Simulation Fitting Method for Setting Motion Parameters of Robotic ...

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4 3 Fish wave Envelope curve 2 Lateral Displacement 1 0 -1 -2 -3 -4 0 1 2 3 4 5 6 7 Longitude Distance from Head Figure 1 Static fish wave Figure 2 Link-based robot fish make the machine swim like a fish, we should set parameters, such as angle at the joint, proportion of each rod, one segment of link, so that the link mimics fish’s shape as well as possible. 3. Traditional strategy in fitting fishcurve with link Traditional method is widely used. It is simple, but there are also some flaws in it. 3.1 Preparation for fitting fish curve Suppose the robot fish acts N times in a period with equal interval. Then, a period should be discretized into N time points. So at each point, fish wave degenerate into N static curves. We may call them fish curves. For 2/;i=0,1...N-1; formula of fish curve i should be:
’ , (2) When N=12, the 12 curves are shown in Figure 3. 2 1.5 1 Lateral Displacement 0.5 0 -0.5 -1 -1.5 -2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Longitude Distance from Head Figure 3 Fish curves on 12 time points After time discretization, we can fit the curves one by one. The fishcurve with 0 phase, that is the first fishcurve, is picked for the following work. 3.2 Joint Location Method Just as stated before, because of different swing styles, we must know which part of a fish curve is to be fitted by robot fish. Suppose the part is from 0 to 2π*R(R>0). The size of R affects fish pushing ability and speed significantly. In this article, set R=0.7 according to our robot fish. Current fitting strategy that is commonly seen is to locate every joint on the fish curve, and ensure the link’s length matches the curve. Then we get the result. We may call this method “Joint Location Method” (JLM). JLM is simple and reliable, but there are some flaws in it. When the derivative of a fish curve remains the same sign, that is, when it’s convex or concave, this method will cause certain accumulative error, and the link we get will distribute on one side of the curve. As a result, the gap between link and curve is relatively large. As in Figure 4, the blue dashed line represents a fish curve with 0 phase, and the red line represents the link we get with this method. We can see that almost the whole link locates beneath the fish curve. So it is the situation with other phases. This result not only distorts the shape of the curve, but also decreases its amplitude. And therefore may affect robot fish’s swimming quality. 3.3 Other way of fitting An easily thought of way to fix the problem is to integrate the difference between fish wave
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Simulation Fitting Method for Setting Motion Parameters of Robotic ...

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