High-Speed Robotic Fish

iSplash-Robotics

Robotics faster than nature

11.6BL/s

Richard James Clapham Ph.D.

Richard James Clapham Ph.D.

Bio-Inspired Robotics

This website presents the work undertaken during my Ph.D. studies 2011-2015 at Essex University UK.

During this period of research I developed four robotic fish:

  • iSplash-I
  • iSplash-II
  • iSplash-MICRO
  • iSplash-OPTIMIZE

 

r.j.c@ieee.org

Please find published papers below:

iSplash-I (Presented at ICRA 2014)

iSplash-I: High Performance Swimming Motion of a Carangiform Robotic Fish with Full-Body Coordination

Richard James Clapham and Huosheng Hu

PDF

Fish !6

Figure 1.   iSplash-I: 1-Anterior actuation; 2-Midbody; 3-Thick peduncle; 4-Transmission system; 5-Driven tail plate; 6-Tendons; 7-Compliant fin.

Abstract—This paper presents a novel robotic fish, iSplash-I, with full-body coordination and high performance carangiform swimming motion. The proposed full-body length swimming motion coordinates anterior, mid-body and posterior displacements in an attempt to reduce the large kinematic errors in the existing free swimming robotic fish. It optimizes forces around the center of mass and initiates the starting moment of added mass upstream. A novel mechanical drive system was devised operating in the two swimming patterns. Experimental results show, that the proposed carangiform swimming motion approach has significantly outperformed the traditional posterior confined undulatory swimming pattern approach in terms of the speed measured in body lengths/ second, achieving a maximum velocity of 3.4BL/s and consistently generating a velocity of 2.8BL/s at 6.6Hz.

I.     INTRODUCTION

Underwater exploration is a physically demanding task. A robotic vehicle must navigate in an unpredictable surrounding environment which includes many disturbances and non-uniformities due to the transient changes exerted from the liquid. These physical forces applied to the underwater vehicle (UV) can lead to inaccurate navigation and even failure of the operation as traditional propeller driven systems are unable to adapt to the dynamic environment. Some operational examples are military surveillance, mine countermeasure, inspection and pollution mapping. UV’s have particularly high cost of transport during low speed mobility [1]. This is where fish excel, generating large transient forces efficiently by coordinating their body motion [2],[3]. In addition, adversely the dynamic environment can be advantageous to fish locomotion, as they demonstrate the ability to extract energy from the upstream vortices [4]. Therefore there is great potential to improve UV’s by imitating the swimming fish with the highest locomotive performance operating within the desired environment and Reynolds numbers. Although there are still many aspects of locomotion to address, linear propulsion could be considered the greatest challenge.

Most work in biomimetic underwater propulsion has focused on hydrodynamic mechanisms. Some examples of novel design approaches and their maximum speeds are Barrett’s hyper-redundant parameterized Robotuna which achieved a velocity of 0.65 body lengths/ second (BL/s) (0.7m/s) [5], Yu’s optimized discrete assembly prototype achieving a velocity of 0.8BL/s (0.32m/s) [6], Liu’s G9 Carangiform swimmer achieving a velocity of 1.02BL/s (0.5m/s) [7] and Valdivia y Alvarado’s compliant structure assembly achieving a velocity of 1.1BL/s (0.32m/s) [8]. Currently the low speeds of robotic carangiform swimmers are unpractical for operation, peaking at speeds of 1Bl/s. In comparison, transient speeds of comparable live fish averaging at 10BL/s have been measured by Bainbridge [9].

Reproducing the propulsive force of fish is a complex challenge. The development of a novel mechanism must take a number of factors into consideration, including morphological properties, weight distribution, efficient transmission principles, power density constraints and kinematic parameters. In particular accurately replicating the linear swimming motion has proven to be difficult and free swimming robotic fish have significant kinematic parameter errors. The lateral and thrust forces are not optimized and as a consequence excessive anterior destabilization in the yaw plane due to the concentration of posterior thrust creates reaction forces around the centre of mass. In turn the anterior creates posterior displacement errors. As a result the body wave motion along the full length of body has large matching errors in comparison to the swimming patterns of live fish leading to reduced performance and high cost of transport.

This research project considered the factors contributing to the low hydrodynamic performance of current robotic fish within linear locomotion and proposed four main objectives: (i) Introduce a new swimming pattern to reduce the kinematic parameter errors by coordinating transverse displacements along the body length. (ii) Allow for efficient energy transfer by engineering a mechanism that takes into account hardware and material constraints so that propulsion is not restricted. (iii) Develop a prototype to improve stability in the vertical and specifically the horizontal plane, by optimizing the lateral and thrust forces around the center of mass. (iv) Validate the proposed swimming motion by realizing a mechanism capable of consistent free swimming operation, measuring its achievement in terms of speed, thrust, and energy consumption over a range of frequencies.

The remainder of the paper is organized as follows. Section II presents the traditional approach of robotic fish and introduces a new full-body length swimming motion approach. Section III describes the construction method of a novel robotic fish, iSplash-I. Section IV describes the field trials undertaken and the experimental results obtained. Concluding remarks and future work are given in Section V.

II.     Design Methodology

A.     Traditional Approach

Modeling from body and/or caudal fin (BCF) swimmers, the selected carangiform swimming mode can be identified by the wave length and amplitude envelope. The Cyprinus carpio (common carp) has been chosen specifically for its high locomotive performance [10].

We only consider modeling within the confinements of the horizontal plane where the kinematics of propulsion are commonly reduced to the form of a traveling wave, concentrated to the posterior, varying in amplitude along the length, smoothly increasing towards the tail [2]. Present robotic swimmers adopted this method which limits undulatory motions, typically to <1/2 the body length towards the posterior and the wave form motion consists of one positive phase and one negative phase. The commonly adopted model proposed in [5], is in the form of:

 

where ybody is the transverse displacement of the body;  is the displacement along the main axis starting from the nose of the robotic fish; k =2π/λ is the wave number; λ is the body wave length; ω = 2πf is the body wave frequency; c1 is the linear wave amplitude envelope and c2 is the quadratic wave. The parametersP = {c1,c2,k,ω} can be adjusted to achieve  the desired posterior swimming pattern.

MATLAB Handle Graphics

Figure 2.   Mode 1:  Wave form is confined to the posterior 2/5. Parameters have been determined from experimental tests.

MATLAB Handle Graphics

Figure 3.   Mode 2:  Full-body coordination. The kinematic parameters have been determined from experimental tests.

 

B.     Proposed Full-Body Swimming Motion

Propulsion of carangiform swimming is associated with the method of added-mass [11]. Each propulsive segment of the travelling wave creates a force against the surrounding water generating momentum. This causes a reaction force FR from water onto the propulsive segment. FR normal to the propulsive segment is decomposed into the lateral FL component which can lead to energy loss and anterior destabilization and the thrust FT component providing propulsion increasing in magnitude towards the tail. The overall magnitude of added-mass passing downstream is approximately measured as the water mass accelerated and its acceleration.

Therefore it is proposed that initiating the starting moment of added mass upstream and optimizing the FL and FT forces around the center of mass would increase the overall magnitude of thrust contributing to increased forward velocity. In consideration of this, we designed a novel robotic fish which can operate in two swimming patterns: (i) Applying a traditional rigid mid-body and anterior. Concentrating the undulations and degrees of freedom (DOF) to the posterior end of the body length which will be described as Mode 1, illustrated in Fig. 2; (ii) Based on intensive observation and fluid flow assumptions a new full-body carangiform swimming pattern is introduced. The coordination of anterior, mid-body and posterior body motions are proposed in an attempt to reduce kinematic parameter errors, this will be described as Mode 2, illustrated in Fig. 3.

The models midline and body motion parameters were first established based on observation and published data from literature providing an initial engineering reference. The wave form motion first developed for a discrete rigid anterior prototype in [7] can be extended to represent the full body motions of Mode 2 in the form:

The relationships between the defined parameters P = {0.44,0,21.6,8} shown in Fig. 3 can first be found by evaluating the x location pivot at 0. In the kinematic pattern of Mode 2, the fraction of body length displaced is equal to the anguilliform swimming mode but reflects changes in the wave form. The anguilliform swim pattern is defined by large amplitude undulations propagating from nose to tail. The newly introduced Mode 2 applies an oscillatory motion to head and mid-body and pivots the entire body around a single point associated with the carangiform fish swimming motion [2].

Although this is the first account of applying full-body actuation to a research prototype fish, mechanisms such as “vortex peg” and “undulating pump” and flow visualization techniques have been proposed [12][13] from published biological studies, indicating a possible fluid body interaction that contributes to propulsive thrust is generated upstream to the posterior section. The muscle activity in the anterior has been measured to be low, suggesting that accurate modeling of the kinematics could be more significant than anterior force in improving energy transfer.

As previously mentioned, anterior destabilization has been difficult to control [6][7][8], as passive rigid anterior mechanisms recoil around the center of mass. Free swimming robotic fish have excessive head swing, similar in magnitude to the posterior which increases drag. The proposed Mode 2 drives the anterior into the unwanted yaw direction, in an attempt to reduce amplitude errors by optimizing the FR around the center of mass. It has also been noted in [2], that the morphological adaptations of reduced depth at the peduncle, increased depth of body towards the anterior and vertical compression minimize recoil forces.

III.     New Construction Method

A.     Mechanical Design

Mechanical structure limitations set a great challenge when modeling the displacements within the travelling wave. Current methods typically adopt either a discrete assembly [6], [7] or compliant structure [8] but both are seen to have limitations. A construction method using structural compliance combined with a rigid discrete assembly is proposed. The arrangement distributes 3 degrees of freedom (DOF) and 1 passive DOF along the axial length shown in Fig. 4. Mode 1 disregards transverse displacements of links I, II, III whereas Mode 2 actuates all DOFs along the axial length to provide anterior and mid-body transversal displacements. The development allowed for both Modes of operation to be applied to the same prototype by adjusting the configuration. Uniform material properties were chosen for links I-III and stiffness distribution begins at DOF 3 and continues to the tail tip. To provide the undulatory motion a compliant caudal fin is attached to the link V and is actuated by tendons anchored to the main housing rear bulkhead. The developed mechanism allows for the expansion of the tendons and material stiffness of the caudal fin to be adjusted experimentally to provide the targeted curves during free swimming at various frequencies.

The approximation of a traveling wave using joints I-V and turning angles of DOF 1-4 are shown in Fig. 4. Details of the fully discretized body wave fitting method are given in [6], [7]. The location of joints in the series can be determined by parameterized fitment to a spatial and time dependent body wave. The discrete construction method can be defined as a series of links or N links. N being the number of links after DOF 1 typically <6 due to structural limitations, more links reduce curve alignment errors. The aim of the design is to improve complexity of motion without an increase of structural parts. The link end points are shown in Fig. 4, it can be seen that the arrangement of DOF’s distributed along the length of the body provides an accurate curve alignment reducing large errors and excrescences in the outer profile. In addition we have observed that the aerofoil section NACA (12)520 based on camber, chord and thickness can be utilized to illustrate the outer structure profile of Mode 2 which we propose contributes to the fluid flow interaction.

MATLAB Handle Graphics

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Figure 4.   Link approximation (top); 1-Plan; 2-Profile; 3-Front (bottom)

B.     Power Transmission System

The developed transmission system providing rotary power to linear oscillations is illustrated in Figs. 5 and 6. All actuated links are directly driven by the five bearing crank shaft providing an equal power distribution. The developed mechanical design required high-precision engineering of the chassis and crankshaft to avoid deadlock and reduce friction. The driven link amplitudes are determined by the offset cranks, L3 represents one of the discrete links of the structure. The maximum amplitude of the link length L3 at point P2 is determined by the predetermined maximum crank offset P1. The coordinates of P1 (P1x, P1y) andP2 (P2x, P2y) can be derived by:

(3)

The length of L3 can be derived by L32= P2x2+P2y2. Assume that ω1 is the angular velocity of the link L3, and the velocity vector VP2 is perpendicular to L3. We have:

                             (4)

where Vp2x and Vp2y are the decomposed vectors of the velocity vector VP2= ω1 L3.

Figure 5.   Power transmission system: 1-Transision plate; 2-Crankshaft;

3-Free end of link and connecting pivot.

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Figure 6.   Schematic drawing of the tail offset drive crank and linkage;

C.   Fabrication

iSplash-I shown in Fig. 7 was engineered as a morphological approximation of the common carp. The physical specifications are given in Table I. We devised a structurally robust prototype allowing for consistency of operation at high frequencies, as force has to be applied to the water and reactively, the opposing force is applied to the vehicle. All structural parts were precision engineered, hand fitted and assembled. A consideration of the development took hardware and material constraints into account, so that geometric and kinematic parameters are not affected. The hydro-static streamlined profile was optimized by favorably positioning the maximum thickness of the cross section, reducing pressure drag. In [10], the cross section has been measured to be optimal at 0.2 of the body length. These aspects relate to amount of resistance during forward motion and were taken into consideration within the design.

Increasing endurance is a desirable feature of a UV. Current robotic fish are still limited to short operational times as energy losses can be produced in many stages of the mechanical transfer. Recent designs have found it is advantageous to utilize a single electrical motor for actuation [8]. The classical actuator is still the most effective way of providing power at high frequencies and reduces energy consumption over multilink discrete assemblies. Mass and volume distribution are key principles of stability in the horizontal and vertical planes. A single actuator power transmission system can be positioned in the optimum location. In contrast multilink servo assemblies are limited as mass and volume are confined to the posterior.

The body has open loop stability if the relative position of buoyancy is higher than the center of mass as the surrounding fluid counterbalances the gravitational weight [14]. Therefore the hydrostatic buoyancy level and stability were solved by adjusting material properties and configuration. Stability was found to be particularly difficult to maintain during free swimming at high frequencies.

Lastly, the inner structure of the prototype is negatively buoyant. A significant development of the prototype was a watertight skin that allowed unrestricted flexing of the external surface and provided the volume needed to maintain neutral buoyancy.

  • Physical Parameters of iSplash-I
Parameter Specific Value
Body Size: mBody Mass : Kg

Maxium Velocity: BL/s (m/s)

Noload Maximum Frequency: Hz

Actuator

Power Supply

Fabrication

Materials

Swimming Mode

Tail Material

Outter Structure & Skin Material

Thickness of Caudal Fin : mm

Caudal Fin Aspect Ratio: AR

 

0.25 x 0.05x 0.0 620.367

3.4 (0.88)

8

Single Electric motor

12V Pb External Battery Supply

Low Tolerance Engineering

Aluminum, Mild Steel, Stainless

Linear Locomotion

Polypropylene Polystyrene anstyrene

1

1.73

IV.     Experimental Procedure and Results

A.     Field Trials

A series of experiments were undertaken in order to verify the proposed swimming pattern by assessing the locomotive performance of Modes 1 and 2 in terms of speed, thrust and energy consumption at frequencies in the range of 2-8Hz. Experiments were conducted within a 1m long x 0.5m wide x 0.25m deep test tank. Stabilized free swimming over a distance of 0.5m was used to measure speed with a 0.5m acceleration distance. The prototype had sufficient space to move without disturbances from side boundaries and the free surface. Measurements were averaged over many cycles once consistency of operation was achieved and steady state swimming was obtained.

Although the prototype was measured to have a higher mechanical efficiency with an oiled filled structure, the developed skin proved inconsistent. Therefore, all runs were completed actuating the prototype with a water filled structure. This method attained consistency of operation providing stabilized swimming and maintaining the required buoyancy within the depth of the testing tank, whilst gently skimming the bottom surface. Velocity greatly reduced during runs when the skin detached, the build became negatively buoyant, destabilized or the cross-sectional area was increased

B.     Swimming Pattern Observation

Fig. 8 shows snapshots of Mode 2 in eight instances with time intervals of 0.02s throughout one body cycle. The midline was tracked at 50 frames per second to provide the amplitude envelopes of the anterior and posterior for comparison. Good agreement with fish kinematic data is a difficult task and current free swimming robotic fish have shown excessive head and tail amplitude errors. When comparing Modes 1 and 2, Mode 2 was found to reduce the head amplitude by over half from 0.17 (0.044m) of the body length in Mode 1 to 0.07 (0.018m). The tail amplitude of the common carp is 0.1 [9] [10], larger values were found to increase performance. Both Modes 1 and 2 were able to attain amplitudes of 0.17 (0.044m). The location of the midline pivot point should be in the range of 0.15-0.25 of the body length [10]. Mode 2 has a reduced error location of 0.33 in comparison to 0.5 in Mode 1. Indicating Mode 2 significantly reduces matching errors.

In addition it was observed that the posterior 2/5 of the body length deforms due to stiffness distribution providing a smooth transition phase between body and tail. Although high aspect ratio (AR) caudal fins have been found to produce greater efficiency [4], in initial testing a low aspect ratio tail provided higher speeds. AR is calculated using: AR=b2/Sc where b squared is the fin span and Sc is the projected fin area. AR in this case was 1.73.

  • Comparison of Test Results between Modes 1 & 2
Parameters Mode 1 Mode 2
Reynold Number: Re (105)Shrouhal Number: St

Maxium Thrust: N

Consistant Maxium Velocity: BL/s (m/s)

Frequency: Hz

Max Power Comsumption Air: W

Max Power Comsumption Water: W

Swimming Number: Sw

Head Swing Amplitude: m

Tail Swing Amplitude: m

Test Run Distance: m

1.40.48

0.63

2.2 (0.55)

6.1

3.48

5.76

0.36

0.044

0.044

0.5

1.70.41

1.17

2.8 (0.70)

6.6

3.76

7.68

0.42

0.018

0.044

0.5

C.     Experimental Results

Fig. 9 shows the average energy economy in relationship to driven frequency, comparing both Modes in air and water. This comparison measured the value of the increased resistance during locomotion due to the surrounding liquid. The measuring of the energy economy and thrust took many cycles to average, as the swimming motion produces fluctuating readings within a single body motion cycle. Both Modes actuating in water resulted in an increase in energy consumption, i.e. Mode 2 increasing from 3.76W to 7.68W and Mode 1 increasing from 3.48W to 5.76W.

As the configurations of robotic fish show various hardware and morphological properties, the main value of comparison has become speed divided by body length (BL/s). In this case the body length is measured from nose tip to the most posterior extremity of the tail.

The relationship between velocity and driven frequency is shown in Fig. 11. The corresponding values of Modes 1 and 2 during consistent swimming were measured and compared to current robotic fish. Mode 1 achieved maximum velocity of 2.2Bl/s (0.55m/s), at 6.1Hz. Mode 2 increased maximum velocity to 2.8BL/s (0.70m/s) at 6.6Hz. Mode 2 has significantly increased performance in comparison with current robotic fish which typically peak around 1BL/s. An initial value of 3.4BL/s (0.87m/s) at 6.8Hz was recorded by Mode 2 with an oil filled structure. Sealing the developed skin when in contact with oil could not be maintained and skin detachment consistently affected stability and buoyancy, greatly reducing performance.

We can notice that Mode 2 had an 85% increase of thrust (Fig. 10) and a 27% increase in velocity over Mode 1 whilst consuming only 7.68W of power at 2.8BL/s. As the power supply contributes to a significant portion of the total mass, high energy efficiency is important. The measured low energy consumption indicates that the next generation could carry its own power supply within a comparable geometric frame with good endurance.

A prominent parameter for analyzing BCF locomotive performance is the Strouhal number (St), defined as St=fA/U, where f denotes the frequency, A denotes the tail amplitude and U is the average forward velocity. St is considered optimal within the range of 0.25 < St < 0.40.  Mode 1 has a peak St of 0.48 under the condition of Re = 1.4 x 105 and Mode 2 consistently measured a St = 0.41 and peaked at a St = 0.34 under a condition of Re = 2.2 x 105. A comparable live fish was measured in [3], to have a St  = 0.34, Re = 2~8 x 105. Applying Mode 2 shows a high performance increase within the St optimal range and achieves the higher cruising speeds of swimming fish.

A significant relationship between velocity and driven frequency was found. As higher frequencies were applied velocity increased in both Modes, matching the reported findings of live fish [9]. From this it can be assumed that a further increase of frequency applied to this prototype may continue to increase its performance.

V.     Conclusion and Future Work

In this paper we show conclusively that by coordinating the full-body length of the carangiform swimming motion a significant increase in performance, in terms of linear swimming speed, is gained over the traditional posterior confined wave form. The innovative mechanical drive system increased maximum velocity over the current published robotic fish. In fact, the robotic prototype can continue to increase its velocity as increased frequencies were applied, indicating, that the high swimming speeds may continue to increase with an increase of frequency.

The proposed swimming motion can coordinate anterior, mid-body and posterior displacements, and is able to reduce the large kinematic errors seen in existing free swimming robotic fish. iSplash-I achieved a maximum velocity of 3.4BL/s and consistently achieved a velocity of 2.8BL/s at 6.6Hz with a low energy consumption of 7.68W.

Future experimental analysis will greatly benefit from visualization techniques accurately measuring fluid flow. However, a few assumptions can be deduced to account for the increase in speed:  (i) The magnitude of propulsive force was increased by initiating the starting moment of added mass upstream; (ii) The developed structural arrangement allowed for smooth transition of flow along the length of body; (iii) Anterior and/or mid-body vortices were formed, coordinated and propagated downstream; (iv) Lateral and  thrust forces were optimized around the center of mass; (v) A reduction in drag resistance due to reduced anterior amplitude errors.

We also aim to improve the performance of iSplash-I by applying higher frequencies, further optimizing of kinematic parameters along the full length of the body and the development of a prototype carrying its own power supply within a comparable sized frame.

Acknowledgements

Our thanks go to Richard Clapham senior for his constant technical assistance towards the project.

References

  • R. Bandyopadhyay, “Maneuvering hydrodynamics of fish and small underwater vehicles,” Integr. Comparative Biol., vol. 42, no. 1, pp. 102– 17, 2002.
  • Lighthill, “Mathematical Biofluiddynamics,” Society for Industrial and Applied Mathematics, Philadelphia, 1975.
  • J. Videler, “Fish Swimming,” Chapman and Hall, London, 1993.
  • S. Triantafyllou, M. S. Triantafyllou, and M. A. Grosenbauch,“Optimal thrust development in oscillating foils with application to fish propulsion,” J. Fluids Struct., vol. 7, pp. 205–224, 1993.
  • S. Barrett, M. S. Triantafyllou, D. K. P. Yue, M. A. Grosenbaugh, and M. J. Wolfgang, “Drag reduction in fish-like locomotion,” J. Fluid Mech, vol. 392, pp. 183–212, 1999.
  • Yu, M. Tan, S. Wang and E. Chen. “Development of a biomimetic robotic fish and its control algorithm,” IEEE Trans. Syst., Man Cybern. B, Cybern, 34(4): 1798-1810, 2004.
  • J. Liu and H. Hu, “Biological Inspiration: From Carangiform fish to multi-Joint robotic fish,” Journal of Bionic Engineering, vol. 7, pp. 35–48, 2010.
  • Valdivia y Alvarado, and K. Youcef-Toumi, “Modeling and design methodology for an efficient underwater propulsion system,” Proc. IASTED International conference on Robotics and Applications, Salzburg 2003.
  • Bainbridge, “The Speed Of Swimming Of Fish As Related To Size And To The Frequency And Amplitude Of The Tail Beat,” J Exp Biol 35:109–133, 1957.
  • Nagai. “Thinking Fluid Dynamics with Dolphins,” Ohmsha, LTD, Japan, 1999.
  • W. Webb, “Form and function in fish swimming,” Sci. Amer., vol. 251, pp.58–68, 1984.
  • W. Rosen, “Water flow about a swimming fish,” China Lake, CA, US Naval Ordnance Test Station TP 2298, p. 96, 1959.
  • J. Wolfgang, J.M. Anderson, M.A. Grosenbaugh, D.K. Yue and M.S. Triantafyllou, “Near-body flow dynamics in swimming fish,” September 1, J Exp Biol 202, 2303-2327, 1999.
  • V. Lauder and E. G. Drucker, “Morphology and Experimental Hydrodynamics of Fish Control Surfaces,” IEEE J. Oceanic Eng., Vol. 29, Pp. 556–571, July 2004.
iSplash-II (Presented at IROS 2014)

iSplash-II: Realizing Fast Carangiform Swimming to Outperform a Real Fish

 

Richard James Clapham and Huosheng Hu

 

PDF

 

Figure 1.   iSplash-I: 1-Anterior actuation; 2-Midbody; 3-Thick peduncle; 4-Transmission system; 5-Driven tail plate; 6-Tendons; 7-Compliant fin.

Abstract—This paper introduces a new robotic fish, iSplash-II, capable of outperforming real carangiform fish in terms of average maximum velocity (measured in body lengths/ second) and endurance, the duration that top speed is maintained. A new fabrication technique and mechanical drive system were developed, effectively transmitting large forces at high frequencies to obtain high-speed propulsion. The lateral and thrust forces were optimized around the center of mass, generating accurate kinematic displacements and greatly increasing the magnitude of added mass. The prototype, with a length of 32cm has significantly increased the linear swimming speed of robotic fish, achieving consistent untethered stabilized swimming speeds of 11.6BL/s (i.e. 3.7m/s), with a frequency of 20Hz.  

I.     INTRODUCTION

 

A.     Background Description

To navigate through a marine environment, a robotic vehicle requires mobility to effectively contend with the physical forces exerted by the surrounding fluid. Live fish can coordinate their body motions in harmony with the surrounding fluid generating large transient forces efficiently, as opposed to rigid hull underwater vehicles (UV) powered by rotary propellers [1],[2],[3],[4]. For a man-made vehicle to achieve greater locomotive capability there is potential to engineer a structure that can accurately replicate the wave form of swimming fish.

Bainbridge’s intensive observational studies measured live fish to attain an average maximum velocity of 10 body lenghts/ second (BL/s) [11]. A single high performance of a Cyprinus carpio was noted, achieving the swimming speed of 12.6BL/s (1.7m/s) with a stride rate of 0.7. Endurance at the highest velocities is limited, burst speeds can only be maintained for short durations of approximately one second. Velocities were measured to decrease to 7BL/s in 2.5s of swimming, to 5BL/s in 10s and to 4BL/s in 20s.

Although most work has focused on hydrodynamic mechanisms, current robotic fish are unable to gain the locomotive efficiencies of live fish, proving a complex challenge. There are two limitations in particular: (i) They cannot achieve accurate replication of the linear swimming motion as free swimming robotic fish generate kinematic parameter errors and therefore reduced propulsion; (ii) They have low force transfer due to the complexity of developing the powertrain, limited by mass, volume, force, frequencies and internal mechanical losses. Some examples of novel design approaches are Barrett’s hyper-redundant Robotuna, achieving a maximum velocity of 0.65 body lengths/ second (BL/s) (0.7m/s) [5], Anderson’s VCUUV with 0.5BL/s (1.2m/s) [6], Yu’s discrete structure with 0.8BL/s (0.32m/s) [7], Essex’s G9 with 1.02BL/s (0.5m/s) [8]; Wen’s carangiform with 0.98BL/s (0.58m/s) [9]  and Valdivia y Alvarado’s compliant method with 1.1BL/s (0.32m/s) [10]. The straight-line speed of current robotic fish, peaking at 1BL/s, is typically unpractical for marine based environments.

iSplash-I [12], a carangiform swimmer, (25cm, 0.35Kg), with an external power supply and formed of aluminum and steel, achieved a high-performance swimming motion. The developed novel mechanical drive system operated in two swimming patterns, a traditional posterior confined undulatory swimming pattern and the introduced coordinated full body length swimming pattern. The proposed swimming motion greatly improved the accuracy of the kinematic displacements and outperformed the posterior confined approach in terms of speed, achieving 3.4BL/s and consistently achieving a maximum velocity of 2.8BL/s at 6.6Hz with a low energy consumption of 7.68W.

It was noticed that throughout the field trials iSplash-I was able to replicate the key swimming properties of real fish. As frequencies were raised the prototype continued to increase velocity in both swimming modes. This matches Bainbridge’s study of swimming fish, measuring no noticeable change in kinematics after tail oscillations are raised beyond 5Hz, indicating that only an altered frequency is required to increase swimming speed. Hence it is expected, that combining the critical aspects of the iSplash-I mechanical drive system with frequencies higher than 6.6Hz may significantly increase maximum velocity. In consideration of this, iSplash-II was developed, as shown in Fig. 1.

B.     Research Objectives

The project aimed to achieve the fastest swimming speeds of live fish with seven main objectives: (i) to devise a prototype which operates in two swimming patterns, for further investigation of the carangiform swimming motion to be conducted; (ii) to significantly increase force transfer by achieving a high power density ratio in combination with an efficient mechanical energy transfer; (iii) to achieve unrestricted high force swimming by realizing a prototype capable of carrying a high powered energy supply; (iv) to develop a structurally robust mechanical drive system based on the critical properties proposed in [12], capable of intensively high frequencies of 20Hz; (v) to greatly reduce forward resistance by engineering a streamlined body considering individual parts’ geometries and alignment throughout the kinematic cycle; (vi) to stabilize the free swimming prototype’s unsteady oscillatory motion during intensively high frequencies to achieve a more efficient force transfer; (vii) to conduct a series of experiments measuring the prototype’s achievements in terms of kinematic data, speed, thrust, and energy consumption in relation to driven frequency.

The remainder of the paper is organized as follows: Section II presents the investigated carangiform swimming patterns. Section III describes the new construction method. Section IV discusses the field trials undertaken and the experimental results obtained. Concluding remarks and future work are given in Section V.

I.     Design Methodology

 

A.     Mode 1: Traditional Approach

The kinematic swimming motion during linear locomotion of the Cyprinus carpio (common carp) is studied due to its high locomotive efficiency [13]. The selected carangiform applies the swimming method of body and/or caudal fin propulsion, identified by the portion of the body length actively displaced. The form of this propulsive segment, within the horizontal plane can be represented by a travelling wave. This body motion traditionally adopted in previous builds applies a rigid mid-body and anterior, concentrating the undulatory motion to the posterior end of the lateral length. Typically limited to <1/2 of the body length, the posterior propagating wave smoothly increases in amplitude towards the tail, consisting of one positive phase and one negative phase [4]. Described as Mode 1 and illustrated in Fig. 2, the posterior confined kinematics of the carangiform is of the form [5]:

where ybody is the transverse displacement of the body; x is the displacement along the main axis beginning at the nose; k =2π/λ is the wave number; λ is the body wave length; ω = 2πf is the body wave frequency; c1 is the linear wave amplitude envelope and c2 is the quadratic wave. The parameters P = {c1,c2,k,ω} can be adjusted to achieve the desired posterior swimming pattern for an engineering reference.

As previously mentioned, accurately matching the kinematic data of real fish is complex and free swimming robotic fish applying posterior confined displacements have shown kinematic parameter errors [8][10]. In particular, the lateral (FL) and thrust (FT) forces are not optimized. As a result, large anterior destabilization in the yaw plane is generated due to the concentration of posterior thrust, recoiling around the center of mass. Consequently the inaccurate anterior kinematics create significant posterior midline displacement errors. Hence, the linear locomotive swimming motion over the full length of body has large matching errors in comparison to real fish leading to reduced propulsive force and a higher cost of transport.

B.     Mode 2: Full-Body Swimming Pattern

Mode 2, illustrated in Fig. 3 is the full body carangiform swimming pattern of the iSplash platforms described in [12], which coordinates the anterior, mid-body and posterior body motions. This was based on intensive observation [12] and fluid flow theory [14],[15] which lead to a greater understanding of the carangiform swimming motion.

The Mode 2 displacements drive the anterior into the direction of recoil, reducing amplitude errors by optimizing the reaction force (FR) of the propulsive elements. This enhances performance, increasing the magnitude of added mass by initiating the starting moment upstream, generating optimized FL and FT forces around the center of mass, increasing the overall magnitude of thrust contributing to increased forward velocity. A full description of the method of added mass can be found in [16]. Furthermore the developed body motion increases performance by allowing a smooth transition of flow along the length of the body, effectively coordinating and propagating the anterior formed fluid flow interaction downstream. We can extend the form of [8], an adaptation of (1) to generate the midline kinematic parameters of the full body displacements:

By evaluating the x location at the center of mass, measured optimal at 0.15-0.25 of the body length and tail amplitude at 0.1 [13], the relationships between the defined parameters P ={0.63,0,21.6,8} shown in Fig. 3 can be found.

The full-body swimming motion of iSplash-I reduced kinematic matching errors over the full body length. Mode 2 was found to reduce the head amplitude by over half, from 0.17 (0.044m) in Mode 1 to 0.07 (0.018m). The tail amplitude was measured to increase performance with larger values than the common carp at 0.1. Both Modes were able to attain values of 0.17 (0.044m) due to achieving anterior stabilization. The location of the center of mass was improved and close to the optimum range, Mode 2 with a reduced error location of 0.33 in comparison to Mode 1 of 0.5. Reviewing the kinematic data we can see, that the prototype achieved high kinematic accuracy producing a low cost of transport. In consideration of this, we aimed to precisely replicate its swimming motion parameters.

II.     New Construction Method

 

A.     Mechanical Design

In order to increase the swimming speed a new mechanical drive system was required, able to effectively transmit large forces at high tail oscillation frequencies. In consideration of this, a feasible design structure to fit the linear swimming patterns of both modes was developed. A powertrain deploying a single motor with continuous rotation was developed, more complex to devise without internal mechanical loss [5], it is advantageous in comparison to  multilink servos or smart materials, which are limited by force, frequency, volume and mass distribution [7],[8],[9].

As the build required a high power density ratio, the structural arrangement was governed by the dimensions of the large electrical motor 83mm long x 50mm diameter. This required a slight increase in body length from 250mm to 320mm and a significant adjustment to the link structure to take the mass of the actuator into consideration, removing the coupled mid-body joint and the associated discrete linkages. The discrete construction method, defined as a series of links or N links, aims to achieve accurate midline kinematic parameters whilst minimizing complexity of the mechanical drive and linkages. The sequence of links can generate the required swimming motion by locating the joints to the spatial and time dependent body wave. The fully discretized body wave fitting method is given in [7], [8].

The assembly of iSplash-II is illustrated in Fig. 6, showing the four joints distributed along the axial length. Three rigid links are coupled to a compliant fourth link and caudal fin with stiffness distribution, devised to generate a smooth body to tail transition phase of the posterior undulations. The developed modular build allowed for both Modes of operation to be applied to the same prototype by adjusting the configuration. Links III and IV are actuated to generate the posterior kinematics of operational Mode 1, Mode 2 actuates all links along the axial length to provide anterior, mid and posterior body displacements.

It was proposed in [12], that the outer profile of the coordinated full-body swimming pattern, represented by the aerofoil section NACA (12)520 aids the fluid flow interaction, producing greater locomotive speeds. In consideration of the simplified link assembly and estimated center of mass, the head and tail amplitudes were increased. We can see in Fig. 6 that the approximation of a traveling wave using link end points I-IV and turning angles of joints 1-3 of the reduced link arrangement provides an accurate curve alignment agreeable with the form of (2), therefore reducing errors and excrescences in the outer profile and achieving accuracy with the required aerofoil section.

    1. Power Transmission System

The leading tail discrete link III is directly driven by the single bearing crank shaft attached to the output shaft of the primary actuator, increasing power distribution to the posterior. As link III is actuated, link IV is passively displaced. This final posterior linkage IV, coupled to the compliant caudal fin is anchored by 4 expandable tendons attached to the main chassis rear bulkhead, crossing through linkage III. The anterior link I is transmitted motion by paired linkages fixed at points P5 and P6, located at the top and bottom of the main chassis. The developed mechanical design required precision fitment of the chassis, crankshaft, cantilevers and linkages to reduce internal mechanical losses, avoid deadlock and reduce friction.

Illustrated in Figs. 5, 6 and 7 is the developed powertrain transmitting rotary power to linear oscillating links. All driven link amplitudes are determined by the single offset crank. L3 represents the leading tail discrete link of the structure.

C.   Fabrication

The prototype iSplash-II is shown in Fig. 8 with the physical specifications given in Table I. The entire body was digital modeled and formed using 3D printing techniques, at layers of 0.09mm in PLA filament. This method produced precise 3D structural geometries of the individual segments and pre-determining alignment tolerances throughout the complete kinematic cycle. It was a key challenge to develop a high power density build, small in size with high structural strength. The individual printed parts were optimized for robustness through physical strength tests and computational stress analysis, highlighting initial areas of weakness. These parts were re-printed many times in order to realize high frequency actuation. As PLA filament has a low melting point softening at approximately 60°C, material wear at the pivots and actuated surfaces was reduced by acetal bushes and inserts, at the cost of additional weight.

It was necessary for the body size to be compact, as increasing the build geometric magnitude will increase the resistance during forward motion and therefore the power consumption required [5],[12]. An accurate approximation of the streamlined body shape of the common carp was achieved within the horizontal plane illustrated in Fig. 4. The maximum thickness of the cross section is measured optimal at 0.2 of the body length [13] and was favorably positioned therefore reducing pressure drag.

The static stability in the horizontal and vertical planes is affected by material density distribution. For linear locomotive research open loop stability is beneficial, this was achieved by the relative position of buoyancy being higher than the center of mass, as the surrounding fluid counterbalances the gravitational weight [17]. The short body length greatly increased the difficulty in achieving open loop stability as the finest weight change in structure of individual pieces distributed across the assembly dramatically affected stability and buoyancy. This was solved by collaborating the individual parts of the modular build by adjusting the geometries and the inner structure’s weight to strength configuration.

The prototype was designed with increased stability in roll and pitch as the large mass of the electric motor, 0.6kg, 75% of the total mass, was positioned low within the structure. To achieve a short body length, contain the embedded system and 11.1V LiPo power supply and counteract the large mass of the primary actuator the build volume was increased vertically. This aided stability, as the lightweight PLA material and increased height positioned the center of buoyancy at the top of the prototype.

Mobility within the vertical plane was achieved to maintain a stable mid tank trajectory during free swimming. Two rigid morphological approximations of pectoral fins were developed and positioned at the leading bulk head of the main chassis, actuated by a single servo motor. A cross beam anchored on both sides of the centralized motor was formed to link, support and actuate the control surfaces. The addition of pectoral fins required a compact mechanism to be devised due to the very restrictive space available.

    • Physical Parameters of iSplash-II

 

Parameter

Specific Value
Body Size: m (LxWxH)

Body Mass: Kg

Actuator:

Actuator Mass: Kg

Power Supply:

Manufacturing Technique:

Materials:

Primary Swimming Mode:

Additional Maneuverability:

Additional Control Surfaces:

Caudal Fin Material:

Thickness of Caudal Fin: mm

Caudal Fin Aspect Ratio: AR

0.32 x 0.048 x 0.112

0.835

Single electric motor

0.63

11.1V onboard LiPo battery

3D Printing

PLA Filament, Acetal, Stainless

Linear Locomotion

Vertical plane

Pectoral fins

Polypropylene

2.3

1.6

 

III.     Experimental Procedure and Results

 

A.     Field Trials

A series of experiments were conducted in order to verify the prototype by evaluating the locomotive performance of Modes 1 and 2 in terms of kinematic parameters, speed, force and energy consumption at frequencies within the range of 5-20Hz. It was required that the measurements were averaged over many cycles to increase the accuracy of data, once consistency of operation was achieved and stabilized free swimming was obtained. The test results are summarized in Table II.  Experiments were conducted within a test tank, 5m long x 2m wide x 1.5m deep. Free swimming between two fixed points at a distance of 4m was used to evaluate maximum speed. The prototype had sufficient space to move without disturbances from side boundaries and the free surface, capable of consistent untethered swimming at mid height of the tank aided by adjusting the angle of pectoral fins during swimming.

Locomotion at high speeds was unachievable without extensive stability optimization. Once achieved, an accurate straight line trajectory was possible. A thorough description of the improvements undertaken on the mechanical structure and the extent of the intensive destabilization are beyond the scope of this paper. In addition, the devised mechanical drive system was found to be very robust, showing no signs of structural failure throughout the field trials whilst actuating at high frequencies over long periods and accidentally hitting the walls of the test tank.

B.     Swimming Pattern Observation

 

The frame sequence of Mode 2 in eight instances, at time intervals of 0.006s throughout one complete body cycle at 19Hz is illustrated in Fig. 9. The obtained midline was tracked at 50 frames per second and is plotted against the desired amplitude envelopes of the anterior and posterior from Fig. 2 for comparison.  When observing the midline of Mode 2 it can be seen, that the desired full body coordination presented in [12], was not achieved. As previously described in Section III-A the build required a simplified link structure due to power density constraints. Although the estimated midline curve alignment tested during stationary actuation was accurate, the excessive mass of the primary actuator held the main chassis (the entire length of link II) fixed in line with the forward heading and no single pivot point was obtained. Consequently, the swimming motion during locomotion was found to produce matching errors over the full-body in comparison to the desired swimming pattern of iSplash-I.

 

Comparing both Modes taking into consideration that the mid-body was held rigid, the anterior amplitude of Mode 2 was measured to be 0.04 (0.013m) of the body length, equivalent to the common carp, whereas Mode 1 was found to generate <0.01 (0.003m) head amplitude. In addition, the large centralized mass arrangement and increased depth of body effectively minimized recoil forces and aided the stability of the posterior, allowing for accurate posterior amplitude and large thrust forces to be generated.

 

It can be seen, that the developed posterior structure can accurately mimic the undulatory parameters of real fish, as the components of link IV can be adjusted experimentally to provide the targeted midline during free swimming at various frequencies. Both Modes were able to generate accurate amplitudes of 0.1 of the body length and attain large tail amplitudes of 0.2 (0.063m) which was found to significantly increase performance. This value is twice the size of the observed value of the common carp at 0.1 and is increased over the first generation at 0.17. This generated amplitude is greater than the highly efficient swimming motion of a dolphin measured at 0.175 [13].
The caudal fin was formed with a low aspect ratio (AR). Although not yet thoroughly investigated, this tail was measured to achieve the highest maximum velocity and acceleration during the initial field trails. AR is defined as: AR=b2/Sc where b squared is the fin span and Sc is the projected fin area. In this case the AR was 1.6.

Comparison of Test Results between Modes 1 & 2

 

Parameters Mode 1 Mode 2
Maximum Velocity: BL/s (m/s)

Acceleration time to Max Velocity: s

Frequency: Hz

Reynolds Number: Re (106)

Strouhal Number: St

Maximum Thrust: N

Max Power Consumption Air: W

Max Power Consumption Water: W

Swimming Number: Sw

Head Swing Amplitude: m

Tail Swing Amplitude: m

Body length displaced: %

11.6 (3.7)

0.6s

20

1.2

0.34

9

120

120

0.58

0.003

0.063

51

11.6 (3.7)

0.6s

20

1.2

0.34

9

120

120

0.58

0.013

0.063

76

 

C.     Experimental Results

In Fig. 10 the average energy economy in relationship to driven frequency is shown, comparing both operational Modes in air and water. It can be seen that both Modes actuating in water consumed a maximum 120W at 20Hz. This measurement was obtained by a connecting tethered power supply and no noticeable increase in energy consumption was measured due to a resistance of the surrounding liquid. The result of high energy consumption can be greatly improved as the tests indicated large mechanical gains when actuating the mechanical drive system without link IV, improving from a 120W to 70W consumption. This was a result of pressure increase at higher velocities, as link IV was actuated, the tendons were required to be tighter to provide the desired posterior kinematics, putting increased strain on the mechanism. Despite the high energy consumption, the prototype can maintain an operational time of approximately ten minutes at maximum velocity (estimated by video recording multiple runs), far surpassing the endurance of live fish, as equivalent burst speeds can only be maintained for short times of around one second. We can assume that engineering a greater mechanically efficient drive of link IV in the next generation may significantly improve endurance, relating to an estimated reduced energy consumption of ~50%.

As illustrated in Fig. 11, the developed build with a high power density ratio can generate a great amount of force of up to 9N. This can be effectively transferred in the water, accelerating both Modes to maximum velocity in approximately 0.6s. The relationship between velocity (speed divided by body length) and driven frequency is shown in Fig. 12. The corresponding values of Modes 1 and 2 during consistent swimming are shown and compared to current robotic fish. Both operational Modes can achieve an average maximum velocity of 11.6Bl/s, (i.e. 3.7m/s) at 20Hz, increasing performance in comparison with iSplash-I and current published robotic fish which typically peak around 1BL/s. This result also outperforms the average maximum velocity of real fish measured at 10BL/s. The values illustrated in Fig. 12 show that applying the operational Mode 2 swimming pattern had no effect on performance due to kinematic alignment errors, discussed in Section IV-B, therefore it is predicted that the magnitude of added mass in both modes is equal. Hence, we can estimate that accurately applying the coordinated full-body swimming pattern of iSplash-I may increase speed by a further 27%.

A prominent parameter for analyzing BCF locomotive performance is the Strouhal number (St), defined as St=fA/U, where f denotes the frequency, A denotes the tail amplitude and U is the average forward velocity. St is considered optimal within the range of 0.25 < St < 0.40 [15]. The measured St = 0.34 under the condition of Re = 1.2 x 106, in both Modes is within the desired range. The prototypes Swimming number (Sw) (distance travelled per tail beat) is highly efficient, measuring a Sw of 0.58 in comparison to the previous build with a Sw of 0.42 and close to the particular efficient common carp with a Sw of 0.70 [11],[13].

We have undertaken experiments to gain knowledge if raising driven frequencies greater than the previous build of 6.6Hz would continue to increase speed without peak or decline. This was achieved measuring a continued increase in velocity up to intensively high frequencies of 20Hz. Mimicking the swimming properties of real fish, frequency has become the key variable to enhance the linear locomotive performance of the iSplash platforms.

IV.     Conclusion and Future Work

This paper describes the development and experimental analysis of iSplash-II. The study aimed to realize the fastest speeds of live fish. A high-performance prototype was developed, robust, compact, naturally buoyant, carrying its own power supply, with a high power density and able to effectively transmit large forces at intensively high tail oscillation frequencies for untethered high-speed propulsion.

Although the desired kinematics over the full body could not be attained due to the power density requirements (with the primary actuator 75% of the total mass), the devised assembly was able to reduce the recoil around the center of mass, therefore generating an effective propulsive mechanism. As a result, large posterior forces and tail amplitudes 0.2 of the body length (with smooth generated undulations from mid-body to tail tip) were attained. The prototype was able to accelerate to steady state swimming in an approximate time of 0.6s, maintain an endurance at maximum speed for approximately ten minutes (greater than the measurement of real fish of approximately one second), realize a highly efficient stride rate (Sw) and attain high tail oscillatory frequencies without early peak, decline or mechanical failure.

iSplash-II, a 32cm untethered carangiform swimmer, 0.835kg, formed in PLA filament, consistently achieved a maximum velocity of 11.6BL/s (i.e. 3.7m/s) at 20Hz with a stride rate of 0.58 and a force production of 9N. Capable of outperforming the recorded average maximum velocity of real fish measured in BL/s, attaining speeds adequate for real world environments

Our future research will focus on the following aspects to further improve the swimming performance: (i) continue to raise driven frequency to achieve greater speeds over the fastest real fish. As the build showed no signs of failure an initial aim of 40Hz can be made; (ii) to accurately emulate the kinematic parameters of the full-body swimming motion [12], indicating that maximum velocity will increase a further 27%;  (iii) to replace the drive mechanism of link IV, to significantly improve the energy consumption; (iv) to optimize the tail amplitude, shape, 3D deformation and magnitude;    (v) to apply the behavioral technique of burst and coast, as live fish generating 10BL/s at the burst stage reduce the cost of transport by approximately 50% [18]; (vi) to develop mobility within the horizontal plane with estimated turning diameter of < 1L.

Acknowledgments

This work was supported by a University of Essex Scholarship. Our special thanks go to Richard Clapham senior for his technical assistance and financial contribution towards the project.

References

    • R. Bandyopadhyay, “Maneuvering hydrodynamics of fish and small underwater vehicles,” Integr. Comparative Biol., vol. 42, no. 1, pp. 102– 17, 2002.

 

    • S. Triantafyllou, M. S. Triantafyllou, and M. A. Grosenbaugh,“Optimal thrust development in oscillating foils with application to fish propulsion,” J. Fluids Struct., vol. 7, pp. 205–224, 1993.

 

    • J. Videler, “Fish Swimming”, Chapman and Hall, London, 1993.

 

    • Lighthill, “Mathematical Biofluiddynamics”, Society for Industrial and Applied Mathematics, Philadelphia, 1975.

 

    • S. Barrett, M.S. Triantafyllou, D.K.P. Yue, M.A. Grosenbaugh, and M. J. Wolfgang, “Drag reduction in fish-like locomotion,” J. Fluid Mech., vol. 392, pp. 183–212, 1999.

 

    • M. Anderson, and N.K. Chhabra, ”Maneuvering and stability performance of a robotic tuna”, Integrative and Comparative Biology,Vol: 42, iss: 5, pp: 1026-1031, Nov 2002.

 

    • Yu, M. Tan, S. Wang and E. Chen. “Development of a biomimetic robotic fish and its control algorithm,” IEEE Trans. Syst., Man Cybern. B, Cybern,34(4): 1798-1810, 2004.

 

    • J. Liu and H. Hu, “Biological Inspiration: From Carangiform fish to multi-Joint robotic fish,” Journal of Bionic Engineering, vol. 7, pp. 35–48, 2010.

 

    • Wen, G.H. Wu, J.H Liang and J.L Li, “Hydrodynamic Experimental Investigation on Efficient Swimming of Robotic Fish Using Self-propelled Method”, International Journal of Offshore and Polar Engineering, Vol.20, pp. 167~174, 2010.

 

    • Valdivia y Alvarado, and K. Youcef-Toumi, “Modeling and design methodology for an efficient underwater propulsion system”, Proc. IASTED International conference on Robotics and Applications, Salzburg 2003.

 

    • Bainbridge, “The Speed Of Swimming Of Fish As Related To Size And To The Frequency And Amplitude Of The Tail Beat”, J Exp Biol 35:109–133, 1957.

 

    • R. J. Clapham and H. Hu, “iSplash-I: High Performance Swimming Motion of a Carangiform Robotic Fish with Full-Body Coordination,” Accepted for 2014 IEEE International Conference on Robotics and Automation, May 31 – June 7, 2014, Hong Kong, China.

 

    • Nagai. “Thinking Fluid Dynamics with Dolphins,” Ohmsha, LTD, Japan, 1999.

 

    • W. Rosen, “Water flow about a swimming fish,” China Lake, CA, US Naval Ordnance Test Station TP 2298, p. 96, 1959.

 

    • J. Wolfgang, J.M. Anderson, M.A. Grosenbaugh, D.K. Yue and M.S. Triantafyllou, “Near-body flow dynamics in swimming fish,” September 1, 1999, J Exp Biol 202, 2303-2327

 

    • W. Webb, “Form and function in fish swimming,” Sci. Amer., vol. 251, pp. 58–68, 1984.

 

    • V. Lauder and E.G. Drucker, “Morphology and Experimental Hydrodynamics Of Fish Control Surfaces,” IEEE J. Oceanic Eng., Vol. 29, Pp. 556–571, July 2004.

 

    • J.J. Videler and D. Weihs, “Energetic advantages of burst-and-coast swimming of fish at high speeds,” J. Exp. Biol., 97:169-178, 1982.
iSplash-MICRO (Presented at IROS 2014)

iSplash-MICRO: A 50mm Robotic Fish Generating the Maximum Velocity of Real Fish

 

Richard James Clapham and Huosheng Hu

 

PDF

Abstract—This paper presents a millimeter scale robotic fish, namely iSplash-MICRO, able to accurately generate the posterior undulatory pattern of the carangiform swimming mode, at intensively high frequencies. Furthermore an investigation into anterior stabilization was made in an attempt to reduce the large kinematic errors and optimize forces around the center of mass. Applying large scale dorsal and pelvic fins relative to body size enabled predictable optimization of the anterior and posterior displacements. During the field trials, the small fish with a length of 50mm has generated an equivalent average maximum velocity to real fish, measured in body lengths/ second (BL/s), greatly improving previous man-made systems, achieving a consistent free swimming speed of 10.4BL/s (0.52m/s) at 19Hz with a low energy consumption of 0.8 Watts.     

I.     INTRODUCTION

During marine exploration a miniaturized underwater vehicle (UV) can benefit operations by allowing greater mobility as the turning diameter and body geometry is small. Current rotary propeller driven vehicles operating during low speed locomotion have particularly high cost of transport [1] requiring large a power supply, increasing body size. In addition the drive method of rigid hull UVs create large propulsive wakes causing increased environmental noise. In contrast, this is where fish excel, generating large transient forces efficiently and smoothly by coordinating their body motion in harmony with the surrounding fluid [2],[3]. Hence, the miniaturization of bio-robotic propulsion can provide greater mobility, unobtrusive navigation, reduced noise to the environment and a lower cost of transport.

Although smaller fish are measured with an overall slower speed in relation to size, they are able to generate higher tail oscillatory frequencies and therefore greater speed, measured in body lengths/ second (BL/s), a great benefit to overcome position destabilization flows. Bainbridge has measured live fish with average maximum velocity of 10BL/s, an exceptional example of a small fish (Cyprinus carpio), 135mm in body length, achieved a maximum velocity of 12.6Bl/s (i.e. 1.7m/s) and a stride rate of 0.7 [4][5].

Micro scale design requires developing the propulsive motion in relation to the developed body size and desired surrounding environment. The required propulsion method can be calculated using the Reynolds number (Re), defined as Re=UL/v, where U denotes the speed, L denotes the body length and v is the viscosity of water. Re relates to the ratio of inertia to viscous forces. If the Re is large, the viscous forces are negligible (Re 103-107) [6]. Viscous force is dominant when the body length is approximately <1mm. The two methods of propulsion are categorized as: (i) Inertia Force Propulsion, generating locomotion by creating a reaction force (FR) against the mass of the water. (ii) Resistance Force Propulsion, adopting a kinematic motion to generate locomotion from the viscosity of the water.

Developing robotic fish at any body-length has proven a great challenge. Although most work has focused on hydrodynamic mechanisms, performance is still low. In particular: (i) Accurately replicating the linear swimming motion has proven to be difficult and free swimming robotic fish have significant kinematic parameter errors. (ii) Actuator selection and mechanical transfer into productive propulsion are limited by force, frequencies and mechanical losses.

The complexity of developing a mechanical structure at the micro scale is increased due to material and hardware constraints. Some examples of novel micro builds and their maximum speeds are Ye’s IPMC actuated fish, 98mm’s in body length which achieved a maximum velocity of 0.24BL/s (24mm/s) [7], Guo’s ICPF actuated prototype, 45mm’s, achieving a velocity of 0.11BL/s (5.21mm/s) [8] and Wang’s SMA manta ray, 243mm’s, achieving a velocity of 0.23BL/s (57mm/s) [9]. Some examples of novel design approaches at larger scales are Barrett’s Robotuna, which achieved a velocity of 0.65BL/s (0.7m/s) [10], Yu’s discrete assembly achieving a velocity of 0.8BL/s (0.32m/s) [11], Liu’s, G9 achieving a velocity of 1.02BL/s (0.5m/s) [12] and Valdivia y Alvarado’s compliant structure achieving a velocity of 1.1BL/s (0.32m/s) [13]. Previously the low speeds of robotic swimmers were unpractical for operation, peaking at speeds of 1Bl/s.

iSplash-I [14], i.e. a carangiform swimmer with a body length of 250mm, introduced a high performance swimming motion.  The novel mechanical drive system was devised to operate in two swimming patterns. A thorough comparison between the traditional posterior confined undulatory swimming pattern and an introduced full body length swimming pattern was made. The proposed pattern coordinated anterior, mid-body and posterior displacements, reducing the large kinematic errors seen in free swimming robotic fish. In particular it achieved anterior stabilization by significantly reducing recoil and optimizing the lateral (FL) and thrust forces (FT) around the center of mass, assumed to initiate the starting moment of added mass upstream. From the comparison, the proposed swimming motion significantly outperformed the traditional approach, achieving a maximum velocity of 3.4BL/s (0.88m/s) and consistently achieved a velocity of 2.8BL/s (0.70m/s) at 6.6Hz. Notably, the mechanical drive system of iSplash-I operating in the simplified body motion of posterior confined undulations also measured a high performance of 2.2BL/s (0.55m/s) at 6.1Hz.

Throughout the field trials the prototype showed no peak or decline in velocity as frequency was raised in both swimming modes. Mimicking the swimming variables of real fish, as measured in the observational studies of Bainbridge, indicating swimming above 5Hz has no variation in kinematics, and only frequency is changed to increase swimming speed, providing a key swimming parameter. Therefore applying higher frequencies to either swimming motion of iSplash-I may continue to increase velocity, and in consideration that fish employ an identical swimming motion of inertia force propulsion at the millimeter scale, we proposed iSplash-MICRO.

The research project aimed to achieve the fastest speeds of live fish and proposed five main objectives: (i) Develop a structural build only 50mm in length, able of accurately replicating the kinematic parameters of the posterior confined undulatory swimming pattern of iSplash-I; (ii) Significantly raise driven frequency in comparison to the first generation, to be capable of intensive tail oscillations of up to 19Hz by fabricating a robust naturally buoyant structure, a complex challenge at such a small scale; (iii) Allow for a high efficiency mechanical energy transfer by engineering a drive system that takes hardware and material parameters into account; (iv) Devise a novel solution to improve the predicted excessive destabilization in yaw, by optimizing the FL and FT around the center of mass; (v) Realize a mechanism capable of consistent steady state swimming, measuring its achievements in terms of speed, kinematic accuracy and energy consumption over a range of frequencies from 5-19Hz.

The remainder of the paper is organized as follows: Section II details the applied swimming pattern and introduces a novel destabilization solution. Section III describes a new construction method for micro builds. Section IV describes the field trials undertaken and the experimental results obtained. Concluding remarks and future work are given in Section V.

II.     Design Methodology

 

A.     Posterior Undulatory Swimming Motion

The selected carangiform swimmer, Cyprinus carpio (common carp), which applies the method of body and/or caudal fin (BCF) propulsion has been chosen for replication due to its exceptionally high locomotive performance [4],[5].

Inertia Force Propulsion of the Carangiform swimming mode is associated with the method of added mass [15]. Added mass is initiated as each individual segment of the undulatory wave passes backwards during the body wave cycle creating a force FR against the surrounding fluid and an opposing force against the body, generating forward motion of the entire body. The FR is decomposed in to FT and FL, which must be optimized for efficient propulsion. The added mass is the product of the water accelerated and the momentum of water accelerated by the propulsive segments. Fish can achieve a low cost of transport by generating the method of added mass efficiently. Hence, there is great potential to improve biological inspired UV’s by accurately mimicking this propulsive method.

The kinematic pattern of the carangiform inertia force propulsion method is represented in the form of a traveling wave and can be identified by its propulsive wave length and amplitude envelope. Traditionally robotic swimmers adopt a method which typically concentrates the wave motion to <1/2 of the body length, initiated at the center of mass, smoothly increasing in amplitude along the body length towards the tail tip [2]. The observed posterior amplitude of live fish is 0.1 of the body length, measured from the midline to the furthest lateral tail excursion. The location of the pivot point is optimum at 0.15-0.25 [4]. The commonly adopted swimming kinematics were proposed in [10] adapted in [12]. The posterior undulatory swimming motion applied to iSplash-MICRO is of the form:

where ybody is the transverse displacement of the body; x is the displacement along the main axis starting from the nose of the robotic fish; k =2π/λ is the wave number; λ is the body wave length; ω = 2πf is the body wave frequency; c1 is the linear wave amplitude envelope and c2 is the quadratic wave. The desired wave form motion consists of one positive phase and one negative phase throughout the complete cycle [4]. The parameters P = {c1,c2,k,ω} can be adjusted to achieve  the required posterior swimming pattern, providing an engineering reference. This operational mode will be described as Mode 1 and is illustrated in Fig. 6.

B.     Anterior Stabilization Approach

It was detailed by Lighthill [2], that several morphological adaptations of carangiform fish reduce the severe yaw destabilization that is seen in free swimming robotic fish, without affecting propulsive efficiency by increasing drag: (i) Vertical compression along the full body length. The measured maximum thickness is 0.2 of the body length and reduces in size towards either extremity [4]. This form must be applied to reduce roll and yaw destabilization and also forward resistance. This structure is realized when engineering a morphological approximation of a carangiform swimmer; (ii) Reduced depth of body at the peduncle, most defined by the thunniform swimming mode [10]. This structural adaptation is complex to fabricate at any scale due to material limitations, particularly at the micro scale as the posterior mechanism must be narrow, structurally robust and mimic the smooth curves of the kinematic undulations; (iii) Accurate weight distribution. Imprecise configurations generate large destabilization within the horizontal plane, as a consequence of the FR not being optimized, typically seen on multi-link servo assemblies [11],[12]; (iv) Increased depth of body towards the anterior, a distinctive adaptation of the carangiform morphological parameters. As previously described, anterior destabilization is challenging to control [14]. Passive rigid anterior mechanisms recoil around the center of mass. Current free swimming robotic fish can be seen with excessive head swing, similar in magnitude to the posterior, greatly increasing drag [13]. As a micro scale structure limits the ability to apply the coordinated full-body motion [15] due to the complexity of the mechanical linkage, we propose a novel approach to significantly increase the anterior depth of body by applying large scale dorsal and pelvic fins, relative to body size.

The anterior destabilization solution of anterior and mid-body fins provides the required surface area without creating excessive resistance to forward motion as the fins are vertically compressed. Flow visualization techniques from published biological studies [16][17] and mechanisms such as “undulating pump” and “vortex peg” have measured a fluid-body interaction, that may contribute to propulsion, is generated upstream to the posterior section. Therefore, it is predicted that reducing the anterior amplitude to the observed optimal value of a common carp at approximately 0.04 of the body length will initiate the starting moment of added mass upstream and optimize the FL and FT forces around the center of mass, increasing the overall magnitude of thrust contributing to increased forward velocity. This operational mode will be referred to as Mode 2, illustrated in Figs. 2 and 7.

C.     Posterior Amplitude Variations

To provide a further investigation into the kinematics parameters of the carangiform swimming motion, and the proposed stabilization solution of operating Mode 2, a variation in tail amplitude was applied. This operational mode will be referred to as Mode 3 and illustrated in Fig. 8. A larger kinematic parameter than the value of real carangiform swimmers will first be applied to Modes 1 and 2, as a large tail amplitude value of 0.17 applied to iSplash-I was previously found to significantly increase performance. Due to the predicted destabilization whilst operating in Mode 1 [14], the body and tail kinematic data during locomotion will be inaccurate. If the anterior destabilization solution of Mode 2 and 3 is operationally correct the posterior kinematic parameters will also align with the desired amplitude value. Mode 3 will further investigate the carangiform swimming motion of Mode 2, by applying structural changes to the mechanical drive offset, to test a tail amplitude which is closer to the observed measurement of a common carp.

III.     New Construction Method

 

A.     Mechanical Design

 

A mechanical drive system able to accurately mimic the displacements of the travelling wave sets a great challenge. This is significantly increased at the millimeter scale. The drive system must be simple, compact, lightweight and robust to provide high frequencies under large forces for high-speed performance. Various novel approaches using the advances in hardware to achieve micro scale actuation have been attempted [18],[19],[20]. Smart materials have mainly been adopted to reduce body size but have shown limited frequencies, response time, actuation and force, therefore measuring low linear velocities [7],[8],[9],[21].

 

We set an aim for the prototypes build length of 50mm. Live carangiform fish of this body size employ identical swimming motions to larger fish of 250mm to generate linear locomotion, by employing the inertia force propulsion method of added mass. Therefore, we aimed to devise a simplified powertrain, capable of replicating the posterior confined undulatory swimming motion of iSplash-I without loss of accuracy.

 

The developed arrangement illustrated in Fig. 2 employs a single electric motor and a single degree of freedom along the axial length. The two rigid discrete links are coupled with a stiffness varying posterior, beginning at link II and continuing to the tail tip. The discrete assembly method can be defined as a series of links or N links. Applying more links reduces midline curve alignment errors and increases mechanical complexity. Details of the fully discretized body wave fitting method are given in [11], [12]. To provide the undulatory motion, a compliant caudal fin is coupled to link II which can be removed. This method allowed the material stiffness of the caudal fin to be adjusted experimentally, to provide the targeted curves during free swimming. The presented design approach achieved complexity of motion with a significant reduction in structural parts, allowing a build only 50mm in length to be realized.

 

In addition, a modular build was devised allowing each part to be easily changed and modified during fabrication, and for all Modes of operation to be applied to the same prototype by adjusting the configuration. Mode 3 can be put in operation by adjusting the single offset crank, driving link II shown in Fig. 3. Mode 2 can be applied by removing the outer structure of link I and replacing with the required form.

 

B.     Power Transmission System

A single crankshaft attached to the output shaft of the primary actuator directly drives link II, by transmitting continuous rotary power to linear oscillations, illustrated in Fig. 3 and 4. The devised powertrain increases power distribution to the posterior and required high-precision of the chassis, link structures and crankshaft to avoid deadlock, reduce friction and significantly improve energy transfer, which can be lost in many stages of the mechanical drive.

The driven link amplitude is determined by the offset crank, L2 represents posterior link of the discrete structure. The maximum amplitude of the link length L2 at point P2 is determined by the predetermined maximum crank offset P1. The coordinates of P1 (P1x, P1y) and P2 (P2x, P2y) can be derived by:

(3)

The length of L2 can be derived by L22= P2x2+P2y2. Assume that ω1 is the angular velocity of the link L2, and the velocity vector VP2 is perpendicular to L2. We have:

                            (4)

where Vp2x and Vp2y are the decomposed vectors of the velocity vector VP2= ω1 L2.

C.   Fabrication

iSplash-MICRO in operational Mode 2 with a total mass of 3.35g (2.45g in Mode 1) is illustrated in Fig. 5, with the physical specifications given in Table I. The build was first digital modelled taking hardware constraints and material properties into account, so that the kinematic and geometric parameters were not affected, reducing the resistance during forward locomotion. The inner structural frames and bulkhead were formed from the material polypropylene, chosen to provide the required density (lower than water) and the structural strength for high frequency actuation. All structural parts were hand cut, fitted and assembled. This devised method produced a structurally robust prototype allowing for consistency of operation at intensively high frequencies, generating large forces relative to body size, which are applied to the water and reactively, the opposing force exerted on to the vehicle [15].

For fast locomotive performance, a high power density is required to attain high frequency actuation. Although complexity of developing the mechanical drive system is increased, a single electrical motor with continuous actuation was deployed and positioned in the optimum location [2], [4], in contrast to other construction methods which limit accuracy of weight and volume arrangement and force production [11],[12],[13]. The power-to-weight ratio was greatly increased by achieving a configuration in which the electric motor is 50% of the total mass in operational Mode 1 and 37% in Modes 2 and 3. To counteract the large weight of the primary actuator relative to body size, the build volume was increased vertically, to realize natural buoyancy.

For operational Mode 2, large fins, 48mm in height with vertical compression were devised, a similar morphological trait as real fish fins. By forming large dorsal and pelvic fins made of polypropylene the buoyancy was greatly increased, this was counteracted by applying weight to the lower chassis of link I. During free swimming stability could not be maintained as frequencies were raised. Although the anterior fins were devised as an initial solution to reduce destabilization within the horizontal plane, the configuration of material properties significantly increased stabilization in roll. This development enabled the prototype to achieve open loop stability, as the relative position of buoyancy is higher than the center of mass. Therefore the surrounding fluid counterbalances the gravitational weight [22].

    • Physical Parameters of iSplash-MICRO

 

Parameter Specific Value
Maximum Velocity: BL/s (m/s)

Body Size: mm (LxWxH)

Body Mass: g

Anterior Fin Size: mm (LxWxH)

Anterior Fin Mass: g

Maximum Frequency: Hz

Actuator:

Actuator Mass: g

Power Supply:

Materials:

Swimming Modes:

Tail Material:

Thickness of Caudal Fin : mm

Caudal Fin Aspect Ratio: AR

10.4 (0.52)

50 x 7 x 16 (Without Fins)

2.45 (Without Fins)

26 x 0.8 x 48

0.9

19

Single electric motor

1.23

4V LiPo external battery supply

Balsa wood, polypropylene, acetal

Linear locomotion

Polypropylene

0.8

1.5

 

IV.     Experimental Procedure and Results

 

A.     Field Trials

 

Experiments were conducted within a 1000mm long x 500mm wide x 250mm deep test tank. The prototype had sufficient space to move without disturbances from side boundaries and the free surface, able to maintain swimming at mid-height of the test tank. A series of experiments were undertaken in order to verify the locomotive performance of all Modes in terms of speed, energy consumption and kinematic observation at frequencies between 5-19Hz. The test results of all Modes are summarized in Table II. Steady free swimming over a fixed distance of 450mm was used to measure speed (shown in Fig. 9), once the prototype had reached its maximum velocity at each tail oscillation frequency. Measurements were averaged over many cycles once the prototype was able to achieve consistent operation.

 

A.     Swimming Pattern Observation

 

Illustrated in Figs. 6, 7 and 8 are the midline kinematic parameters of the full body length, taken at every 0.006s to provide the anterior and posterior wave forms of Modes 1-3 during swimming for comparison. We aimed to achieve and analyze the kinematic parameters of live fish and iSplash-I. Good matching with live fish kinematic data is a complex task, as the wave forms of free swimming robotic fish have shown extensive head amplitude errors and inaccurate displacement parameters over the full body length.

 

When comparing Modes 1 and 2, Mode 2 reduced the head amplitude from 0.12 (6mm) of the body length  in Mode 1 to 0.02 (1mm), generating a smaller value than the common carp at 0.04 [4]. The observed tail amplitude of the common carp is 0.1 and iSplash-I is 0.17. Mode 1 with anterior destabilizing, lost posterior amplitude displacements and measured 0.12 (6mm), in comparison Mode 2 was able to generate a large value of 0.20 (10mm). Analyzing the midline sequence of the Mode 1 illustrated in Fig. 6, we can notice the excessive head swing amplitude equivalent to the posterior value as predicted, based on previous work in [15] and current robotic fish [12][13]. The stabilizing solution of Mode 2 has significantly improved matching errors, greatly reducing the recoil from the concentrated posterior thrust and in turn creating accurate posterior displacements. Fig. 8 shows that Mode 3 has a reduced posterior amplitude of 0.14 (7mm), closer to the observed measurement of live fish and an equivalent anterior displacement to Mode 2. We were able to calculate the tail amplitude of Mode 3 prior to the experimental testing using (3), as the devised anterior fins of the free swimming robotic fish have enabled a predictable kinematic optimization. In addition, it was found that Mode 1 had an erratic forward heading during test runs, affected by the tethered cables. In contrast, Mode 2 provides a very directional forward heading, not deterring once in motion.

 

A principal aim of the research was achieving accurate posterior kinematic matching to iSplash-I, with a significantly simplified assembly. The tracked midline shows that the developed prototype generates a precise travelling wave ½ the body length and has achieved a smooth transition phase from body to tail tip, due to the compliant structure. The formed caudal fin provided higher speeds in initial testing with a low aspect ratio, future optimization is planned. AR is calculated using: AR=b2/Sc where b squared is the fin span and Sc is the projected fin area. AR in this case was 1.6.

 

    • Comparison of Test Results between Modes 1,2 & 3

 

Parameters Mode 1 Mode 2 Mode 3
Reynold Number: Re (104)

Shrouhal Number: St

Swimming Number: Sw

Maxium Velocity: BL/s

Maxium Velocity: m/s

Frequency: Hz

Max Power Comsumption Air: W

Max Power Comsumption Water: W

Head Swing Amplitude: mm

Tail Swing Amplitude: mm

Test Run Distance: mm

2.6

0.22

0.54

10.4

0.52

19

0.68

0.8

6

6

450

2.6

0.36

0.54

10.4

0.52

19

0.68

0.8

1

10

450

1.6

0.41

0.33

6.4

0.32

19

0.68

0.8

1

7

450

 

B.     Experimental Results

The average energy consumption in relationship to driven frequency is shown in Fig. 10. A comparison measuring the cost of transport in water and actuation air was made. We can notice that all Modes actuating in water resulted in a slight increase in energy consumption, from 0.6W in air to 0.8W, at the maximum frequency of 19Hz. The very low cost of transport measured indicates the replicated swimming motion of [15] and the novel mechanical drive system is energy efficient. We can calculate that the next generation will be capable of carrying an onboard power supply.

The relationship between velocity (speed divided by body length) and driven frequency is shown in Fig. 11. The corresponding values of all Modes during consistent swimming were measured and compared to current robotic fish. Modes 1 and 2 consistently achieved a maximum velocity of 10.4Bl/s (0.52m/s) at 19Hz. Mode 3 had a decreased maximum velocity of 6.4BL/s (0.32m/s) at 19Hz.  Although the tail amplitude of Mode 3 was closer to the value of the common carp, performance was lower, reaffirming data from the first generation [15]. In addition, no energy consumption was saved from the tail amplitude reduction. Hence, we estimate the next generation may have enough power to further increase of tail amplitude beyond the value of Mode 2 (the furthest lateral excursion that could be applied to this structure). iSplash-MICRO has significantly increased performance in comparison with current robotic fish which typically peak at approximately 1BL/s and has equivalent speeds of the fastest real fish, measured with an average maximum velocity of 10BL/s [5].

Identical to the previous generation as frequencies were raised, velocity increased in all Modes. From this we can assume that raising this key swimming parameter of the developed mechanical drive system beyond 19Hz will continue to increase performance further.

Despite Mode 2 significantly improving displacement parameters along the full body length, no noticeable increase or decrease in velocity was found. This result was not expected as the coordinated full-body swimming motion of the first generation increased velocity by 27%. Differences in structure can be noted as previously mentioned in Section II-A, as a consequence the midline kinematics do not generate a smooth curve from head to tail. This may have stalled the fluid flow interaction at a point located around the center of mass. The location of the pivot point is inaccurate, due to structural constraints, the optimum range being 0.15-0.25 of the body length. All Modes were measured at 0.5.

A prominent parameter for analyzing BCF locomotive performance is the Strouhal number (St), defined as St=fA/U, where f denotes the frequency, A denotes the tail amplitude and U is the average forward velocity. The St is considered optimal within the range of 0.25 < St < 0.40 [23].  Mode 1 has a St of 0.22 under the condition of Re = 2.6 x 104, Mode 2 has a St of 0.36 under the condition of Re = 2.6 x 104 and Mode 3 measured a St = 0.41 under a condition of Re = 1.6 x 104. The St of Mode 2 is within the desired range with both Modes 1 and 3 approximately optimal. The prototypes Swimming number (Sw) (distance travelled per tail beat) of Modes 1 and 2 is highly efficient, measuring a Sw of 0.54, increasing performance over the previous build with a Sw of 0.42 and close to the particular efficient common carp with a Sw of 0.70 [4].

In addition, the prototype was actuated at high frequencies for long periods during construction and test runs, without need of rebuild or showing wear, indicating the robustness of the developed micro prototypes mechanical drive system.

V.     Conclusion and Future Work

This paper describes the development of a small robotic fish prototype iSplash-MICRO, a man-made system able to generate the average maximum velocity of real fish. A greatly simplified structural built at the millimeter scale is able to accurately replicate the kinematic parameters of the posterior confined undulatory swimming pattern of iSplash-I [15]. Considering that the kinematic model over the full body length has large matching errors, a novel stabilization technique was deployed. The large scale dorsal and pelvic fins relative to body size optimize the FL and FT around the center of mass, generating accurate anterior amplitude and effectively stabilizing the platform in the horizontal and vertical planes. This enabled a predictable adjustment of the anterior and posterior kinematic amplitude parameters so that large posterior propulsive forces and amplitudes could be generated and accurate straight-line trajectories attained.

The developed prototype is compact, natural buoyant and robust, with a high power density and the ability to actuate at intensively high frequencies. Notably, the applied high frequencies increased velocity in all Modes without peak, decline or failure. We can therefore estimate that a further increase of frequency applied to this developed mechanical drive system may continue to increase its maximum velocity beyond the fastest live fish. iSplash-MICRO 50mm in body length achieved a consistent free swimming speed of 10.4BL/s (i.e. 0.52m/s) at a frequency of 19Hz with a stride rate (Sw) of 0.54 and a low energy consumption of 0.8W.

The experimental analysis has shown potential to improve the high performance swimming further, the following points are of significant interest: (i) The low energy consumed during propulsion indicates the next generation is capable of carrying a power supply; (ii) Posterior amplitudes of a magnitude greater than 0.2 of the body length may improve propulsion; (iii) The robust structure may generate higher tail oscillation frequencies. An initial aim of a 50% increase can be made, predicting an equivalent increase in performance; (iv) Optimize the tail shape and aspect ratio [22]; (v) The devised mechanical system is suitable for further reduction in scale as appropriate hardware becomes available.

Acknowledgments

This research was supported by a University of Essex Scholarship. Our special thanks go to Richard Clapham senior for his technical assistance and financial contribution towards the project.

References

    • R. Bandyopadhyay, “Maneuvering hydrodynamics of fish and small underwater vehicles,” Integr. Comparative Biol., vol. 42, no. 1, pp. 102– 17, 2002.

 

    • Lighthill, “Mathematical Biofluiddynamics”, Society for Industrial and Applied Mathematics, Philadelphia, 1975.

 

    • J. Videler, “Fish Swimming”, Chapman and Hall, London, 1993.

 

    • Nagai. “Thinking Fluid Dynamics with Dolphins,” Ohmsha, LTD, Japan, 1999.

 

    • Bainbridge, “The Speed of Swimming of Fish As Related To Size And To The Frequency and Amplitude of The Tail Beat”, J Exp Biol 35:109–133, 1957.

 

    • W. Webb, “Simple physical principles and vertebrate aquatic locomotion”, Amer. Zool., vol. 28, pp.709 -725 1988.

 

    • Ye, Y. Su, S. Guo and L. Wang, “Design and Realization of a Remote Control Centimeter-Scale Robotic Fish”, Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 25-30, 2008.

 

    • Guo, T. Fukuda and K. Asaka. “Fish-like Underwater Microrobot with 3 DOF”, In Proceedings of IEEE International Conference on Robotics and Automation, Washington, USA, pp. 738−743, May 2002.

 

    • Wang, Y. Wang, L Jian and G. Hang, “A micro biomimetic manta ray robot fish actuated by SMA”, Proc. IEEE Int. Conf. on Robotics and Biomimetics (Guilin, February) pp 1809–13, 2009.

 

    • S. Barrett, M. S. Triantafyllou, D. K. P. Yue, M. A. Grosenbaugh, and M. J. Wolfgang, “Drag reduction in fish-like locomotion,” J. Fluid Mech., vol. 392, pp. 183–212, 1999.

 

    • Yu, M. Tan, S. Wang and E. Chen. “Development of a biomimetic robotic fish and its control algorithm,” IEEE Trans. Syst., Man Cybern. B, Cybern., 2004,34(4): 1798-1810

 

    • J. Liu and H. Hu, “Biological Inspiration: From Carangiform fish to multi-Joint robotic fish,” Journal of Bionic Engineering, vol. 7, pp. 35–48, 2010.

 

    • Valdivia y Alvarado, and K. Youcef-Toumi, “Modeling and design methodology for an efficient underwater propulsion system”, Proc. IASTED International conference on Robotics and Applications, Salzburg 2003.

 

    • J. Clapham and H. Hu, “iSplash-I: High Performance Swimming Motion of a Carangiform Robotic Fish with Full-Body Coordination,” Accepted for 2014 IEEE International Conference on Robotics and Automation, May 31 – June 7, 2014, Hong Kong, China.

 

    • W. Webb, “Form and function in fish swimming,” Sci. Amer., vol. 251, pp. 58–68, 1984.

 

    • W. Rosen, “Water flow about a swimming fish,” China Lake, CA,US Naval Ordnance Test Station TP 2298, p. 96, 1959.

 

    • J. Wolfgang, J.M. Anderson, M.A. Grosenbaugh, D.K. Yue and M.S. Triantafyllou, “Near-body flow dynamics in swimming fish,” September 1, 1999, J Exp Biol 202, 2303-2327

 

    • Deng and S. Avadhanula, “Biomimetic micro underwater vehicle with oscillating fin propulsion: System design and force measurements,” Proc. of IEEE International Conference on Robotics and Automation, pp.3312-3317, April, 2005.

 

    • Fukuda, A. Kawamoto, F. Arai and H. Matsuura, “Mechanism and Swimming Experiment of Micro Mobile Robot in Water”, Proc. IEEE Con. on Robotics and Automation, Vol.1, pp.814-819, San Diego, California, May 1994.

 

    • Lee, “Design of a soft and autonomous biomimetic micro-robotic fish” In Proceedings of IEEE Industrial Electronics and Applications (ICIEA), pp. 240 – 247, June 2010.

 

    • Rossi, W. Coral, J. Colorado and Barrientos, “A motor-less and gear-less bio-mimetic robotic fish design”, Proc. IEEE Int. Conf. on Robotics and Automation, pp 3646–51, Shanghai, May 2011.

 

    • G.V. Lauder and E. G. Drucker, “Morphology and Experimental Hydrodynamics of Fish Control Surfaces,” IEEE J. Oceanic Eng., Vol. 29, Pp. 556–571, July 2004.

 

    • S. Triantafyllou, M. S. Triantafyllou, and M. A. Grosenbauch,“Optimal thrust development in oscillating foils with application to fish propulsion,” J. Fluids Struct., vol. 7, pp. 205–224, 1993.
iSplash-OPTIMIZE (Presented at IAS 2014)

iSplash-OPTIMIZE: Optimized Linear Carangiform Swimming Motion

Richard James Clapham and Huosheng Hu

PDF

 

Abstract. This paper presents a new robotic fish, iSplash-OPTIMIZE, which is 0.6m in body length and deploys a single actuator to drive discrete links across the full-body length. The main focus is on optimizing the kinematics parameters of its linear carangiform swimming motion in order to improve the distance travelled per beat. The experimental results show that the fish can be actuated at high frequencies up to 20 Hz due to deploying a continuous rotary power source. Each discrete link is able to be precisely tuned, providing accurate kinematics with little mechanical loss.

Keywords: Robotic fish · Carangiform swimming · Mechanical drive system · Full-Body length.

I

  • Introduction

Live fish are able to generate locomotive forces resourcefully in comparison to underwater vehicles (UVs) powered by rotary propellers [1,2,3,4]. The fish locomotion is able to extract energy from upstream vortices. A passive body resonating within the Karman Vortex Street can generate forward locomotion, with the highest locomotive efficiency [5].

A prominent parameter for analyzing body and caudal fin locomotive performance is the distance traveled per body length during one caudal fin oscillation. This can be calculated using the Swimming number (Sw) defined as Sw=U/fl where U denotes swimming velocity, f denotes the tail beat frequency and l denotes the body length [6]. The distance travelled per tail beat of the Cyprinus carpio (common carp) is highly efficient measuring a Sw of 0.66, with the highest recorded example of the Tursiops (Bottlenose dolphin) with a Sw of 0.82.

Research into biomimetic underwater propulsion has developed several innovative hydrodynamic mechanisms, such as Barrett’s Robotuna which achieved a maximum velocity of 0.65 body lengths/ second (BL/s) (i.e. 0.7m/s) [7], Yu’s prototype achieving a maximum velocity of 0.8BL/s (i.e. 0.32m/s) [8], Essex’s G9, achieving a maximum velocity of 1.02BL/s (i.e. 0.5m/s) [9] and Valdivia y Alvarado’s build achieving a maximum velocity of 1.1BL/s (i.e. 0.32m/s) [10].  To date, the speed of robotic fish is approximately 1BL/s, but real fish have an average maximum velocity of 10BL/s with the common carp peaking at 12.6 BL/s [3], [11].

Our first prototype iSplash-I [12], which is 0.25m in body length, weighs 0.345kg, and has a tethered power supply, achieved a high performance carangiform swimming motion. Its novel mechanical drive system operated in two swimming patterns, a traditional posterior confined undulatory swimming pattern and the introduced coordinated full-body length swimming pattern. The proposed swimming motion significantly improved the accuracy of the kinematic displacements and greatly outperformed the posterior confined approach in terms of speed, achieving 3.4BL/s and consistently achieving a maximum velocity of 2.8BL/s at 6.6Hz with a low energy consumption of 7.68W. Based on intensive observation, the predetermined offsets of the discrete link assembly were set to generate the kinematic parameters of a common carp.

Optimizing the discrete structure was limited as only the final link of over the full-body length was able to be adjusted. Experimental testing found that its Sw of 0.42 was lower than a common carp’s. The coordinated full-body length swimming motion provided accurate kinematics directly related to increased swimming performance, we estimate that further tuning of the kinematic parameters may provide a greater increase in maximum velocity and reduce the cost of transport. In consideration of this iSplash-OPTIMIZE was proposed, shown in Figs. 1 and 2.

 

Fig. 1. iSplash-OPTIMIZE

This research aims to improve the efficiency of the linear swimming motion with eight main objectives: (i) to develop a new build mechanical drive system, capable of distributing power from a single actuator to discrete links across the full-body length; (ii) to allow each discrete link of the assembly to be precisely tuned by devising a powertrain with innumerable adjustments; (iii) to attain a structurally robust mechanical drive system capable of intensively high frequencies of 20Hz; (iv) to devise a prototype able to carry a high capacity power supply to obtain consistent high force free swimming; (v) to gain high speeds by developing a compact design taking into consideration geometric and kinematic parameters throughout the full tail beat cycle; (vi) to obtain a low cost of transport by developing a mechanical drive system considering methods that may cause internal mechanical losses; (vii) to deploy an electrical system accurately measuring energy consumption, destabilization, with perception sensing, wireless communication and ability to produce control signals for multiple actuators for future autonomy; (viii) to validate the study by conducting a series of experiments measuring the prototype’s achievements in terms of energy consumption and kinematic parameters.

The remainder of the paper is organized as follows: Section 2 presents the linear carangiform swimming patterns to be investigated. Section 3 describes the mechanical design and construction method of the new build iSplash-OPTIMIZE. Section 4 describes the experimental procedure and results obtained. Concluding remarks and future work are given in Section 5.

  • Linear Swimming Patterns to be Investigated
    • The Traditional Swimming Motion Approach

This study aims to significantly improve the accuracy of replicating the wave form of the carangiform swimming mode, specifically the common carp, due to its high locomotive performance [6]. Identified by the portion of the body length actively displaced, the selected carangiform applies the swimming method of body and/or caudal fin propulsion, associated with the method of added mass. A full description can be found in [13]. Fish have an improved cost of transport over man-made systems by generating the method of added mass efficiently [3].

The body motion traditionally adopted in previous robot fish can be represented by a travelling wave, applying a rigid mid-body and anterior, concentrating the undulatory motion to the posterior end of the lateral length, typically limited to <1/2 of the body length consisting of one positive phase and one negative phase [9][14]. Initiated at the center of mass, the posterior propagating wave smoothly increases in amplitude towards the tail. The observed common carp lateral excursion is 0.1 of the body length. The posterior confined kinematics of the carangiform is of the form [7]:

 

where ybody is the transverse displacement of the body; x is the displacement along the main axis beginning at the nose; k =2π/λ is the wave number; λ is the body wave length; ω = 2πf is the body wave frequency; c1 is the linear wave amplitude envelope and c2 is the quadratic wave.

Free swimming robotic fish applying posterior confined displacements have shown significant kinematic parameter errors [9,10]. In particular, the lateral and thrust forces are not optimized around the center of mass, resulting in extensive anterior destabilization in the yaw plane, generated due to the posterior concentration of thrust. Consequently the inaccurate anterior midline parameters generate significant posterior kinematic displacement errors. Hence, the linear locomotive swimming motion over the full length of body has large matching errors in comparison to real fish leading to reduced propulsive force and a higher cost of transport. In addition the Sw may also be improved by applying large reaction forces (FR) at the cost of energy consumption without certain gains in maximum velocity.

  • The Additional Swimming Motions

The full-body swimming pattern of the iSplash platforms proposed in [12] coordinates the anterior, mid-body and posterior body motions. This was based on intensive observation [12] and fluid-body flow interaction research [15,16] which lead to a greater understanding of the carangiform swimming motion. The coordinated full-body swimming motion was found to significantly reduce kinematic matching errors over the full body length and therefore attaining a low cost of transport. Our primary aim of this study is to further optimize this swimming motion by adjusting parameters, estimated to enhance performance.

In particular the displacements of full-body swimming pattern drive the anterior into the direction of recoil, reducing amplitude errors by optimizing the FR of the propulsive elements. Furthermore the developed body motion enhances performance by producing a smooth transition of flow along the length of the body, effectively coordinating and propagating the anterior formed fluid flow interaction downstream. We can adjust the form in [9], an adaptation of (1) to generate the midline kinematic parameters of the full body displacements:

where the values c1, c2, k, ω can be adjusted to achieve the desired posterior swimming pattern for an engineering reference.

The developed mechanical drive system can generate innumerable variations of the wave form, allowing a thorough investigation to identify the most efficient swimming motion within the limits of the structure. Some key deployed kinematic patterns are:

  1. The Ostraciiform swimming mode [3], confining the kinematic displacements to the caudal fin.
  2. The Anguilliform swimming mode [4]. Notably the fraction of the body length displaced of the full-body swimming motion of the iSplash platforms is equal to the anguilliform swimming mode (eel) but reflects changes in its kinematic form, as the full-body pattern applies an oscillatory motion to the anterior and mid-body segments and pivots the entire body around a single pivot point associated with the carangiform swimming mode [6].
  3. Continued analysis of the full-body swimming motion by disregarding displacements of individual segments, to identify the contribution of each portion of the body length to the propulsion method.
  4. Advancing and retarding the timing of individual segments within the sequences of the spatial and time dependent full-body wave motion.
  5. Lastly, a series of tests investigating the effect of allowing individual segments to be passively moved by the surrounding fluid.
  • New Construction Method
    • Mechanical Design

The engineered platform 0.6m in body length is directly scaled from the structural link assembly of the first generation. This method provides an arrangement that has previously achieved high performance, in which we aim to improve further by precisely optimizing the kinematic parameters. Previously the accuracy of replicating the wave form parameters has been limited by hardware and material constraints. The structural approach of the multi-link servo assembly has typically been applied to optimize the kinematic displacements. This method is limited by force, frequencies, volume and mass distribution which are also typically confined to the posterior, reducing accuracy of the wave form [8],[9],[14]. Alternative methods deploying single continuous rotary actuators have measured large internal mechanical losses due to the complexity of the mechanism [7].

Fig. 2.    1-Plan; 2-Side; 3-Front view.

The presented prototype deploys an assembly with structural compliance combined with rigid discrete links. The arrangement distributes 3 degrees of freedom (DOF) and 1 passive DOF along the axial length to provide anterior, mid-body and posterior displacements and accurate midline curve alignment. The final posterior link V is coupled to a compliant scaled caudal fin, and is passively driven by four expandable tendons attached to the main chassis rear bulkhead, which can be adjusted experimentally to provide the targeted curves during free swimming at various frequencies, as achieved in [12]. Each of the discrete links across the body length can be configured to be actively displaced or held aligned with the centerline of the build. This development will allow analysis of each segments’ contribution to the overall propulsion of the full-body wave form. In addition a significant aspect of drive system is the ability to attain free movement of individual links, allowing them to be passively moved by the surrounding fluid, as our subsequent work will investigate if the prototype is capable of extracting energy from the surrounding flow.

  • Power Transmission System

The power transmission system was developed to transfer power to and provide precise adjustments of the discrete links (with innumerable sequences) with the smallest mechanical loss as possible, whilst actuating at intensively high frequencies due to deploying a single continuous high torque actuator. The developed powertrain transmitting rotary power to linear oscillating sliders (with 13mm displacements) is illustrated in Figs. 3 and 4a. The three key sliders are directly driven by the three adjustable offset discs (which are secured to the drive shaft after adjustment), achieving equal power distribution, capable of transmitting power to discrete links

 

Fig. 3.    Schematic drawing of the tail offset drive crank and linkage.

 

 

across the full-body length from the lightweight tendons. Each of the discrete links was constructed with four adjusters increasing accuracy of the swimming patterns alignment by tuning the tendons (Fig. 4b). The developed mechanical drive system has high accuracy with unrestricted offset combinations, high structural strength and is small in size. This development is key to attaining an optimized swimming motion. The devised power transmission system required precision fitment of the chassis,

 

Fig. 4.    Inner structure of the central drive system (a);       Adjusters for link I curve alignment (b).

 

.

 

crankshaft, cantilevers and linkages to avoid deadlock and reduce slide friction.

  • Fabrication

The modular prototype iSplash-OPTIMIZE shown in Fig. 5 was engineered as a morphological approximation of the common carp, fabricated using precision manufacturing techniques. The physical specifications are given in Table 1. A primary consideration of the development took into account the additional weight of the adjustable drive system, power supply and large electric motor (with dimensions of 85mm in length and 40mm in diameter), therefore no errors and excrescences in the geometry were required or kinematic parameters affected to compensate for the additional complexity of mechanical drive system. The geometric frame (the maximum cross section measured to be optimal at 0.2 of the body length) and midline camber was required to be accurate, as the outer profile of the coordinated full-body swimming pattern proposed in [12], represented by a deep camber aerofoil section (e.g. NACA (12)520) is estimated to aid the fluid flow interaction, producing greater locomotive speeds.

Table 1.

 

Fig. 5.     iSplash-OPTIMIZE: Showing interchangeable parts of the modular build.

 

Physical parameters of iSpalsh-OPTIMIZE

Parameters Specific Value
Body size: m (L x W x H) 0.62 x 0.11 x 0.16
Body mass : Kg 0.9
Primary actuator: Brushed DC motor
Power supply: 11.1v onboard LiPo battery
Manufacturing technique:

Primary swimming mode:

Additional maneuverability:

Additional control surfaces:

Tail Material:

Thickness of caudal fin : mm

Caudal Fin Aspect Ratio: AR

Communication: (Additional)

Tested signal distance: m

Microcontroller:

Data Storage:

Sensors:

 

Materials:

 

Precision engineering, machining

Linear locomotion

Yaw, pitch.

Pectoral fins

Polypropylene

2.3

1.6

2 x Zigbee 802.15.4, (27MHZ RF)

7.5

Arm Cortex M3 96Mhz

SD card

Current, voltage, encoder, infrared, compass, accelerometer, gyroscope.

Carbon Fiber, aluminum, stainless steel, acetal, low density foam.

 

The additional mass affected buoyancy, this was counteracted by improving the structures weight-to-strength ratio, deploying a combination of low density foam with carbon fiber layers, aluminum space frames and acetal inserts to strengthen sliding surfaces. This fabrication method achieved a structurally robust prototype, required for consistency of operation at high frequencies. In addition, natural buoyancy and open loop stability was achieved by positioning the large mass low and distributed across the main chassis (i.e. from DOF 2-3), therefore providing accurate density distribution properties to the first generation, as it is optimal for the principal pivot point of the carangiform swimming motion to be positioned within the range of 0.15-3 of the body length.

Additional mobility mechanisms were devised for autonomous locomotion: (i) to turn within the vertical plane. Two rigid morphological approximations of pectoral fins were developed and positioned at the leading bulk head of the main chassis, actuated by a single servo motor (with 180° actuation); (ii) to turn within the horizontal plane. A mechanism was developed to adjust the swimming pattern to generate the form of a C-sharp turn [4], by offsetting the posterior tendons using adjustable cross sliders actuated by a single servo motor.

  • Embedded System
Fig. 6.    Inner Structure of link I showing the installed electrical system.

 

A modular electrical system was built, employed to measure and control the robotic fish motion, positioned within link I shown in Fig. 6. The first study aims to measure various kinematic sequences in an attempt to reduce the cost of transport during linear locomotion. The central processor is a 32bit 96MHZ ARM Cortex-M3, which samples and filters data from multiple deployed sensors (i.e. incremental encoder, current, voltage and an inertial measurement unit (IMU)), is employed to measure the energy economy and the extent of destabilization at various frequencies and swimming patterns. The energy consumption of iSplash-I was sampled by external electronics. The new onboard electronic system and free swimming robotic fish allows for measurements unaffected by a tethered power supplies or support beams. The data can be logged, onboard by the SD module or sent instantaneously (tested up to a distance of approximately 7.5m) to an external PC for analysis by two onboard 802.15.4 wireless radios.

Our planned future work is to achieve autonomy at high locomotive speeds. The system has been installed with four infrared sensors (tested to produce accurate data up to approximately 1m) and two control surface actuators so that the central processor will process data of the state of orientation, surrounding environment, energy economy and frequencies rate, and therefore perform decision making and produce the required control signals. The structure is shown in Fig. 7. This will be

Fig. 7.    The structure of the energy and stability measurement and actuator control system;

great challenge as locomotive speeds increase due to the deployed limited sensors.

  • Experimental Procedure and Results
    • Mechanical Energy Transfer

A series of experiments were undertaken in order to show the feasibility of the new prototype, evaluating performance in terms of kinematic parameters, robustness, open loop stability and energy consumption at frequencies within the range of 5-20Hz. The test results are given in Table 2. The embedded system was employed to sample data reaffirmed by external electronics. The measurements were required to be averaged over many cycles to increase the accuracy of data, once consistency of operation was achieved. The initial experimental testing highlighted areas of required development. During actuation at high frequencies we found that the chosen materials and configuration enduring high forces failed as the build design was not suitable for the large increase in scale, which produced a significant increase in pressure in comparison to the first build. Rebuilds were undertaken and the appropriate materials suitable for intensively high frequencies within an aquatic environment were found. The rebuilds took into consideration mass and volume distribution and material properties, so that open loop stability was realized, which is a requirement for precise optimization of the swimming motion during linear locomotive. For the development of autonomy with mobility in yaw and pitch it is required that the weight is greatly concentrated at the center mass [17].

Once consistency of operation was achieved the devised mechanical drive system was found to be very robust, showing no signs of structural failure throughout experimental testing, whilst actuating at intensively high frequencies for long periods in air at 10Hz and short test periods of actuation at 20Hz in water.

The power supply will contribute to a significant portion of the total mass therefore an efficient energy transfer is required for high performance. In Table 2 the average energy economy in relationship to driven frequency is shown, during non-productive power consumption (i.e. while operating in air). This comparison was used to measure the value of the increased resistance during actuation of each discrete link and during various link sequences. We measured the energy economy over many cycles, as the inertia of the oscillatory motion produces fluctuating readings within a cycle. Operation whilst actuating all links at 10Hz at their maximum lateral excursion resulted in a small increase in energy consumption to 9.7W compared to the unloaded motor at 6.1W and the mechanical drive adjusters at 6.4W. Actuation of link I measured an energy consumption of 7.2W, links II and III measured 6.4W, link IV and V measured 6.8W. We can see that the developed mechanical drive system transfers continuous rotary motion to discrete oscillatory links across the platform with little internal mechanical loss. Therefore we can calculate that the prototype may be capable of carrying an onboard power supply within the current geometric frame.

Table 2.    Experimental Test Results of iSpalsh-OPTIMIZE

Parameters Specific Value
Max Frequency tested in air: Hz 10
Max Power Consumption Motor No Load: W

Max Power Consumption Mechanical Drive Adjusters: W

6.1

6.4

Max Power Consumption only link I: W 7.2
Max Power Consumption only link II and III: W 6.4
Max Power Consumption only link IV and V: W

Max Power Consumption all links: W

Link I – Max Head displacement: m (Joint angle°)

Link II – Max Mid-body displacement: m (Joint angle°)

Link III – Max posterior link displacement: m (Joint angle°)

Link IV –  Max Tail displacement: m (Joint angle°)

Link V –  Max Tail displacement: m (Joint angle°)

Total anterior amplitude: m (of the body length°)

Total posterior amplitude: m (of the body length°)

6.8

9.7

0.060 (22)

0.020 (14)

0.020 (11)

0.048 (28)

0.040 (41)

0.060 (0.1)

0.167 (0.3)

  • Kinematic Parameters

The midline kinematics of the full-body swimming pattern were tracked at 50 frames per second during actuation in air to provide the amplitude values of the anterior, mid-body and posterior, for comparison with real fish and iSplash-I. Good agreement with live fish kinematic data is a difficult task and current free swimming robotic fish have shown excessive head and tail amplitude errors during locomotion. All links were tested at half the maximum frequency (i.e. 10Hz) so that the build was not damaged due inertia forces. Link I was able to attain a maximum amplitude of 0.1 (0.06m) of the body length, measured from the midline to the maximum lateral excursion at a turning angle of 8°. Link II and III attained a maximum amplitude of 0.03 (0.02m) with 14° and 11° respectively. Link IV attained a maximum amplitude of 0.08 (0.048m) with 28° and Link V attained a maximum amplitude of 0.07 (0.040m) with 41°. The maximum lateral head (i.e. 0.1) and tail (i.e. 0.27) excursions generated are significantly greater than the observed common carp, and iSplash-I (Notably the tail amplitude of iSplash-I was measured to increase performance with larger values than the common carp at 0.1 of the body length able to attain values of 0.17 (0.044m) due to achieving anterior stabilization). We can assume that applying the maximum attained amplitudes of iSplash-OPTIMIZE during locomotion will generate negative propulsive forces, therefore providing adequate displacements to find the optimized swimming pattern. Significantly, we were able to adjust the mechanical drive system to generate numerous link sequences (with innumerable combinations of the cross sliders), therefore producing accurate swimming patterns during non-productive actuation.

  • Conclusion and Future Work

This paper details the design, fabrication and mechanical efficiency tests for a bio-robotic marine vehicle, showing its feasibility as a platform to accurately optimize the carangiform straight line swimming motion over previous methods. Devised to reduce the kinematic errors by precisely tuning the reaction forces of the propulsion elements during locomotion, the developed mechanical drive system has shown the capability to generate accurate spatial and time dependent discrete link sequences during non-productive actuation at 10Hz with a small energy consumption of 9.7W over a non-loaded motor at 6.1W. The swimming patterns at high frequencies were attained by realizing a powertrain with high accuracy unrestricted disc offset combinations, small in size and with high structural strength, able to transfer power to and provide precise adjustments of the oscillatory discrete links across the full assembly from a single continuous rotary actuator. The details of the onboard electrical system were given showing its practicality for measuring and controlling the energy consumption, stability and mobility by deploying control mechanisms for the actuation of pectoral fins and adjustment of the linear swimming motion to generate the form of a C-sharp turn.

The achievements of conducted mechanical tests have indicated the following significant aspects to improve the next generation: (i) The devised adjustable mechanical drive system is suitable for a reduction in scale, relating to reduce forward resistance; (ii) An autonomous parameter adjustment system may be deployed, utilizing a series of servo motors, to attain swimming motion adjustment across the range of frequencies during locomotion; (iii) The robust structure may allow a continued raise in frequencies; (iv) The compact drive mechanism is suitable to distribute power to additional links, increasing redundancy without greatly increasing mechanical complexity and the geometric frame.

Our future research will now focus on the experimental testing of iSplash-OPTIMIZE, a series of experiments will be conducted in order to verify the prototype by evaluating the locomotive performance in terms of kinematic parameters during linear locomotion, speed, force, energy consumption, horizontal and vertical plane mobility and autonomous operation at intensively high frequencies within the range of 5-20Hz.

 

Acknowledgments. Our thanks go to Richard Clapham senior for his financial contribution and technical assistance towards the project. This research was financially supported by the research grant “ECROBOT: European and Chinese Platform for Robotics and Applications,” project No 318971.

References.

  1. P. R. Bandyopadhyay, “Maneuvering hydrodynamics of fish and small underwater vehicles,” Integr. Comparative Biol., vol. 42, no. 1, pp. 102– 17, 2002.
  2. J. Lighthill, “Mathematical Biofluiddynamics”, Society for Industrial and Applied Mathematics, Philadelphia, 1975.
  3. J. J, Videler, “Fish Swimming”, Chapman and Hall, London, 1993.
  4. J. Gray, “Studies in Animal Locomotion,” J Exp Biol 10, 88-104, January 1933.
  5. G. S. Triantafyllou, M. S. Triantafyllou, and M. A. Grosenbauch, “Optimal thrust development in oscillating foils with application to fish propulsion,” J. Fluids Struct., vol. 7, pp. 205–224, 1993.
  6. M. Nagai. “Thinking Fluid Dynamics with Dolphins,” Ohmsha, LTD, Japan, 1999.
  7. D. S. Barrett, M. S. Triantafyllou, D. K. P. Yue, M. A. Grosenbaugh, and M. J. Wolfgang, “Drag reduction in fish-like locomotion,” J. Fluid Mech., vol. 392, pp. 183–212, 1999.
  8. J. Yu, M. Tan, S. Wang, E. Chen. “Development of a biomimetic robotic fish and its control algorithm,” IEEE Trans. Syst., Man Cybern. B, Cybern., 2004,34(4): 1798-1810
  9. J. Liu and H. Hu, “Biological Inspiration: From Carangiform fish to multi-Joint robotic fish,” Journal of Bionic Engineering, vol. 7, pp. 35–48, 2010.
  10. Valdivia y Alvarado, and K. Youcef-Toumi, ”Modeling and design methodology for an efficient underwater propulsion system”, Proc. IASTED International conference on Robotics and Applications, Salzburg 2003.
  11. Bainbridge, “The Speed of Swimming of Fish As Related To Size And To The Frequency And Amplitude Of The Tail Beat”, J Exp Biol, 35:109–133, 1957.
  12. J. Clapham and H. Hu, “iSplash-I: High Performance Swimming Motion of a Carangiform Robotic Fish with Full-Body Coordination,” IEEE International Conference on Robotics and Automation, May 31 – June 7, 2014, Hong Kong, China.
  13. W. Webb, “Form and function in fish swimming,” Sci. Amer., vol. 251,pp. 58–68, 1984.
  14. Nilas, N. Suwanchit, and R. Lumpuprakarn, “Prototypical Robotic Fish with Swimming Locomotive Configuration in Fluid Environment,” Proceeding of the International Multi-Conference of Engineers and Computer Scientists 2011, page 15 -17, March 16-18, 2011.
  15. W. Rosen, “Water flow about a swimming fish,” China Lake, CA, US Naval Ordnance Test Station TP 2298, p. 96, 1959.
  16. J. Wolfgang, J.M. Anderson, M.A. Grosenbaugh, D.K. Yue and M.S. Triantafyllou, “Near-body flow dynamics in swimming fish,” September 1, 1999, J Exp.
  17. V. Lauder and E.G. Drucker, “Morphology and Experimental Hydrodynamics of Fish Control Surfaces,” IEEE J. Oceanic Eng., Vol. 29, Pp. 556–571, July 2004.

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