. 3. Piscine propulsion vs. Propellers <ul><li>Undulating-finned robot preserve undisturbed condition of its </li></ul><ul><li>surroundings for data acquisition and exploration (stealth). </li></ul><ul><li>Fish can reverse direction without slowing down and turning </li></ul><ul><li>radius only 10 to 30 percent of length of body. </li></ul><ul><li>At low speeds, traditional propeller propulsion mechanisms can </li></ul><ul><li>have efficiencies below 50%, while energy efficiency of fish </li></ul><ul><li>propulsion in nature is estimated to range from 70% to 90% </li></ul><ul><li>Able to stay still in currents. Moves through water without </li></ul><ul><li>creating ripples and eddies. </li></ul>
  4. 4. Propeller Mechanism <ul><li>Projection of mass of water in a direction opposite to that of required vessel </li></ul><ul><li>motion. </li></ul><ul><li>Relation between mass of water acted upon and acceleration imparted to it </li></ul><ul><li>should be such that product shall equal estimated resistance of ship, and size </li></ul><ul><li>and rate of motion of propelling apparatus </li></ul><ul><li>In a motor-driven craft, efficiency is ratio of useful power (thrust times forward </li></ul><ul><li>velocity) divided by power expended by motor to drive foil or propeller. </li></ul><ul><li>Efficiency is always less than one, because some of motor’s power is wasted </li></ul><ul><li>in wayward vortices and other undesirable turbulence as well as heat. </li></ul><ul><li>For performance, most important factor is propulsor efficiency at reasonably </li></ul><ul><li>high levels of thrust. </li></ul>
  5. 5. Hydrodynamics of Piscine Propulsion <ul><li>Any object in a flow, like a swimming swordfish, creates a trail of spinning vortices. </li></ul><ul><li>Tail of a fish pushes water backward (jet),set a column of moving fluid that includes thrust-producing vortices. </li></ul><ul><li>These Jet vortices play Fig 1 central role in generation of thrust, and their optimal formation would increase efficiency tremendously. </li></ul>Fig 1
  6. 6. Vortices / Strouhal Number <ul><li>Fluid-dynamics parameter known as Strouhal number to study Vortices. </li></ul><ul><li>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. </li></ul><ul><li>Number indicates, how often vortices are created in wake and how close they are. </li></ul><ul><li>Ratio remains constant at about 0.2 for a variety of flow conditions and object shapes. </li></ul><ul><li>Analyzed data from flapping foils, indicate that thrust-inducing vortices form optimally when Strouhal number lies between 0.25 and 0.35. </li></ul><ul><li>Efficiency should be at a maximum for these values. </li></ul>
  7. 7. Fish Swimming Modes <ul><li>Classification of fish is based on two main factors </li></ul><ul><ul><li>Extend to which propelling process is based on undulatory motion versus oscillatory motion, and </li></ul></ul><ul><ul><li>Body structures or fin segments that contribute most in generating propulsion. </li></ul></ul><ul><li>Fish swim either by using </li></ul><ul><ul><li>Body and/or caudal fin (BCF) locomotion, </li></ul></ul><ul><ul><li>Median and/or paired fin (MPF) locomotion, </li></ul></ul><ul><ul><li>Combination of both BCF and MPF locomotion . </li></ul></ul>
  8. 8. MPF Propulsion <ul><li>Swimming types identified by the MPF propulsion </li></ul>Fig 2
  9. 9. Rajiform Mode <ul><li>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. </li></ul><ul><li>Mostly, body of fish is held straight when swimming. </li></ul>Fig 3
  10. 10. <ul><li>Typical examples are stingrays, skates and mantas, characterized by large, triangular-shaped and flexible pectoral fins </li></ul>Fig 4
  11. 11. Other Swimming Forms <ul><li>Propulsion in Amiiform is achieved by undulations of a long-based dorsal fin with body held straight </li></ul><ul><li>Propulsion in Gymnotiform is by undulations of a long-based anal fin. Example knifefish does not have dorsal and caudal fins . </li></ul>Fig 6 Fig 5
  12. 12. <ul><li>Fig. 7 shows fin diagram of any fish, including that of cuttlefish, performing undulations. </li></ul><ul><li>Universal Joint that permits two degree of freedom movements at base of each fin ray. </li></ul>Fig 8 Fig 7
  13. 13. Mechanical Modeling of Undulating Fins <ul><li>Motion in one degree of freedom from originally two degrees of freedom at base of each fin ray. </li></ul><ul><li>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. </li></ul>Fig 9 (a)
  14. 14. <ul><li>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 </li></ul>Fig 9 (b)
  15. 15. Undulating Fin Mechanism Models- Robotic ribbon fin by the Northwestern University Fig 10
  16. 16. Squid-type underwater vehicle by the Osaka University Fig 11
  17. 17. Nanyang Knifefish (NKF-I) robot by the NTU Fig 12
  18. 18. Modeling of Fin Mechanism NTU <ul><li>Produce undulation motion by virtue of designed crank-slider linkages. </li></ul><ul><li>Complete fin mechanism is able to provide various waveform shapes. </li></ul>Fig 13 Fig 14
  19. 19. Crank Slider Linkages <ul><li>Fin consists of specified number of servomotors. </li></ul><ul><li>Each of them drives a crank that is connected to slider. </li></ul><ul><li>Sliders can retract and extend on their own within an allowable length </li></ul>Fig 15
  20. 20. Kinematics Diagram <ul><li>Rotational Axis is perpendicular to Longitudinal wave direction </li></ul><ul><li>With slider, Amplitude of fin motion can be varied. </li></ul>Fig 16 Fig 17
  21. 21. Kinematics Modeling of Fin rays <ul><li>Modeled as a ruled surface in 3-D space. </li></ul><ul><li>Fin baseline is directrix of the ruled surface, while fin ray is generatrix. </li></ul>Fig 18
  22. 22. <ul><li>Undulation can be generated through a sequential oscillating of generatrix on ruled surface. </li></ul><ul><li>Given by ruled-surface expression Fig 18. </li></ul><ul><li>P (r, s, t) = b (s, t) + r.d (s) .c (s, t) , 0 ≤ r ≤ 1 </li></ul><ul><li>b (s, t) is fin base curve that describes change of respective fin </li></ul><ul><li>ray’s starting point along fin base, </li></ul><ul><li>c (s, t) is a time-varying vector overlapping fin ray at y = s </li></ul><ul><li>d (s) is length of fin ray at y = s, </li></ul><ul><li>t is time </li></ul><ul><li>r is normalized </li></ul>… (1)
  23. 23. <ul><li>In order to model multi-degree-of-freedom propulsor / undulating fin motion function used : </li></ul><ul><li>x is amplitude of undulating wave, </li></ul><ul><li>y-axis is centre line of wave, </li></ul><ul><li>c 0 is profile of undulating fin at initial or starting point. </li></ul><ul><li>c 1 is linear wave amplitude envelope </li></ul><ul><li>c 2 is quadratic wave amplitude envelope, </li></ul><ul><li>α is wave frequency </li></ul><ul><li>k = 2 π / λ is wave number </li></ul>… (2)
  24. 24. Discrete Model of Sinusoidal waveforms <ul><li>Crank’s root point at horizontal line shows position of each respective servomotor. </li></ul><ul><li>Lines away from root points represent respective cranks (example, ac and db) </li></ul><ul><li>Lines connecting tip points of cranks form resulting fin wave, which is pushing away water to provide locomotion. </li></ul><ul><li>Basic sinusoidal function, formed by roots of fin rays oscillating at same frequency but out of phase . </li></ul>Fig 19
  25. 25. Waveform of Fin Rays generated by Servomotors and Inter-Connected Sliders <ul><li>R is crank length, </li></ul><ul><li>L is distance between two servomotors, </li></ul><ul><li>S is length of slider, </li></ul><ul><li>S min minimum (when slides are fully retracted), </li></ul><ul><li>S max maximum (when sliders are fully extended), </li></ul><ul><li>θ 1 angular position of a crank attached to 1st servomotor, </li></ul><ul><li>θ 2 angular position of a crank attached to 2nd servomotor. </li></ul>Fig 20
  26. 26. Basic Layout for the Waveform <ul><li>A is amplitude of a resulting sinusoidal movement, </li></ul><ul><li>x is vertical height from crank end to reference line, </li></ul><ul><li>θ i is angular position of a crank attached to i th servomotor, where i = 1, 2,. . . ,m, where m is total number of motors </li></ul>Fig 21
  27. 27. <ul><li>To provide an arbitrary and predictable fin wave (a fin profile), with arbitrary amplitudes along fin, at each individual segment by controlling actuator angles, θ n . </li></ul><ul><li>Joint variables θ n are related to wave amplitude, crank length and phase angle γ n </li></ul><ul><li>Substitution yields </li></ul>… (3) … (4) … (5)
  28. 28. Joint Control Law to drive Servomotors <ul><li>Since γ n rotates reciprocately, we can assume that it subjects to following function phase angle γ 2 is only variable </li></ul><ul><li>Substituting general expression for angular position θ n (t) of a crank attached to n th servos at time ‘t’ can be written in nonlinear form as </li></ul><ul><li>n is servomotor number along longitudinal axis, </li></ul><ul><li>α is fin undulating frequency, </li></ul><ul><li>β = γ n - γ n1 is phase difference (difference of the two adjacent </li></ul><ul><li>phase angles), </li></ul><ul><li>A n is amplitude of n th undulating fin crank </li></ul>… (6) … (7)
  29. 29. <ul><li>Use fin segment to generate a sinusoidal wave, say, a harmonic wave. </li></ul><ul><li>Resulting wave can x be interpreted as vibrations of infinite successive particles. </li></ul><ul><li>λ is wavelength of whole undulating fin </li></ul><ul><li>Distal end point of crank, B, acts as oscillating particle to generate harmonic wave described above. </li></ul><ul><li>Independent variable y will then be discretized as </li></ul>… (8) … (9)
  30. 30. <ul><li>Wave equation in discrete form associated to distal end of individual cranks as </li></ul><ul><li>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. </li></ul><ul><li>Control law for a single motor in one vibration cycle can be simply expressed by linear equations as </li></ul><ul><li>where </li></ul><ul><li>in which θ max is extreme position of crank, which is determined by waveform amplitude A </li></ul>… (12) … (10) … (11)
  31. 31. Parametric Study of Workspace <ul><li>Workspace: Space generated by motion of two cranks with parameters defined Fig 22. </li></ul><ul><li>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 </li></ul><ul><li>All crank angles in series are in the range of -90 to +90 ; Three designated positions have been marked </li></ul>Fig22
  32. 32. <ul><li>Slider moves smoothly within working area, position P1, </li></ul><ul><li>Slider reaches end of track when it hits blue lines, position P2 (left-right boundaries), </li></ul><ul><li>Slider gets disconnected when hitting red lines (up-down boundaries), position P3. </li></ul>Fig 23
  33. 33. Effect of Phase Difference β on fin waveforms <ul><li>Assuming L = 70 mm, R = 60 mm, and A = 41 mm. </li></ul><ul><li>For a suitable fin design, phase difference β should be between 30 deg and 90 deg to generate a sinusoidal locomotion. </li></ul><ul><li>Fig 24 Illustrates workspace and wave profiles of fin segments in terms of various phase differences β </li></ul><ul><li>Motion with phase difference, β = 10°. Not a sinusoidal movement of fin locomotion </li></ul>Fig24(a)
  34. 34. Workspace and Waveform of the respective Fin segments <ul><li>Motion with phase difference, β = 30°. Producing a sine wave of 180°, suitable for fin locomotion </li></ul><ul><li>Motion with phase difference, β = 90°. Producing one and a half unsmooth sine wave. </li></ul><ul><li>Motion with phase difference, β = 120°. The wave produced is not a sinusoidal movement </li></ul>Fig24(d) Fig24(c) Fig24(b)
  35. 35. <ul><li>Resulted workspace of the selected fin dimension with five different phase differences (30–90 deg). </li></ul>Fig 25
  36. 36. Effect of Amplitude on Fin Waveforms <ul><li>Different amplitude trends of crank series will generate different </li></ul><ul><li>sinusoidal waveforms. </li></ul><ul><li>Change in amplitude (with same phase difference) will have a </li></ul><ul><li>significant effect on waveform, i.e. larger amplitude will lead to </li></ul><ul><li>bigger waveform, and vice versa. </li></ul><ul><li>Maximum allowable amplitude will depend on allowable </li></ul><ul><li>workspace </li></ul>
  37. 37. Fin sinusoidal waves vs Amplitudes <ul><li>Maximum allowable amplitude will depend on allowable workspace </li></ul>Fig26(a) Fig26(b) Fig26(c)
  38. 38. Effect of sliders length on Fin Waveforms <ul><li>Length of slider S between two cranks is changeable by combination of two independent joint angles. </li></ul><ul><li>Length of slider S can be derived Fig 20 as follows: </li></ul><ul><li>in which </li></ul>… 13 … 14 … 15
  39. 39. <ul><li>S in terms of two crank angles, range of angles θ 1 </li></ul><ul><li>and θ 2 is between -90 and +90 deg. </li></ul><ul><li>Larger crank angle will produce higher amplitude. </li></ul><ul><li>Increase of crank angle will however decrease allowable phase </li></ul><ul><li>difference, which constrains performance of whole fin. </li></ul><ul><li>Devise a method to balance both of them. </li></ul>… 16
  40. 40. Workspace Area Ratio <ul><li>Area ratio is introduced to compare different workspaces for a comprehensible solution </li></ul><ul><li>Q is a constant (Q = 180) and P (P = min {P1, P2}) is the smaller length to determine the working square area (P2). </li></ul>Fig 27
  41. 41. <ul><li>With area ratio η , find out a set of parameters of single fin segment by investigating different workspaces Table 1. </li></ul><ul><li>Ratio implies how much usable area of workspace, limits set as P1, P2 and P3 </li></ul><ul><li>Maximum ranges can be obtained for a given fin waveform in terms of joint angles </li></ul>Table 1
  42. 42. Specifications of NKF-II . <ul><li>Fin dimensions obtained in parametric study, </li></ul><ul><li>L = 70 mm and R = 60mm, used for all cranks. </li></ul><ul><li>Fish robot comprises of three individual modules: </li></ul><ul><ul><li>Buoyancy tank module, </li></ul></ul><ul><ul><li>Motor compartment module, </li></ul></ul><ul><ul><li>Undulating fin module </li></ul></ul><ul><li>Control for buoyancy tank and undulating fins require μ P one BasicX-24p μ P while undulating fins required another BasicX-24p μ P and one servomotor controller – Servo 8 T. </li></ul><ul><li>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. </li></ul>
  43. 43. Fully Assembled Nanyang Knifefish II (NKF-II) Fig 28 Fig 29 Nanyang Knifefish II Detailed View of crank’s dimension
  44. 44. Features <ul><li>Modular and scalable design, various types of bio-mimetic can be modeled by different number and arrangement of undulating fin(s). </li></ul><ul><li>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 </li></ul><ul><li>Approximation of Sinusoidal (Fin) wave with adjustable amplitudes. </li></ul><ul><li>Able to attach single or multiple sets of fin spines to any position of fish body </li></ul><ul><li>. </li></ul>
  45. 45. Limitations /Improvements Requ ired <ul><li>Scenarios introducing Errors </li></ul><ul><ul><li>Distal end point of cranks doesn’t perfectly fit a sinusoidal wave at a specified time </li></ul></ul><ul><ul><li>Connecting segment between two cranks is a straight and rigid link, which is unable to resemble a sinusoidal curve. </li></ul></ul><ul><ul><li>Actual path of distal point of crank is a circular arc, which is not exactly same as desired vertical path (dash line) shown. </li></ul></ul>Fig 29
  46. 46. <ul><li>Basis of Assumptions are not given: </li></ul><ul><ul><li>Larger amplitude of fin motion provides higher thrust force </li></ul></ul><ul><ul><li>in workspace q = 180 </li></ul></ul><ul><ul><li>In following computation, crank length and distance </li></ul></ul><ul><ul><li>between servomotors are selected as R = 60 mm and L = </li></ul></ul><ul><ul><li>70 mm </li></ul></ul>
  47. 47. Exploring Research Areas <ul><li>Understand impact of design parameters to robot’s performance and efficiency. </li></ul><ul><li>Investigating different undulating layouts depicted for more energy efficiency. </li></ul><ul><li>Hydrodynamics incorporated for efficient swimming and a better controlling of fish robot response to external disturbances. </li></ul><ul><li>Improve design of existing prototype for compactness, easier waterproofing, energy-saving fin motion, etc. </li></ul><ul><li>Useful body/fin materials, effective payload capability, communication, and team coordination of fish robot </li></ul>
  48. 48. <ul><li>Study of Swarm Intelligence and other Control strategies can provide insight in designing bio-mimetic underwater robots for complex group coordination tasks. </li></ul><ul><li>Hybrid driving system with smart materials and servomotors for Actuation, </li></ul><ul><li>Passive or elastic components (EAP) could be a way to optimize energy application of flexible fin materials. </li></ul>
  49. 49. Videos <ul><li>Northwestern Uni Knifefish </li></ul><ul><li>Osaka Uni SquidFish </li></ul><ul><li>NTU RoboFish 1 </li></ul><ul><li>NTU RoboFish 2 </li></ul>
  50. 50. References <ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul><ul><li>Biomemetic Robotic Swimming www.stanford.edu/~hoffert/projects/robots/robots.pdf </li></ul>

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