A Numerical Analytical Method of Parameter Optimization for Fast-starting of the Bionic Robot Fish

In this study,the alloy sheet,the giant magnetostrictive material (GMM), was stuck on the sheet, and the external magnetic field were simulated as the framework of the fishtail, respectively; the muscle of the fish and the nerve are to control the swing of the fishtail for simulating the fast-starting of some natural fishes. Simulate the Faststarting of fish different environment of nature. A mechanics model and new numerical method are presented by analyzing the vibrational modes. Optimization for External Parameter was conducted by using numerical computation, the best environment and material for Faststarting of the Bionic Robot fish is revealed. Results show that the suit material can help the robot fish complete the fast-transition from the lower order mode to the higher order mode. The method and results provide theoretical foundation and applies basis to designing bionic robot fish. Do not cite references in the abstract.


INTRODUCTION
With the development of modern science, it becomes more and more urgent to access a new mini-tube robot [1] which can move stably and flexibly in water or watermedium in medical domain and industry application, including bionic robot fish of GMM [2][3][4]. The robot can be driven wirelessly in a tiny room, such as in people's vessel.
Quick start-up can be divided into C shape start and S shape start by swing morphology of fish when fish starts. Different start modes are formed due to different rigidity of fishtail and natural surroundings such as liquid surroundings. For example, Northern Pike can start instantly, and its maximum acceleration is 25 times of acceleration of gravity [5]. Several countries have conducted study on the way bionic robot fish starts to reveal the principle. For example, bionic robot tuna and bionic barracuda developed by MIT are driven by motor. American Naval Weapon Laboratory discovered shape memory alloy in 1963, realizing SMA driven robot. Professor Toshio Fukuda in Nagoya University developed mini underwater mobile robot, and it utilizes piezoelectric ceramics(Pb(Zr,Ti)O3) to drive the swing of two symmetric legs to move it. Festo developed a kind of pneumatically artificial muscle called pneumatic tendon MAS, and a swing structure consists of two tendons is developed. The disadvantages of driving system above are that they're wired or with power plant. A mini robot will overcome two disadvantages above to be driven by external field if it can absorb energy from a certain external field to obtain sufficient energy.
GMM is a new kind of function materials developed in 1970s. It is regarded as a strategic function materials related to improve comprehensive competitiveness of national high technology in 21 century. The emergence and development of GMM provides a better choice to utilize no-cable control and design special mini robot fish. The study chooses GMM as fishtail materials. Robot fish is controlled through external magnet field in this study. Then the S shape start and C shape start are revealed through relative principles obtained by optimizing fish material and external surroundings parameters. The study provided the foundation of quick start-up [6] of bionic robot fish [7,8].

ROBOT FISH
Bionic robot fish of GMM consisted of fish body and fishtail, and the fishtail is formed from pasting or plating giant magnetostrictive material. The change of bulk and size of giant magnetostrictive material under the changeable external magnet can lead to a dynamic loading distribution of alloy sheet, driving the fishtail to swing.
A. structure model of bionic robot fish Figure 1 shows that Cartesian coordinate is utilized, and the length is L, the width is b and the height is h. The thickness ) (x ! of giant magnetostrictive material by pasting or plating (the width of the sheet remains unchanged) is thinner than alloy sheet, namely (1) The strain caused by external magnetic field intensity B 0 and ! are amplitude of external magnet induction intensity and frequency of magnet field, respectively, and µ is the permeability. Giant magnetostrictive material pasted or plated in the elastic sheet is flexible with the change of external magnet field. The effect produces on sheet can be concluded a shear force distribution and finally transferred to bending moment distribution.

B. The mechanism of bionic robot fish
The problem can be simplified to a cantilever beam model by ignoring the influence of giant magnetostrictive material. It is assumed that the fishtail doesn't reverse or transform, and the liquid resistance the fishtail suffers is approximately the same as the resistance generated in the flow field [10,11]. Referring to the resistance given by Gerhart [12] etc., in low Reynolds number, the damping coefficient [11] C can be approximated to The control equation of fishtail swing is When the giant magnetostrictive material is linearly distributed, The corresponding boundary conditions are ! ! " Initial conditions are Incorporate the control equation (5) Incorporate boundary conditions (6) and initial conditions (7) with equation (8)

B. The solution of control equation
The variables separation method [13] is utilized to obtain the solution of equation (11), namely.
After substituted by equation (14), equation (11) is multiplied by ) (x Y j , and the result is integrated along the whole beam. Then orthogonality of vibration function is introduced as follows:

C. Driving force of fishtail swing
During a magnetic field change interval, the average driving force generated by fishtail swing can be expressed as

IV. NUMERICAL RESULT AND ANALYSIS
To study the problem quantitatively, the following parameters are chosen.
[ ] . Aluminum alloy material is utilized in fishtail, and TbFe 2 is utilized in giant magnetostrictive material [9]. The first five order modal are superposed.

SPECIAL FOCUS PAPER A NUMERICAL ANALYTICAL METHOD OF PARAMETER OPTIMIZATION FOR FAST-STARTING OF THE BIONIC ROBOT FISH
The optimal length [3] in stable state is chosen to represent fishtail length (l=0.09). Time during the third time the tail passing through the horizontal axis is chosen as start time.     Figure 5 show that the robot fish is in C shape mode, such as crucian in fresh water, under the external frequency corresponding to maximum average propulsion when 0 µ =1.0, and the modality of robot fish start exactly transits from low order modality to high order when 0 µ =1.5. The modality of fishtail swing also change from low order modality to high order when 0 µ =2.0. It illustrates that the transition from low order modality to high order is crucial for the start of robot fish in the whole process. It is also showed from the figure that the bigger the viscosity coefficient of liquid when fishtail swing, the easier to realize the transform from low order modality to high order. It is the reason that loach transits faster to S shape mode when starting in mud. ) are selected to compare with the skeleton of fish. The relation between average driving force and frequency of external magnet field is shown in Figure 6. Figure 6 shows the max average driving force of fishtail made from alloy steel is much smaller than fishtail made of aluminum. This illustrates that the relatively hard fishtail material is unfavorable to small robot fish. In the frequency of external magnet field corresponding to max average driving force, the swing mode of robot fish doesn't transit from low order modality to high order modality. Its start is in C shape. Meanwhile, the fishtail of robot fish made of aluminum alloy material transit from low modality to high order modality in a not very big frequency of external magnet field, namely S shape start, and it can obtain bigger average driving force. Figure 7 shows different swing modality when fish swims in nature. Turning amplitude of fishtail in the far right of the figure is the smallest, reflecting the swing mode in which the rigidity is relatively big, and the viscosity coefficient is relatively small. Turning amplitude of fishtail in the far left of the figure is the biggest, reflecting the swing mode in which the rigidity is relatively small, and the viscosity coefficient is relatively big. This also verifies the rationality of the model in the study. The start speed of bionic robot fish of giant magnetostrictive material can be adjusted by choosing proper fluid environment and fishtail materials. The startup speed of bionic robot fish is related to material constants, geometric parameters, fluid environment and the frequency and intensity of external magnet field. It can make the robot fish successfully transit from low order modality to high order modality to choose proper parameters when it starts. The driving force is closely related to the intensity of external magnet field. The study results verify the rationality of S shape start of fish, and provide evidence for the design on bionic robot fish's quick start-up.